 Physics can do many wonders and we heard about many of them during this conference and we'll probably be hearing about them for the rest of it. But life sciences can do even more wonders. And in case you didn't pay much attention to the developments if life sciences, there was one. And actually it happened this April. The definition of middle age has been predefined. It's actually a serious study which was done in Austria and also in Ostony Brook, so it's kind of bona fide. And 60 is now the new middle age. And the news here, the internet, you can find all these articles and some even go further as to define 40 as the new middle age. And I think for this particular instance I'm going to agree with life sciences because in this room we have a living, breathing proof that 60 is actually below the middle age. And this young gentleman here on a photograph actually taken I think somewhere around here. We see someone who is full of spirit, full of energy. Happy birthday, Borya, and happy birthday. And for those of you who would like to congratulate Borya's in his native language, that's at transliteration. Okay, so now I'm coming to the subject of this talk which I think hardly needs motivation these days. In this audience I'm talking about what will happen in a Fermiliquid with a twist. And twist is coming from spin orbit R coupling. And if you look around, spin orbit these days is everywhere. So the interactions and these are just few images to bring the memories of the R combination of these two effects. This is a work done in a collaboration with some of my students and postdocs at UF and also with Prajba. There will be plenty of Prajba Archimaltonians in this talk, but this is Prajba himself as a person and wonderful person. It is. I got interested in the subject actually while visiting Basel. I'd like to thank Danielos and members of his group for introducing me to the world of spin tronics. And also, I'm an experimentalist. We are keen to spend their time listening to some of our crazy proposals. I would like to thank Charlie Marcus who is also somewhere here. Klaus Hansen and Floran Perez for giving us their ears. And actually for a while, we were covered by the same grant with Daniel Prajba and Charlie Marcus. So part of it is coming from this work. Okay, so I'm going to address a really simple problem. It's not going to be topological. I'm going to talk mostly about simple-minded Prajba-like interaction and turn on election interaction in addition and see what happens. There are three avenues of work which has been started and are going for the time being. One of them is simply well to ask, do we have a thermo-liquid at all? What happens if we turn on the election interaction in assisting with spin orbit? Is it going to have some dramatic effects as in bringing us to a non-firm liquid? And this is not going to happen. For obvious reasons, near each of the thermo-surfaces we have well-defined aquasic particles with abnormalized masses and there is a long line of papers which tell us how to do the preservation theory in a particular basis of orbit as per its states. Then there is an issue of collective modes which I'll spend probably most of the time today and also an issue of a general structure of a thermo-liquid which I will probably talk at the very end of the talk. So this is my outline. I will talk mostly about a simple side of the theory and I will talk mostly about it because there are some predictions for the experiment. There is no clear experiment done yet. I'm not going to explain it and I have no data to show but we hope to stimulate some experiment. And then I will talk about the analogy of a thermo-liquid with not the spin orbit coupling. And while talking about a collective mode, I will be working in a pretty simple up-regime when a spin orbit is small in some sense compared to the thermo-liquid. Okay, now the collective modes I'm going to be talking about have some similarity to spin waves in a partially spin polarized thermo-liquid which is a very old subject and you can think about, let's say, helium-3 which you place in a magnetic field. In the absence of the interactions, all spins are going to precess with the same frequency but phases are going to be random because there is no relation between different electrons. And what the interaction does, it locks the phases of these precessions into a collective mode. And so in more detail that's how it looks like on the energy versus the wave-number diagram. We have a spherotational invariant thermo-liquid. A lambda function is parameterized by two functions of the angle and for the purposes of this talk we'll be only just in a spin-spin part of the interaction. This function f as a function of theta between the angle of the angle between the momentum gives us the strength of the effective interaction here. There are several points on this vertical axis. If we do the usual procedure to solve the kinetic equation in the presence of the field and in the presence of the interaction, we'll find that the non-clibrium part of the distribution function can be decomposed into a set of harmonics and each of the harmonics precess with its own frequency and this frequency I in general are normalized by the interactions and this is a whole infinite set of other frequencies which start from 0 and go all the way up to a continuum. This big yellow area here is a continuum of spin-flip excitations and the endpoint of the continuum is the Zeeman energy of a quasi-partically in the magnetic field and the Zeeman energy is randomized also by the interactions. But if we look at the microscopic magnetization to which the real microscopic field can couple to, well, we need to take the distribution function multiplied by the power matrix, take a trace and integrate over the momentum and because of this integral only one l equal to 0 harmonic of the distribution function will survive. So the microscopic field can couple only l to 0 harmonic so we can forget for a while about all others and if we focus only l to 0 harmonic if I substitute l equal