SMU Physics Department Speaker Series - Tongyan Lin

okay okay all right well it is 4 o'clock everybody and people are still um trickling into the room right now so I'll just go ahead and get the boiler plate introduction started and and buy them some time to to finish connecting welcome back of course to the SMU physics department speaker series for fall 2020 and we're continuing our November Series in its theme of New Frontiers in physics so in a moment I'm gonna hand things over to Professor jod kolie to introduce our speaker Professor tonyan Lynn but before we get started a few reminders especially for the audience on Zoom we've got everybody muted by default uh if you want to ask a question just go into the chat window type the word speak either during the talk or in the Q&A part after the talk and that'll create a little speaker and we'll get to you in the order we see that appear we usually try to interrupt the speaker at the end of the next uh slide you know during the next slide change that kind of thing um you'll only be able to speak when a moderator unmutes you so I'll I'll try to handle that today for everybody um this event is being recorded and it's also being simultaneously live streamed on YouTube that stream is non- interactive so hello to our viewers on that stream as well and without further Ado let me welcome Professor jod K to introduce today's speaker so Jody take it away hello everyone and uh welcome to the SMU physics department colloquium um I'm very pleased to be able to introduce tangan Lynn uh as today's speaker she's an assistant professor of physics at the University of California in San Diego she obtained her PhD from Harvard and was previously a post-doctoral scholar at The cavali Institute for cosmological physics um at the University of Chicago and at the University of California in Berkeley um she's a theorist who studying ways to detect particle interactions of Dark Matter including signatures in astrophysical data and underground direct detection experiments I also want to mention uh that tangan is one of the co-conveners of the cosmic Frontier subtopic working group one which is on particle dark matter um so she is seen as someone in the community that is a real leader and I know that in my experiment we're always very interested um to hear about her ideas and her thoughts um as many of them are relevant uh to the super cdms program so tongyan thank you again for coming and talking with us today and I can't wait to hear your talk um yeah thank you so much for the invitation and the and the kind introduction so we did check the setup earlier but um I was having a small amount of trouble again so I really apologize that for that we just checked it sure sure sure it's fine yeah what's happening is um if I do play it says sharing is paused so do you see any transitions uh no it's it's a blank screen unfortunately yeah yeah yeah so let me see you are set up as a co-host so um you don't see even anything right now well now we do yeah so we just don't see it full screen go ahead Jody oh sorry um so tan because I have I also use keynote and I've had all kinds of difficulties with zoom I found something that works out really good if you go um in keynote into um Let me let me check remind myself what the menu is again let me call my keynote um go into the um menu menu that says play and then play show in window okay and then from here when you share your screen just share the window that that is playing your slideshow okay let me try that again yeah perfect okay this seems yeah I I accident yep perfect this looks perfect I accidentally tripped upon this trick several weeks ago and it has made my life so much better yeah thank you very that's very helpful because I already went through like one cycle of how to make Zoom work with kenot Okay so sorry about that uh but thank you again for the in the nice introduction and the opportunity to tell you about some of the work I've been doing so I work a lot on various ways to detect Dark Matter from a dark matter theorist perspective and in this talk I'll be giving an overview of some of the techniques and approaches for looking for Dark Matter below the GV Mass scale how do we detect nucleo recoils from such low mass dark matter and I'll describe some of the different like Crystal targets we can use to search for such low mass Dark Matter so here's a picture showing a broader motivation for why I want to study this Mass range so these are some of the existing limits for Dark Matter Nuclear recoils So the traditional approach is to say we're living in a dark matter Halo the dark matter is coming towards us there's a dark matter wind and it has pretty high kinetic energy when the dark matter is very heavy so it can knock a nucleus and that's like a hard recoil that um that can be easily observed if it's energetic enough and uh there are many experiments that not only observe this but have pushed the background so extremely low that they can observe one such event happening um in a year with a kilogram of detector material so that's all of these types of bounds on the on the other hand you see that they're dropping off in sensitivity quite rapidly as we go to the GV Mass scale and below so these are bounds on the cross-section and you see there's like 10 orders of magnitude between the limits at 10 GV and 1 GV so the question is how do we explore this pretty big wide openen parameter space for dark matter and how do we test um there are a lot of interesting theories I I won't have to get into them but how do we test lots of interesting theories for Dark Matter below the GB Mass scale so let me go over some of the challenges and general approaches to this problem so the fundamental challenge for why these uh why the sensitivity it drops so much is that the kinematics are just not optimal for subv Dark Matter The Recoil energy from Light Dark Matter scales as Dark Matter Mass squared over the target nucleus square target nucleus so for subg Dark Matter this is dropping rapidly and that's where you get this huge suppression below Dark Matter mass is about 10 GV currently the best nuclear re recoil threshold is around 30 EV uh that was shown in the previous plot from Crest 3 with a dark matter reach of about 160 me so the first consideration I'll describe is how we can better understand on the more theory side how does Dark Matter actually interact in the material when it's so light the point I want to make is that dark matter scattering should not be always described as scattering against free nuclei uh when Dark Matter oh when the mass is very low this free nucleus recoil picture does not actually describe the response very accurately we have a crystal so the we have to account for all the crystal Dynamics