Capone, Arita and Fabrizzio

Massimo Capone (SISSA, Italy)

Blogged by Maxim Dzero(See below)

Ryotaro ARITA (ISSP, Tokyo)

Density functional theory for superconductors and its application to layered nitride superconductors

Blogged by Genady Chitov(See below)

Michelle Fabrizio  Break-down of ergodicity in quantum phase transitions
Blogged by Piers Coleman (See below)

Massimo Capone (SISSA, Italy)

Blogged by Maxim Dzero

In his talk Dr. Massimo Capone has presented very intriguing theoretical results on superconductivity in organic molecular superconductors_. After spending the first 15 min. of his talk reviewing the current challenges in our understanding of superconductivity in various “aromatic” molecular conductors. The examples specific examples discussed were K_3.3picene (T_c=18K) , Rb_3.3picene (T_c=7K) and K_2.9picene (T_c=7K).  Massimo noted that it seems there is a magic number=3 of electrons per molecule corresponding to the maximum value of superconducting transition. Massimo emphasized that one of the major challenges is to understand the role of correlation effects in stabilizing superconductivity. To address this challenges, Massimo suggested to use fullerides as a reference (North Star) point to get an insight into the microscopic nature of superconductivity. In the remainig part of his talk, Massimo has presented the results of the DMFT calculations for fulleride Cs₃C_60. He argued, that contrary to common expectations, correlation effects may actually lead to the enhancement of superconductivity as opposed to suppressing it. The subtle issue was the renormalization of an interplay between electron-phonon and magnetic interactions. Massimo’s talk induced quite a bit of discussion in the audience. Here are the few questions that has been asked:

Q: Is it known where ordered moment resides? What is it size?

A: The exact location of the moments are not known, since neutron scattering experiments have not been done. NMR measurements suggest that the moments are on carbon. The size of the moment correspond to the full S=1/2 state.

Q: What is the symmetry of the superconducting order parameter in Cs₃C₆₀?

A: It is likely an s-wave

Q: Are superconducting and AFM orders co-exist for certain values of U/W or the phase separation takes place?

A: It is likely a phase separation, although co-existence cannot be fully ruled out.

Q: What is known about the nature of the normal state?

A: Bad (i.e. poor) metal

Q:  How phonons are treated in the DMFT analysis?

A: Phonons are integrated out to provide an effective bath for the conduction electrons. The treatment is essentially exact.

Q: The classical single-site version of the DMFT has been used, which clearly excludes the d-wave order parameter?

A: Yes, motivated by the experimental findings only superconducting instability in the s-wave channel was analyzed.

Q: Did you calculate the frequency dependence of the normal and anomalous self-energies?

A: Yes.

Ryotaro ARITA (ISSP, Tokyo)

Density functional theory for superconductors and its application to layered nitride superconductors

Blogged by Genady Chitov 

Nice well-thought introduction. Especially useful for someone unfamiliar with those materials.           The speaker made a strong case to show that the strong electron-phonon interactions are not            sufficient to explain the SC properties, most notably the large BCS ratio. It seems however that the shortcomings of the electron-phonon analysis do not necessarily indicate towards an  unconventional SC, but could also be a sign of strong electron interactions. Various Peierls-type transitions provide examples of fermionic interactions driving the BCS ratio away from the  free-fermion (mean-field) value.                                                                                                                
 

Overall, a nice talk, gives a strong motivation to take a closer look at the nitride superconductors                                           
                                         

Michelle Fabrizio  Break-down of ergodicity in quantum phase transitions
Blogged by Piers Coleman

Michelle discusses how, in a classical phase transition, broken symmetry means a break-down of ergodicity.  Question is - what happens for quantum systems. He talks about Anderson localization and Many Body localization as examples of a kind of "quantum ergodicity breakdown".

Now we are turning to photo-induced phase transitions. Here light is exciting the system. Commonly, optical pumping is regarded as a non-equilibrium, heated state.  One would like to use photo-excitation to induce phase transitions from insulator to metal. This would, he said, have important technological applications.

Q: How is this something to do with ergodicity.
A: But because of an ultra-fast laser, one can heat very rapidly.  Pumping is not heating - but perhaps ergodicity is broken - so we can't think of it as heating. There isn't enough time to explore all phase space - so is it really true that one explores typical areas of phase space.