to 0 you see that the denominator cancels the numerator and the frequency of this mode is just 2 BB which is the normal frequency of a free electron that's thanks to the quantum theorem which tells that the skin part of the Hamiltonian commutes the betagal part of the Hamiltonian. It doesn't mean though that the interactions are completely gone because this frequency here is just the endpoint of the actual collective mode which is a dispersive mode and in the helium-3 arcane community it is known as silicon-legged mode. The stiffness of this mode is made, if you wish, of the interaction it contains the same harmonics of Landau function which were measured in the frequency and also this mode is damped by the residual interaction between a quasi-particles and the damping are coefficient also contains other interaction parameters. And as of late 60s and 70s it was big business in helium-3 and to some extent in in simple metals to extract the parameters of the chemical theory from ESR or NMR in case of helium-3 measurements of this mode and this particular plot is from a Candela group at Columbus. This is a very clever experiment when this mode was turned into a standing wave by applying the gradient of the magnetic field. All right, now thanks to Peter Fuldestock I don't really need an introduction to a project with a bit of coupling but just to set annotations I'm going to be talking about a two-dimensional system which is asymmetric up is not equal to down and because of that the Hamiltonian has an interesting term which looks like a magnetic field which acts on the electron except for this field depends on the momentum of the electron and this is the threat field it provides a twist on the spin of the electron in such a way that the spin is at plus 90 on one of the spin-split thermal surfaces and it is at minus 90 on the other one. And the relevant energy scale as long at least as we talk about spin orbit our coupling is two alpha-alpha has units of the velocity times the Fermi-Peyton number. Okay, so now we fill these bands by electrons and we let them interact and let's look at the collective modes. And so these are the carol spin waves that's how we go in this ideal thing field and from the beginning I will make a simple assumption or simplifying assumption which is that the strength after which our coupling is weak or in terms of this approximate velocity alpha it's much smaller than the Fermi velocity or which means that the typical energy scale is much smaller than the Fermi energy. Life is then simplified tremendously. I can forget about a coupling between charge at degrees of freedom such as plasma and spin at degrees of freedom which are the modes I'm going to be talking about. Spin orbit also is not going to affect the structure of the SU2 invariant Rwanda function so far this will be the second part of the talk. So what we need to do is to solve a kinetic equation which I have here in the most general term which also in principle has other right-hand side coming from a damping and residual interaction between quasi-particles. Well that's certainly too complicated. So let's first look at a simple case when the motion is uniform, appears equal to zero and also there is no damping. Then this is a simplified form of the kinetic equation and then we're looking not at modes, we're looking at resonances and they are chiral spin resonances which were started first by Schachter-Hodex and Arthinquilstein. So I'll spend just one slide on what seems to be a technical subject but it will help to understand what's going on later on. Still the problem of interaction seems to be too difficult why don't we just solve the Fermi-Gas problem? So we have three Rajba affirmions, no interactions and we want to know how the distribution function of this gas will change. Well it is convenient to switch to a basis of new Pauli matrices and those are minus sigma z, sigma dot k and the third Pauli matrix repeats at the structure of the Rajba term in the Hamiltonian. Locally in the methanol space the algebra of these Pauli matrices is the same as of the original Pauli matrices. So I apply a perturbation to the energy in my system which is the Rajba term in the Hamiltonian and as a result I have a change in distribution function which has two terms. Simply kind of shift of the chemical potential if you reach in this two-by-two space and there is a really non-equilibrium part which depends on time and on the momentum and this is a vector which is dotted into the vector of these Pauli matrices. So when I apply a time derivative it hits the vector here when I calculate the acceleration function I have a tau matrices tau x and tau y now you have to equate this equation to this one and you have a simple system two-by-two which tells you that the components of the distribution function precess the three-dimensional space the third component does not move and this is a case of circular polarization. Okay, so now when we turn on the electron-electron interaction the only change is that the change in the energy will have two parts one is still the same orbit or coupling term and the other one is the system term which tells how the changes in the distribution function feedback to the changes in energy through the Landau interaction function we spread the Landau function into harmonics to the same for the vector of distribution functions well the commutators become a little bit more difficult because now we have to be on a local electron space this is the algebra of the Pauli matrices and as you see when k is equal to k prime it goes back to the usual algebra now we need to recall that we are working to lowest order in spin orbit so we will derive the equation of motion which I will only order alpha order alpha squared is to be discarded and then the equations are similar to what we had in other three cases except for the coefficients here are polymerized by a harmonics of the Landau function and the scale set by a spin orbit is also polymerized by itself and this effect of polymerization of a spin orbit was well