so let me illustrate that with this uh plot showing as a function of Dark Matter Mass various energy scales so this is the total available Dark Matter kinetic energy Halo which is scales as M and this is if you have a free nuclear recoil and I even picked a pretty low mass nucleus here uh helium and so that you see is dropping off as dark matter Mass squared uh and it's dropping well below the K scale which is where a lot of the experiments are operating if the energy scales are low enough the uh the available excitations are actually phonons so the typical phonon exitation is milev to 100 m and that that's describing just the lattice vibrations so the collective excitations of these nuclei in the lattice so somewhere in between here you'll have something a little bit more complicated multiple phonons being produced so that's one way uh in which the the behavior of dark matter in a material differs from the traditional picture another way to think to um look at the material response and detect lower Mass dark matter is by using electron recoils so this red line is showing the energy you could extract from a dark matter electron scattering event so here the fundamental process is a little bit different because we're talking about Dark Matter electron coupling versus Dark Matter nucleus coupling but if there is a dark matter electron coupling then you see in this regime you could extract a bunch more energy out of the electron recoils than out of the nuclear recoil this red line I've shown is assuming a free electron which is also not the case a typical material will have a complicated electronic band structure um Ian states that you have to consider to actually calculate this dark matter electron scattering so uh furthermore this line which goes down all the way to Mev is not accurate either so here's a slightly more accurate picture it's still a cartoon showing what the actual thresholds are for those electron recoils so you have uh for an insulator for instance you might have a threshold of about 10 EV and semiconductor a threshold of EV and for other materials like superconductor direct material you might even have very tiny thresholds so all this is to say that uh when we look below the GV scale we really have to consider the material properties and consider what kind what kinds of excitations are available and the dispersions of those excitations so far everything I've talked about is still kind of a what I call a two to two process meaning Dark Matter comes in it creates one exitation and then it leaves but you can also have uh inelastic processes and so that will actually be the main subject of my talk you can have dark matter comes in it kicks a nucleus and the nucleus also excites an electron at the same time so it's a two to three process and that will be able to extract even more Dark Matter kinetic energy out so again putting this all together below the GV scale we have a variety of interesting processes to understand on the theory side for how dark matter is interacting in a realistic Target now let me move on to how that interfaces with the experimental side uh and this is a cartoon that's shown often for how direct detection works when a nucleus gets kicked the energy in the nuclear recoil could ultimately get deposited into a few different channels including heat or phonons Lotus vibrations uh since ventilation photons or light and charge by which I mean either an ionized atom or an excited electron whole pair in a semiconductor and often for the experiments on looking for heavy dark matter you want to get a couple of these channels say two of these channels to distinguish your signal from potential backgrounds so one Big Challenge is that two of these channels start to get lost when the Dark Matter mass is below a GV so in particular if you have a nuclear recoil below about a few hundred EV it's not very well understood but it's expected that the light and charge channels becomes very very weak so expect it to be zero or maybe you get a fluctuation once in a while but not many uh electrons or photons coming out and that's challenging uh in part because these can be helpful discriminators and also in part because uh the thresholds on some of these channels can be quite low for instance the threshold on a charge signal could be one electron but the threshold on a uh on the heat Channel could be somewhat higher as I said earlier like few hundred EV or 50 EV uh and so if you only rely on this one then um it it is challenging to be able to see these nuclear recoils okay so with those challenges let me now go into what the some of the strategies are that um me and many other people are taking to try to look for these nuclear recoils that are from low mass dark matter one is simply to decrease that heat threshold that I mentioned you've lost the other channels but there's a lot of very interesting work that Jody can tell us a lot more about to uh reduce those heat thresholds to about EV or maybe even below and on the theory side what I was describing is that we also want to calculate what how dark matter directly excites these phonons which can be on the scale of 100 milev and this is particularly relevant once we're looking at dark matter below the me mass scale as I mentioned again there we can't treat it as a free nucleus and we really have to directly calculate these processes so if we can combine these two approaches then certainly we could access dark matter as light as um tens of Kev with very small thresholds uh that's something that is impressive but it's also going to be hard it's not going to happen immediately so there's kind of complimentary approach that that number of people are taking which is to look for ways to increase the charge signal so I said that the average expectation for uh charge being produced in nuclear Reco is very small but you can rely on a low probability event that gives you a larger charge signal so you pay a rate Penal but you get it above the threshold for these charge signals which can be just like one electron or two electrons being produced so one know well-known example of that is the atomic mcdull effect and so this has been applied for liquid Xenon detectors so we model those as just Xenon atoms and when Dark Matter hits the nucleus there is [Music] where anron can be excited at the same time so the idea will be that the wave functions haven't yet caught up to the new uh to the new moving nucleus so there's like a small transition probability uh and that's already been used to set limits on subv dark matter with liquid Xenon experiments another effect is the brm strol of transverse photons when this nucleus is kicked as well so it's kicked instead of the electron being cited there's a photon being radiated so those