Now he defines a kind of Lanzcos procedure for the operation of H on a starting state. This generates  a set of states |psi_n> with parameters t_n and E_n, this produces a tight-binding Hamiltonian, and the quantum evolution of the initial wavefunction is equivalent to a particle that starts at time t=0 from the state 0 of the chain.  The underlying dimensionality is hidden in the correlation of the various parameters.

The quantum evolution of |Psi_0> is not ergodic if a particle that starts at the intial site of the Lanczos chain does not propagate to the end. (Becomes localized, stops defusing.)

Natan Andrei points out that you don't need full ergodicity -but what you need is "typicality" - splitting up into sections that are somehow typical of the entire Hilbert space.

So - next - a case study - the Bose Hubbard model, hopping of bosons in a 2D lattice. Experiments on cold atoms trapped in optical lattices offer an opportunity to explore the ergodicity issue experimentally.   In a recent expt, Trotkzky et al used Rb atoms in a 1D optical lattice, and let them propagate from their intiial density cofiguration - does the system equilibrate to uniform denity? Indeed, they found that the density did rapidly equilibrate, and the result were consistent with a density functional renormalization calcn.

But! The Bose Hubbard odel in 1D has a Mott transition for integer filling and large enough U/J. Worth considering the case of n=1, rather than 1/2.  So to examine this case, Fabrizzio and collaborators did a numerical simulation with 2-0-2-0 inital configuration.  He says that they found that for large U, the denisty remains inhomogeneous for extremely long times - the system does not relax.. the density kind of oscillated between 2 and 0 without any clear relaxation.  So they decided to define a relaxation time - n_odd(t_R)=1.  They found a sharp dynamical crossover at Uf~ 4.5 - a genuine transition though? Above this value of interaction, the system is trapped into an inhomogenious state.

So to examine this using the protocol MF and co. used the Lanczos chain approach, with up to 1k sites. For the U=2K - the ti are smooth, as are the energies, but for large U there is an oscillating component to the "potential" that lasts out to 300 or so sites. So does the particle propagate along the chain?  This depends on U/J. For small U, the state is able to move to the end and is reflected back and so on, but for U = 10J, he says, the R(t)/Rmax never exceeds 0.2 - the state is localized.

Natan Andrei comments that this is related to his talk yesterday - that in a Leib Linniger model, you get localization for large interaction strength.

MF says that the simplest explanation of this situation can be made in terms of an effective spin chain description - from a kind of Schrieffer Wolff transformation. up spin is doubly occupied, down spin is empty.  The singly occupied states are much lower energy and can be integrated out.

H* = 2 J^2/U  sum [-8 S_z(i)S_z(j)+ (S+(i)S-(j) + h.c)]

For large enough U, you stay in an AFM.  (Blogger didn't understand).

Further evidence of glassy-like dynamical transition, Study the correlation function

C(t) = (1/L)\sum i=1^L <delta n_i delta n_j>

One defines tau_R as the first time where C(t_R) =0, then one finds a sharp increase in tau_R. To explore this further, MF and co have applied variational Monde Carlo and found evidence of a dynamical transition around U~ 4.5.



MF ends with a speculation: he argues that there has to be a mobility edge separating low energy eigenstates of H, which are translationally invariant, from high energy eigenstates that are not translationally  invariant.  He argues that the dynamical transition will occur when E^*~ N.


A very nice talk. What is not clear is the relation between this and many body localization. It would appear to be quite similar (bloggers state).

Yu Lu states that  it appears that you are making a description of the Upper Hubbard band.  You are providing a snap shot of this.
AF agrees.

Natan Andrei (Rutgers): Quench dynamics of the interacting Bose gas in one dimension complementary to Aditi's talk

Quenching and time evolution

Start in H0, turn on interaction at t = 0, propagate with full Hamiltonian.  New experiments allow us to do exactly this in cold atoms, nano-devices etc, since the time scales are much longer than in typical condensed matter systems.

Interesting questions:
- how do the observables evolve?  correlations functions are now functions of two times (time difference and waiting time).

Example:
Quantum dot with tunneling turned on suddenly, measure appearance of the Kondo effect, how does the resonance evolve with time?

Bosons in one dimension - what are the effects of interactions on the dynamics?
One dimension because strong quantum fluctuations enhance all interactions, plus powerful mathematical methods - RG, bosonization, CFT and *Bethe Ansatz* (BA), which allows one to diagonalize an integrable Hamiltonian and find all its eigenvalues.  Many integral models, like Hubbard, Heisenberg etc are experimentably realizable.  So how can one use the BA to solve hte quench dynamics of many body systems?