known before the Tchenenreich and Daniel Loss and Saraga so if you look at the vector of the distribution function it still processes in the momentum space except for because the frequencies are now different we have an elliptic rather than a circular polarization the frequency which is again the scale of a spin orbit times this combination of Landau harmonics so going back to the diagram we got also as the case of the usual spin wave mode we have an infinite set of modes starting from zero, harmonic and up now there is a change if you look at macroscopic monetization it contains now two harmonics L equal to zero and L equal to one as opposed to the case of a spin wave when it was normally L equal to zero and then we can forget about all but two if we're talking about coupling to macroscopic field and it's pretty obvious why there should be two rather than one mode because we broke this meritational symmetry in plane and out of plane are not the same so there should be at least two collective modes which corresponds to oscillations of in plane and out of plane are components of monetization we'll keep only these modes we label them for convenience as X and Z because if we look back at what is going on with monetization we actually have a linearly polarized wave along X, Y and Z and also if I make even more drastic simplification namely I will assume that my Landau function is very simple it contains only one harmonic and not addressed these are the only two frequencies which are going to provide in this limit but just for the purposes of simplicity I will keep on with this approximation what it means is that I will still have the same modes as I have in a full-fledged theory but the frequencies of this mode are not the same as in a full-fledged theory but we don't know what these Landau functions are anyway so it's not a big price to pay so what happens if we now start to look at a non- and only from case so now this is really a mode rather than a frequency each of the resonances the equation of motion takes this form of a wave equation with a massive term and it's also pretty much obvious why it should be the case we haven't broken the temporal symmetry so the equation has to be second order in time while we still have the rotational symmetry in plane so it can be only second order in position and we have the massive mode therefore we have the massive term once we choose the direction of propagation in plane we also broke the symmetry which means that the stiffnesses of this mode are going to be different so we'll have three modes one of them is going to be longitudinal one transfers in plane and the other one also transfers in plane so this is small q approximation one can really compute these coefficients but it's not very informative if we just look at the plots the stiffness as a function of the direction of the parameter while they have some form and the change sign depending on whether we're in a weak coupling limit or a strong coupling limit but if we kind of limit ourselves with what we should expect for n-type two-dimensional gas in Gallemars tonight where these parameters are more or less known well then we're here in this range of not too strong, not too weak interactions and that means that we'll have two downward modes and one upward mode if we want to study the mode in its entirety we can either solve numerically the Dyson equation or we can even abandon the Fermi-Lepid theory go to simple-minded RPA which would allow us also to work for a forward spinor with error coupling and that's how the spectrum of this mode looks like so these are the two modes which started off to be being generated at a critical to zero then they separate, hit the error continuum and the third mode which corresponds to out-of-plane oscillations is more or less similar to this to the student-alleged mode in a partially polarized Fermi-Lepid it runs, it merges with the error continuum at this moment and it is similar work on the same issue in the context of apological insulators and also in the context of cold atoms where one can produce a multi-facial approach to coupling so now, since I started with a real magnetic field let me also then I turn it off and we have a collective mode of resonances which one can think of ESR resonances in the absence of the field and so that's the effect of RASB field on a given electron with a given momentum which doesn't lead to polarization of my system so now I can go back and turn on a real field and what it does, well, let's say this field defines the x-axis in my plane it shifts the momentum along the y-direction and now what happens is that at one particular value of the field the Fermi surfaces of spin-speed band touch when they touch it means that there is no gap for single-particle excitations so the arc continuum, this blue area here hits the zero here and so the gap in the continuum disappears to the right of this point we are in a strong field regime and there is only one mode and this mode, if we go to larger and larger field we'll grow into the ceiling-legged mode with the frequency which is unapronormalized by electron-electron interactions to the left we'll have three modes and if we turn off the field then these two modes will occur less into one degenerate mode and these two frequencies are the two spin-accurial resonances what happens with this polarization? so if we start from here we have three linearly-apolarized modes once we apply the field two of these modes become elliptically polarized the one which is still along the field is linear once we hit this point we only have one mode these modes are elliptically polarized and as we go to higher and higher fields it becomes an elliptically-circular polarized so now this would be the picture of ESR but because we have a spin orbit in the system we can also do better than simple ESR which has low sensitivity and especially in systems which have only three electrons so what we can do is we can apply an asymmetric field an independent field which is a long static polarizing field and because electrons