uh those are very interesting techniques and so far they've only been applied in um in at Atomic targets so what I actually want to talk about today is new work where we study this effect in semiconductors and we show that you can do even better in semiconductors because the threshold for those charge signals are even smaller and as I take you through it you'll see that again uh these many body effects thinking about the details of the material and the Crystal Target are important to calculating all of these so to summarize my introduction I just want to give a big picture of some of the ways in which we can detect nuclear recoils for sub GV dark matter in this me to mass R me to GV Mass range uh we can use inelastic processes to look for extra charge being produced and for subm we can rely on phonon excitations and uh continue to push the development of these really low threshold detectors so in the remainder of my talk I'm going to to discuss this migdal effect and Plasma on emission in semiconductors but before that uh I think I might just pause for a moment to see if there's any questions comments yeah if anybody has a question go ahead and type speak in the chat window this is a good place to pause and catch up okay uh Tom Cohen has a question for you you should be able to unmute Tom no no hi I is there any assumption that's made on the type of in in these um in this scattering it's it's always been a mystery to me there's no assumption made about um the type of interaction between dark matter and and the nucleus I'm still struggling for a picture yeah that's a good question I'm I'm assuming a interaction which is the same for both neutrons and protons okay so dark matter just couples to neutrons and protons equally so that uh all the cross-sections kind of scale with the atomic mass squared okay okay great thanks yeah but part of the yeah I guess part of the reason that we don't always make those assumptions clear is because I could make a different assumption and it would move the lines around but it wouldn't necessarily change the qualitative picture so it's not that important to the final result is what I mean to say Okay I I don't see any more questions I think you're good to go at least for now okay yeah feel free to interrupt there's anything else okay so in the remainer of my talk I'm going to be describing how we can use this migdal effect in semiconductors to detect Nuclear recoils So the basic picture that I want to introduce is that dark matter is hitting a nucleus and I'm going to really treat the nucleus as an ion meaning the nucleus plus the very tightly bound core electrons so for instance in Silicon which is what I'm primarily going to be looking at binding energy of these is above 100 EV and above so I just consider them as very tightly bound whereas um the energies I'm talking about are generally going to be lower than that so picture is dark matter is hitting now recoiling ion and the ion uh in Silicon it has a charge of four and uh when it recoils it can emit uh it can create a basically an electric field which excites electrons in the material so that's the interpretation of the migdal effect that I'll introduce in this talk it's a little bit different from the standard one so I will take you through the whole argument for why I think this is a way to think about the mdle effect so let me go back and um give some context for how uh I started thinking about this with my collaborators um we were actually motivated by an interesting preprint that appeared early this year from a number of these authors and these authors were pointing out that there are low energy observed rates in a number of semiconductor direct detection experiments so here they've plotted those rates as a function of the depth of the location of the experiment so this one one is uh doic which is very far underground and then these are more like surface runs and what they were pointing out is that there's a number of semiconductor experiments like here you see blue as silicon which have somewhat large and similar rates and there's also germanium and another semiconductor here with red red which is also somewhat similar whereas if you have an atom Target Xenon it's green it's down here uh so what they were suggesting is that maybe these excess rates these large rates could be due to dark matter and more specifically these rates are being um these rates are observed in the counts for one electron or two electron events so meaning they you see two electron whole pairs at the end because they're mainly observed in the semiconductor experiments these authors suggested that you could be sensitive you could be seeing a collective effect uh which is the plasmon and I'll describe some more what the plasmon is but it's a collective oscillation of the electrons and it's mainly present in crystals wouldn't be present as much in Xenon and so they suggested dark matter is hitting a nucleus and during this process a plasmon is being produced and the plasmon can Decay and will give rise to these uh one electron or two electron events so this was a interesting excess um what we were interested in is what is this uh what is this probability to actually produce a plasmon and how do we understand these plasmons that could be produced from Dark Matter so our goal was um not necessarily to explain the rates though if we could then we would certainly say that but to just understand the process because it represents a new interesting process for how dark matter could interact in semiconductor and maybe that would give us another way to search for it which is the point I want to make right so if the plasmon does give rise to extra charge then it could be an example of that inelastic process it's an example of the inelastic process which is low low probability but gives you enough of a charge signal that you can still look for a really low energy event so Tongan can I ask a silly question please go ahead yes so plasmons would be oscillations in a plasma right and the Quant of that would be the plas the plasmon what is the plasma exactly in this situation since these are cold crystals yeah I think we can still think of the um we can think of if we just take ignore the semiconductor for a moment and we just think of a metal then we have fixed ions and we have the degenerate electron gas so it's the oscillations in that degenerate electron gas okay okay so it's it's yeah it's purely that that electron gas that then has these collective oscillations in them that can couple to photons in the same way that phonons can couple to things right so the the plasmon and I'll actually I have a the next slide is on that but the plasmon is basically the longitudinal Photon in in a medium so yeah it's a longitudinal