Setting it up:

A given state can be time evolved knowing the energy eigenstates.  These are known via the BA.
Standard approach - impose periodic boundary conditions, generate BA equations with quantized momenta, get spectrum and reconstruct thermo.  Nonequalibrium requires overlaps, summing over the whole basis and take infinite volume limits, but typically has required heavy numerics, while we want to be elegant.

BA review:

General N-particle state generally very complicated, but BA-wave-function is much simpler - it is a product of single particle wave-functions and S-matrices (describing scattering phase shifts of two particles).  Illustrating on Lieb-Linnigar model - bosons on line with delta-function interaction.

Divide configuration space into N! regions (labeled by Q), within each region there is no interaction, wave-function is product of exponentials.  Regions are related by S-matrices - interaction on the boundaries.  Assign amplitude to each region, A(Q), and S(ij) relating the regions.  However, we have to be careful to do this consistently, if say we are exchanging between three regions there are two ways to do it and they must be the same.  This consistency relationship is called the Yang-Baxter equation: S(12)S(13)S(23) = S(23)S(13)S(12), which is satisfied only when the system has enough conservation laws (eg - integrable).

Calculating overlaps is still difficult.  Directly going to the infinite system can simplify things since momenta are unconstrained, and so can be integrated on a contour in the momenta space - which may be complicated, but allows a certain simplification using the non-interacting overlap. Dominated by the poles in the full-fledged Bethe eigenstates. Unfortunately, implementing the formula is very system-specific, really a guide for how to go about doing the problem.

Piers Q: New way of writing completeness? (yes) Does it only work for integrable systems?
A: Not really - would be similar formulas if we have a set of lambda where we know the poles.

Applications to bosons in optical traps:
(can make predictions for experiments - noise etc)

Lieb-Linniger model - standard model for bosons in 1 or 2 dimensions.  Short range interaction - kinetic energy + local interaction when bosons are on top of one another.  Coupling constant can be either attractive or repulsive, can be controlled experimentally via a Feshbach resonance.
Conventional BA results: Eigenstates labeled by momenta.  Dynamic factor - normally 1, negative if they cross.  Momenta real for repulsive, c > 0, complex pairs for attractive, c < 0, forming bound states.

Initial condition 1 - relax periodic lattice
Intial condition 2 - relax trap and allow bosons to expand and interact - interested in how they interact.

Central theorem: Expand state in term of eigenstates in contour representation.  Must use real contours for repulsive case, complex strings for attractive case.  Using contour represntation, can easily write down time-evolved state analytically.

Q: number of particles? A: any number of particles.

Keldysh: Time-evolving operator, O is non-perturbative Keldysh (forward and backwards in time on contour C) - not expanding in interaction, just solving exactly.

Okay - let's calculate.
1. Evolution of density -> time of flight experiment.
2. Evolution of noise correlation (more physics than in average density) -> time-dependent Hanbury-Brown Twiss effect.
C2 = <rho(1) rho(2)>/<rho(1)><rho(2)>

HBT - vanishing correlations between two sources (stars) - measure photons find bunching (C2 ~ cos x), fermions find anti-bunching (-cosx)
Many free particles gives more structure, time-dependent - curious about effects of interactions -> repulsive bosons evolve into fermions, attractve bosons evolve to a condensate.

Prepare initial state with two bosons, weakly overlapping.  Evolve in time.  Can carry out all integrals for two particles.  Calculate B\dg b.  Results: no interaction, then bosons quantum broaden and nothing interesting happens, density just decays in time.  Repulsive interaction - pretty much like free bosons.  Attractive interaction competes with the diffusion, as it favors more of an overlap, increasing the effect of interactions, and get much more interesting, oscillatory structure of the density(t).

For simplicity look at the long time limit - bosons turn into fermions - expression develops antisymmetric correlations and can rewrite original bosons in terms of fermions interacted on by free fermion Hamiltonian (Tonks-Girardeau Hamiltonian is c = \infinity limit, where hard-core bosons are effectively free fermions - it flows to this fixed point for any c > 0).
Scaling interaction fails for attracive bosons.

Q: How does time flow on the contour?
A: Time flows only forwards - back is just taking bra.