will be moving back and forth along the electric field there will be an induced polarizing field which will be perpendicular to the polarizing field and so now we'll have ESR but not in the real field coming in this electric field but in the induced polarizing field and this gives a tremendous amplification of the signal so when we're at larger fields to the right of the critical field there will be one frequency of the resonance which will be still somewhat abnormallyized by the interactions and there will be a hump due to our continuum if we're to the left of the physical field well then if we're lucky we can hit both modes because both of them are active the third one is not going to be optically active in this regime because it corresponds to auto-plane components and also a hump in our continuum so that's one of the predictions here okay so what one can do in order to measure these modes many things one can try to do and we hope that some of them will work first of all one can certainly probe this mode absorption of magnetic appropriation this is just probing the resonances at Q equal to zero the total conductivity which is a correlation function of velocity our velocity has not only the usual adruda theorem but also because the velocity couples to spin the total losses couple to spin spin susceptibility and so the mode which is a pole of the susceptibility will be seen in optical absorption so this is a cartoonish picture how the mode will look like so this is the adruda peak and this is the rajba continuum which will be seen even in the creatinine picture but also there is a collective mode which kind of excuse the continuum to probe the dispersion of the modes one can certainly think about Raman so one mode here in plane is infrared active therefore it's not Raman active but the other one will be Raman active but one can also try to implement what people in helium-3 are doing that is to form standing waves out of these spin-carrel modes and one can try to do it by producing modulation in spin orbit asplitting which can be done by imposing a large gate so that it's much larger than at the Fermi wavelength so that the motion of electrons is not quantized but the motion of spins is in this case the microscopic of motion formatization takes on a quasi-shredding return where the potential energy is being played by the position-dependent spin orbit-splitting we have these three modes and in a typical range of parameters some of them have upward dispersion so they have these particles in this quantum mechanical world and some anti-particles that have downward dispersion and that means that the pattern of absorption is sensitive to the sign of the gate wall which namely if I change this potential hump into a potential barrier it will bind one type of particles and not the other while if I have a hump it will bind particles this negative mass so to put some numbers on this picture the frequencies of this mode given some reasonable assumptions about the interaction are in the tens 30-60 gigahertz range for aluminum-gallium arsenide if we look at indian-gallium arsenide it brings us to 1 to 2 terahertz space-wise there's this limiting momentum here it gives us at a scale which can be seen in Raman is 10 to 3 in gallium arsenide or 10,000 in indian-gallium arsenide so if we look at various systems it seems that for the purposes of absorption one would need a good sample with mobility 10 to 5 two-way damping of indian-gallium arsenide EDSR gallium arsenide will probably do and resonant Raman we can listen from Floran Perez that cadmium-magnum tellerite I think went well off should do work so this is the second part of the talk which is probably going to be one slide so let me tell you what it's all about so the purpose now is to abandon a dissection of the spinner with a coupling and to ask how a spinner with a coupling actually modifies Landau interaction function the same innovation asked about a partially spin-polarized Fermi liquid which was back in 1958 but there is a change in the story because we have no real field we have two quasi-particles with a de-momentum each of them is in the field of Rajbo which is associated with its own momentum but also one can do more things with this field because the cross-product of two Rajbo fields is not zero and it's out of the plane and that breaks the spin-rotational invariance so if you go through the symmetry consideration you end up with a very long Landau function all this invariance time reversal, permutation and see infinity to be symmetry one can check in the interpretation theory if it works yes it does one can play many things in the charge sector derive optimization of the effective mass incompressibility etc etc and as you would expect this is more toys and whistles you have intra-band matrix elements intra-band matrix elements and this is maybe useful but the stumbling point comes when we think about spin-sectability which is not a Fermi surface property even in a Fermi gas of Rajbo fermions what it means is that when we try to construct a Fermi liquid theory the changes in energy and the and the activation numbers are necessarily off-diagonal and the equation which is supposed to relate the g-factor of a Fermi liquid to the g-factor of a Fermi gas has an integral part which is integral over the space in between two Fermi surfaces now when the Fermi when spin orbit accompanying is weak is a problem that's a narrow interval when it's large spin orbit we have a region in between where our quasi-particles are not defined and what it means is that we cannot formulate spin-sectability in terms of few Landau parameters which are projected onto the Fermi surface so that's kind of a frustration which we still don't know how to recomb and there is a similar study of Fermi liquid on the helical surface of the state of the dimensional archeological insulator which ran into the same stumble but because of the difference of this system they seem to have found a way around this and with that I would like to thank you for your attention and I'll finish