oscillation of the yeah maybe let me just skip directly to this so I can answer that I'll go back to the previous one so yeah this uh this picture is not entirely accurate because I don't have a fixed lattice of ions but same idea um like you said that I have Plasma oscillations in the electrons and so that's just coming from displacing electrons by some amount and getting a restoring Force so we get the familiar plasma frequency uh which is proportional to the number density so these uh electric field so in addition to the number density of electrons kind [Music] of you also have the electric field Ting and it's a longitudinal electric field so that's why I'm calling it um that's one reason I'm calling it like a longitudinal Photon it's a longitudinal mode for E Fields so it's as if the photons have acquired Mass it's uh it's a it's a broken symmetry situation effectively in this Collective oscillation yeah yes exactly and the dispersion is a little bit different than if it just had acquired Mass but yeah effectively so our goal was uh the first step of our goal was actually to treat this kind of as a brst strol on calculation but to use a longitudinal mode basically being produced rather than the usual transverse Photon being produced and as I said the kind of assumptions we're making are that we're treating this re recoiling uh ion as we're still going to treat this as a free particle which is valid in a certain Mass range where the recoil energy is well above the phonon energy about 100 m uh but it's not that high so we we don't have to worry about these core electrons we just treat it as one object the ion so this is roughly in the dark matter Mass range of 10 m to 1 GV that I'll be working in okay so back to plasmons which are uh the quantized version of these oscillations we started with just a simple toy model for how to think about the plasmon in in a semiconductor by uh just going to a metal so not worrying about the details of the semiconductor but just having a degenerate electron gas uh in this model then you can directly compute brm strol along of this plasmon in a analytic way which is nice so let me give a little bit more information about this plasmon uh so if I look at ga's law without an external Source I've written it here it has the uh dialectric function the important point is that the plasmon is appearing when this dialectric function is going to zero so when this dialectric function goes to zero that means you can have a source free solution with non-zero e field and it's longitudinal because k. e uh is non zero so then I have oscillating longitudinal Fields another way to view it is this is a propagator 1 over k s and if I put in screening then I need to put in the dialectric function so when the dialectric function goes to zero then I get a pole in the Kum propagator which means I have a particle which I'm calling the plasmon this is what the dispersion of the plasma looks like in this electron gas model so this is momentum Q versus energy Omega and the plason is here so it's not exactly the same as if we added a mass term to a photon because it's actually pretty flat uh and it's around 15 to 20 EV in energy and it's flat in momentum and it only exists for somewhat low M momentum just kind of in keeping with the idea of think you as a collective exitation uh up here the plasmon can Decay to electron hole excitations so all this blue region is available electron hole excitations so that's why we say the plason doesn't really exist up here but down here where it's sharp in this toy this plasmon is actually infinitely long lived okay so this plasmon um can't be directly produced actually by dark matter if we take dark matter with a typical Halo velocity of about 10 the minus three and you just kind of plug in the kinematics uh to see what's the available momentum and energy deposition from the Dark Matter uh it's not enough it's or it's outside of the region where this plasmon exists but we can produce it by this inelastic 2 to3 process so that means Dark Matter nucleus plus Dark Matter nucleus and plasmon and in this uh electron gas model it's pretty straightforward to compute this it's actually just like breem stong uh except for some small changes so if you calculate brm Str along then normally you would get the elastic scattering rate times some factor in front which tells you the probability to emit the photon and it's the same thing here um there's a factor of two difference because I don't have two polarizations and the dispersion here this is the dispersion of the plasmon of course is also different for uh than a photon so now uh with this with this en hand we can already few things about what this plasma production looks like if you plug in the numbers it will actually be much larger than bmst along of transverse photons because for transverse photons Omega would be approximately K so it would rise as a function of K but here it would be just around 20 EV so you get a much larger value so that's one thing that's very interesting um to go back to the main point uh this is going to be a low probability event so if you plug in the numbers this factor in front is going to be 10 the minus 4 or something like that but because the Plasma on decays into charge signals it allows even very low energy nuclear R coils to be detected I think there's a question oh yes I you're right there is uh so Rob and then Richard let me get to Rob here I was in the middle of taking notes Rob go ahead yeah so I mean the brch long channel has kind of had this rate hit compared to the standard nuclear recoil so coincidentally it it's sort of about four or five orders of magnit two below the migdall rate does this kind of put it at the same at a comparable rate for for different Target nuclei or is it really Atomic dependent if you if I compare this with the uh transverse rate let me actually just go to this so yeah this is elastic this is the plasmon and then this is transverse so plasmon is actually very similar to migdal and as I'll show PL plasmon is actually migdal you know is a forms a portion of the migdal rate so maybe that's really that's consistent with what you're saying I think sorry Rob remed himself here yeah there we go yeah yeah I think okay yep okay and Richard you had a question as well yeah um the naive question is what distinguishes this process from neutrino interactions on electrons uh so good question are you asking like would neutrinos also give the same effect well we know that neutrino uh colliding with electron will transfer most of its energy to the electron uh that's been calculations by daus and somebody years ago uh and and you're entering the energy range which is consistent with solar neutrinos that's what I'm trying to understand what is the difference here on the observations yeah so one thing is that the what I'm looking at I'm just I'm assuming the Dark Matter dominantly couples to neutrons and protons so that it's not directly scattering off the electrons you're right if dark matter can directly scatter off the electrons then then in a particular model that might be a larger rate than what I'm looking at but in some models the dark matter has a small coupling to electrons and it wouldn't it wouldn't produce much dark matter electron scattering and the other thing is that uh you're definitely right that neutrinos would also give the same effect so you could redo kind of everything here for neutrinos instead okay thank you okay I don't think we have any more questions at this stage oh wait I take that back Tom has a question go ahead Tom yeah I was just um when you mentioned U plasmons you had uh you know you had this expression for a simple harmonic oscillator and it just got me thinking that the plasmons presum presumably have uh quantized energy levels I mean there's um there's no um there's no resonance effect that might enhance the detection probability in the sense that um I don't know you you excite one of these uh excitations uh higher order excitations of the of the simple harmonic oscillator and maybe this liberates more than the one or two electrons yeah so I think you're you're saying like we um we're looking at exciting one plasmon and I think the picture you have is right it's like you're resonantly exciting the electrons in a way that you get the plasmon but you could have like two plasmon is that what you're saying like yeah well for example yeah yeah also have the two Plasma on yeah and then I was thinking you could then maybe I don't know this is um by a a judicious choice of the crystal you might increase the likelihood that the interaction couples to the an equal to level say oh interesting you know I haven't I haven't thought much about the two plasmon um the two plasmon right I think the uh in terms of like Silicon the two plasmon part is weaker like if you take this I'll show you a version of this plot which is for more realistic and you look like up here twice Omega P it is a weaker resonance but I haven't looked much into that I'm teaching Quantum so I have simple harmonic oscillator on the brain yeah well a lot of a lot of my talk is just Quantum and electromagnetism so okay I don't see any more questions for now okay okay so I was here and I was just describing what the rates look like in this toy model so we get a much larger rate for this plasmon emission compared to compared to Branch Tong of transverse modes and uh this is nice we can use it to increase our sensitivity but uh you might not you might say this is just a toy model uh what about an actual material so for the rest of my talk I'm going to start to introduce the things I need to deal with an actual semiconductor so if you remember that plot I just showed with the plasmon and the electron hold pair in the toy model um this is a numerical calculation of what the response looks like in an actual semiconductor so everything gets washed out a lot of course you still see the plasmon resonance here it's this thing this dark blue region it's a lot wider you see it's actually pretty wide uh and then this is all electron hole excitations so some of the differences for a semiconductor uh one include the fact that you have to account for a band gap of course you have to account for all the electron wave functions and also uh account for this width of the plasmon that's appearing so we can't deal with that in the toy model uh instead the way we dealt with this was to rewrite the the uh rate the plasmon emission rate in terms of just this dialectric function in that way we can use numerical calculations of the dialectric function that are well numerical calculations that are first principles for particular materials okay so let me give you the one slide derivation of that um it's just electromagnetism so I treat the ion now as a current source so it has V ion and it turns on at some time T when Dark Matter hits the ion the energy transfer to the material will be this j. e and then I solve for the E Fields using Maxwell's equations so I use the longitudinal part of Maxwell's equations specifically and here you see that the source which is this current um will Source this e field with a dialectric function in front and so from xl's equations I plug it back in the E field in here and or here sorry and you'll see I get uh energy transfer rate which is just in terms of currence and one over this dialectric function so that's what it looks like uh and this is the energy loss rate and you see this imaginary part of my one over Epsilon U for any of you who do like charge energy loss of charg particles in materials this might look familiar it's called the um energy loss function uh which so it's commonly studied our material or our object so the picture is now we create this um current and uh this current will lose energy through this loss function and you you see also this minus one over the dialectric function well when the when the dialectric function goes to zero that's when I have the plasmon so you see there can be a a resonance in this function that's the plasmon and this is a plot showing what that function actually looks like the energy loss function so here this is a zero momentum and the solid line is from an x-ray scattering experiment and this resonance is exactly the plasmon so if you send in like an electron then it can lose energy to this one plasma at zero momentum the dotted line is actually the toy model we started with where we just modified it a little bit to include the width this finite width of the plasma and so here you see different the energy loss function at different moment momentum transfers and that actually the toy model is pretty decent at reproducing the broad features of this okay so with that in hand that mostly valid uh what we found was that mostly validated this toy model where we calculated plasmon production and we found um as was noted earlier rates that were about 10 the minus 4 10us 5 of the actual nuclear recoil so we pointed out in that first paper how you could use this to um set much better constraints or do stronger searches for Dark Matter nucleus scattering uh but there's something else interesting here which will lead to the final part of my talk which is that uh this energy loss function it does contain a plasmon resonance as you saw in the plot uh but it also contains lots of other things so it contains all electronic excitations you can look off the resonance there's no reason to look on the that you have to look at the plasmon and as I mentioned earlier you can use um numerical calculations to try to see how big all of those contributions are and get this full rate for plas for uh for this inelastic process which I will stop calling Plasma on production shortly because as I'll show we actually get a lot more off of the poll okay so uh I'll pause again if there's any questions but in this last part I'll explore now all our uh gory calculations of this quantity and what the actual numerical rates look like okay yeah any any questions before she gets to that last part all right I don't I don't see anything so I think you're you're safe to proceed okay thanks just like to pause no that's very healthy you're you're a good model for uh for students that are are doing their teaching practicum this semester okay good all right so I paused because I was about to show this this large equation on the next slide so in uh our newest work which appeared last week we looked at this in more detail in semiconductors uh we did a couple of things Beyond just numerically calculate the dialectric function so let me explain this diagram a little bit so when when we scatter off a nucleus inside a lattice we can think of the nucleus as sitting in this harmonic potential and the frequency associated with this harmonic potential is uh actually Omega phonon about 100 m so in the process we're Computing Dark Matter scatters and we immediately emit this migdal electron as I'll explain shortly and then eventually the nucleus might go off and lose energy as it goes to this part of the potential andit phonons so because the nucleus the ions are not actually free in a Target material one of the things one of the other things we did to firm up our result was to look at this um to treat this more quantitatively so in particular we wanted to treat the fact that the initial nucleus is actually in this uh harmonic potential in this harmonic Crystal as opposed to being free so if we combine everything I'll just show you the rough ingredients of this final cross-section so this is the cross-section for the elastic process and as before we'll factor out the usual Dark Matter nucleus scattering so everything else is the probability we account for these uh this harmonic potential with a form factor this this is um what I just alluded to and then everything else here is actually just the energy loss function uh written in a slightly more complicated way but just the energy loss function and there's more indices now because I'm actually accounting for the periodicity of the of the lattice but otherwise it's pretty similar to before just slightly uglier notation and here are some plots showing the numerical calculations of the energy loss function now uh that's this red line gpaw as again compared to various um measurements with x-rays or Optical data that's the blue note that if if we had measurements along every direction and every momentum then you could also just use the measurement directly but uh not all uh the the data is not you know available for every single momentum in every single Direction so just used a one of these AB initio codes to calculate the energy loss function okay so we calculate this and it's all interesting but um there's another interesting layer to this it which is that it's actually uh related to the atomic mdal effect so to explain that let me go back and review what the atomic migdal effect is so dark matter uh in this picture is coming in hitting this nucleus here's the electron in its bound State and the picture is when the nucleus moves suddenly uh the electron wave functions are still in their original state as indicated by this cartoon and that has some overlap with the excited States about the moving nucleus in this last picture so the way that's calculated is then by saying the initial State we boost to the frame of the moving nucleus so that's the wave function in the second part and then we just take the overlap with the final possible States for the third one and that will we square that to get our transition probability so that's kind of the um standard way to explain the atomic migdal effect uh attributed to MD the issue with this um explanation is that it's not very obvious how it generalizes to semiconductors the problem is you have a whole lattice of nuclei so if you boost your electron wave functions it's really as if you were recoiling all your nuclei which is not really what we want right so there's a preferred basically there's a preferred frame of reference in a crystal and you can't just boost so easily it's not so OB VI that you can use the boosting thing so the claim uh that we're making is that the rate that we derived is actually a generalization of the atomic migdal effect to semiconductors which doesn't rely on this boosting argument and furthermore we think it there's another simple way to understand the effect without relying on the Boost uh and you can see it again through just um you can see it just through quantum mechanics like I said earlier a lot of my talk is quantum mechanics and electromagnetism so the Matrix element for the atomic mdal effect was given by this dipole moment R which came in apologies it came in because Dark Matter uh because for Dark Matter nucleus scattering this velocity is very small so you can just take the first term so I can rewrite this Matrix element for the atomic migdal effect uh for a dipole I can rewrite it using the momentum operator and then again I can rewrite that Us in terms of the commutator of momentum and the hamiltonian because these are energy states and then finally um the this commutator uh will just give what the force on the electrons is and force on the electrons is coming from the nucleus right so it's just DVD and so finally what we see is that this Matrix element can be Rewritten in terms of the potential from the recoiling nucleus and this is actually the dipole potential so you see here VN um dotted into R so that it's like our usual p. R potential for a dipole and this is just the for transform in time accounting for the fact that we're looking at energy I States so that gives a interesting physical interpretation already that we're looking at the we're just looking at the potential from a recoiling nucleus which can excite an electron I'm going to take one more uh for transform to turn it into a form that looks a lot like the semiconductor effect that we derived so if I do the spatial uh 40 transform then I get this emission probability for or this probability to excite an electron and you can see that actually has a it does have a very similar form to the semiconductor migdal effect right so they both have overall scaling with some charge time Alpha over Omega to 4th and they both have some Matrix element with this the KR and uh this VN also appears so essentially they have very identical forms and there are some small differences because of course the systems are still different and this this last piece is what we we derived basically so the interpretation we take from this is that we can think of the migdal effect as some analog of brem strol along that that's happening in a medium where you have all these electrons around when you kick a nucleus it will generate uh potential a Time dependent potential and that can excite an electron so that's a fairly I think simple thing that we expect to happen but I think what we're we're trying to say is that in the atomic migdal effect we can also use this as an explanation we don't necessarily have to rely on this boosting argument and as I just showed the form of the rate is can then be cast in very similar way in both cases so you might wonder at this point like uh if you know the first thing here is equivalent to the last thing here and you just rewrote it like what was wrong with just starting from this first Matrix element in the first place and you know using it in semiconductors the problem is that if you go through this op logic um at the end in a lattice you would get the contribution of the dipole Potential from all of the nuclei in the potential right if you take this commutator you'll just you'll get a sum over all ions in the lattice and so this operator relation does not actually hold in semiconductors if you start from the left side versus the right side you'll get different answers and particular if you're starting from this side you would generate the dipole potentials of all nuclei is kind of consistent with what we were saying at the beginning that you know if you apply a boosting argument you're really boosting all the nuclei as opposed to just one okay so what we're arguing for is starting from thinking about this in a dipole potential way and starting from this latter form of the Matrix element all right so I've shown now the connection to the atomic effect and why I think this should be called the migdal effect in semiconductors let me show you finally some results at the in the last few minutes these are the rates in uh silicon so on the left um there's a couple different lines this uh blue line is where we cut the rate off at small momentum transfer and this bump is actually the plasma resonance but you see when we included everything in our numerical calculations we get the green line which is a much larger rate um the scaling of this rate goes as one over energy to the one over Omega to the 4th so when you have a lower threshold material you tend to get larger rates and so you can see that for instance in comparing with the dotted Orange Line the dotted orange line line is if you took an atomic silicon Target which has a higher threshold that's the rate you would get so we think looking for this migdal effect in semiconductors is particularly powerful because of this lower Gap uh and for the experts in the audience you can also turn this rate into the actual number of detected electrons so it's a histogram of one two electron whole pairs Etc and that's what the rate would look like okay so then finally this is my uh last summary slide or last summary slide of this of this topic uh putting that all together we um show these curves which are projected sensitivity to Dark Matter nucleus scattering and this is with this migdal effect in Silicon and geranium these are the projected sensitivity if we have a kilogram year exposure and um put a threshold of two electron hole pairs these numbers are very similar to some exciting lots of exciting uh experimental proposals and um developments so uh maybe jod can comment more but I'll just say these seem like um in Target for a lot of different experiments uh but the current but if we take if we try to take current um experimental results um here is one for example this is from a surface run from Sensei with fairly small exposure um then you would get this red limit up here you can also compare with what a Xenon Target would do so this is a liquid Xenon 100 kilogram year so a lot larger exposure and same to electron threshold you can see uh because the threshold is going to be higher in these Atomic targets um this sensitivity is actually a little bit weaker despite the larger exposure okay and the last thing I'll just comment is that these bands are showing uh our theoretical uncertainty due to these to the fact that we're not accounting for the phonons in um in detail here so we're we're well let me restate that that wasn't quite accurate uh when the Dark Matter mass is very low we produce single phonons and when the Dark Matter mass is very high we kick a single nucleus and in between something a little bit more complicated happens and requires more work to treat that properly so dark matter is exciting a bunch of phonons at once and so the fact that these bands are kind of growing is showing that that's um the mass range where we have to treat it with a different approach to account for the multiphone on processes okay so just to wrap up um we introduced this migdal effect in semiconductors and we showed how you can use it to improve the sensitivity Now by using charge rare charge signals for sub GB dark matter and in my last slide I'll just connect it back to the bigger picture of looking for Dark Matter below the GV scale through a range of different approaches all the way down to Dark Matter massive KB or so and with that I'll conclude thank you so much for listening okay no thank you very much and we'd try to give you a little Applause here at the end oh great it's something right yeah um so we have a question from Tim Hobs uh Tim let me get you unmuted here go for it Tim can you hear me yeah okay great yeah I think this is a really interesting talk I have a a question which you may have alluded to I think during the course of your prepared comments which is similar to what I always ask in these kinds of direct detection um discussions so you presumably have some theoretical uncertainty just from the nuclear wave function or the nuclear recoil that aspect of the Dark Matter nuclear crosssection that you've been talking about you had mentioned at some point abono calculations I'm wondering is that is that um a contribution to the exclusion plots that you showed toward the end or how well is that under control at this level would you say so let me see if I'm understanding correctly so for the dark matter and nucleus scattering side uh for for very um heavy dark matter there can be uncertainty because of the Dark Matter wave sorry because of the nuclear wave functions and how basically there's like a form factor for how the Dark Matter interacts with the nucleus is is that roughly the uncertainty you were talking about or is it a different one because here I'm talking about um because I'm looking at sub GV dark matter the nucleus nuclear wave functions um don't present a large uncertainty because the Dark Matter nucleus scattering it's so low so low in momentum transfer that we just we can coherently sum over all the all the nucleons without any like nuclear uncertainty about the form factor but I'm not entirely sure if that's that was the okay yeah thank you I I couldn't unmute while you were asking that is that is the gist of what I was getting at I mean my assumption is was more or less what you were saying that it's so low energy that that indeed you make this assumption but yeah that that sounds reasonable um so in general there's there's no input in other words really directly from nuclear modeling or anything of that sort then directly in this calculation that's right yeah we do have like the theoretical uncertainty you mention you were alluding to the abono calculations right so yeah indeed for the energy loss function uh we're using numerical calculations that agree reasonably well but there might still be you know order one right uncertainties there right and what is that exactly I mean can you say a word about I mean what are these calculations exactly these are the like the density functional Theory codes I see yeah there are a lot of those and we used one of those to that can calculate this dialectric function very good okay all right thank you sorry there's a actually a discussion going on on the YouTube channel which I think has never happened before so thanks who's talking about phone on over on YouTube um if while we're waiting to see if anyone else has any more questions I I had one for you Tongan um the migdal effect help me out here has that ever actually been detected I seems like a pretty inevitable consequence of quantum mechanics applied to these systems but has it ever actually been observed for um there are a lot of uh there's a bunch of literature [Music] from I want to say I'm not going to get the decade right so there's a bunch of literature looking at um if you take a neutron and you hit a nucleus you should see the same effect and if you take um another effect is if a nucleus decays into an alpha and it emits an alpha it also will recoil and you should see an effect so I think it has been observed in like nuclear Decay and I think also the nucleon nucleus scattering but in all those cases it's also Complicated by other interactions like in dark matter we kind of have the you know we we can say Okay Dark Matter only talks to the nucleus in one particular way that simplifies things we don't have to worry about the alpha also has the electromagnetic interaction um or if for in the nucleus nucleon case you can also get some like resonant strong interaction kind of effects uh so yeah it's been observed I'm not sure the data is extremely clean on um the interpretation because of these other all these effects that you have to include so I mean since in a sense you've maybe generalized isn't the right word but broadened this effect into the context of whole semiconductors um what what are your thoughts on like if you if somebody said okay we're g to give you X millions of dollars to construct an experiment to actually try to observe this effect in a controlled set of conditions um you know it seems like well maybe you'd want to put this near some low energy neutrino Source or something like that or maybe a very low energy Neutron Source although yeah presumably you you'll be competing against the capture cross-section as well there so um what would you do what would you do if you wanted to build an experimental team to go and actually observe this effect and get data on it before you apply it to a dark matter experiment good question as a theorist I don't know if I'm going to give the best answer but I think then I mean if you could do it with neutrinos that would be that would be great like put it next to a reactor um I mean the trick is you want I mean ideally you'd want to know Beam on beam off and so having a beam that can do spills where you know you've got pulses of neutrinos coming through in a certain direction is ideal but maybe not necessary for this maybe you just need to cool a detector down somewhere in the vicinity of a low energy neutrino source and just watch yeah the thing is well I'm not I can't comment on you know which which source do you want to use neutrinos or neutrons from the perspective of like teasing out this effect I I get the sense neutrinos would be a little bit better because it did sound like for neutrons there can be some resonant effects right so that I yeah from what I saw neon source and try to do this that complicates things through the strong interaction presumably so uh okay you know I was curious because I mean Richard brought up earlier this question of neutrinos and I mean obviously if neutrinos can strike the nucleus which they certainly can they could also induce this effect so it should be detectable if you flood a semiconductor with neutrinos and just wait right yeah on the other hand neutrinos can also kick out some other kick out electron in other ways so right but they won't double scatter the probability the neutrino hits a nucleus and then hits an atomic electron is vanishingly small right whereas the alpha particles you mentioned earlier will create Havoc because of the electromagnetic interactions they'll then also generate so yeah I guess another thing is like even if the neutrino is scattering off the electrons I think the the Spectrum would be really different from this effect so that might help right and presumably there you well maybe if it's low energy enough it it wouldn't actually eject the electron but presumably it would lead to some other signals that would be distinct from the nucleus getting struck MH but uh well that's a good question though that's a very good question yeah I I mean I've heard this discussed obviously in the context of dark matter experiments before but the experimentalist in me hungers to actually measure the effect itself independent of say dark matter so yeah absolutely all right any other questions I don't see any more right now in the speaker chat but we did have a lot of things during the talk so clearly your subject was interesting or you wouldn't have gotten so many questions during your talk all right I don't see any more questions so I think let's go ahead and thank tongyan for her uh kind offer to do this presentation today and for all the information she's provided and I'll just wish you all a good night and uh a safe Thanksgiving I hope everyone has a a safe and and easy Thanksgiving okay all right yeah thanks again yeah no thank you byebye bye everybody thank you