Looking at corrections to long time - can use stationary phase approximation at large times. Attractive has saddle point + poles and  bound states.  xi = x/2t only t-dependence.

C2(x1,x2,t) -> C2(xi1,xi2).  Develop antipeaks in the C2(x1-x2) at zero, indicating fermionic behavior (bosons develop peak that sharpens in time).

Can do for any number of particles - always fermionic physics, with antidip, and then more structure at longer distances.

Q: Piers - origin of periodicity in 10 particle? A: Starting from periodic initial state (lattice)
Q: Bosons as fermions - wavefunction is antisymmetric?  A: Really hardcore bosons, just changing variables into fermions. (okay because 1D)

Time-evolution Renormalization Group:
time flow is RG flow - increasing time plays role of increasing bandwidth, since flows to c = +/- infinity in long-time limits.  Can argue that there are basins of attraction, so adding perturbations (short range interactions beyond delta-function), dominated by same fixed points - eg - Bose-Hubbard model (putting LL on the lattice) -> hard core bosons hopping on lattice in long time limit.

Conclusions:
Don't need spectrum of H or normalized eigenstates.  Just need theorem on initial state.  Takes into account bound states without summing over strings, and is mysterious.  Can completely calculate all asymptotics, and can compare to experiments, especially as results are universal.

Working on applying to more models, adding impurities, finite volume, density, temperatures.  Approach to steady state, testing dynamical RG hypothesis.

Big Questions:

- what drives thermalization of pure states? is it canonical typicality, entanglement entropy?
- general priciples out of equilibrium?
- what is univeral?

Questions:
- HBT results recovered for bosons and fermions?
A - not yet compared to experiments, but should be recovered.
Chubukov: large time asymptotics means what time scales compared to experiments?
A: time scales are milliseconds.  t > 1/coupling (and coupling is known)

Comment: von Neumann did work on thermalization - considered quantum ergodic thm, related to quantum central limit thm - system in long time limit goes to thermal limit.
A: not everyone accepts that this has been answered, but this is even more general and we have full control - not all states thermalize - they remember their initial conditions.

Piers: Vacuum is absence of bosons, and is eigenstate.  Could do for magnons against FM vacuum.  But what about nontrivial background, like AFM?
A: Can start with Neel state (not eigenstate), act with H and propagate - where does it go?  Or can take XXZ model, has phase transition so prepare as eigenstate of Ising model, propagate with XY model.

Girsh Blumberg (Rutgers): CaMn2Sb2 (CMS) with buckled hexagonal Mn plane structure: removal of Hund's spin blockade

Blogged by Eoin O'Farrell

The tittle compound is a new material, on which the erstwhile blogger found just 2 papers in the literature; in the spirit of new materials the cover slide showed several single crystals a few mm in dimension. The structure is the 122 structure (made famous by the FeAs superconductors) and the physics is somewhat related to that presented earlier in the week by Christian Haule.

The Mn ion is in the 2+ state and the 3d orbitals are half filled so Hund's rule gives a large spin 5/2 state. The interesting physics is in the MnSb bilayer which can be viewed as a hexagonal bilayer wherein the Mn ion coordinates with 3 Mn ions in the adjacent layer. Dr. Blumberg explained that the reason to consider this material as strongly correlated is the difference between the bare bandwidth and that measured from Raman is about 2 orders of magnitude.

The behavior of CMS is as follows: at 300K the material is a paramagnetic metal, at 200K CMS becomes weakly ferromagnetic and the resistivity increases following a standard activated behavior and then at ~100K orders AFM. Finally at low temperature the resistivity has increased by about 6 orders of magnitude. The main experimental exhibit is Raman spectroscopy and the explanation of this by hopping in the AFM state, this was used to explain the difference between the optical gap (~1eV) and the transport gap (40meV).

Hybridization between the Mn-Sb produces a finite (~10%) occupancy of 3d6 states on the Mn site, so that adjacent Mn sites are like so:

This gives rise to a flat band with bandwidth 10meV, but  Dr. Blumberg stuck to a localized, hopping picture in his explanation.

The key to resolving the discrepancy between the optical gap and the transport gap was the binding of pairs of polarons by the Heisenberg interaction. This gives rise to the possibility of certain photon assisted or activated hopping mechanisms which change the component Sz=5/2 -> 2 and reduce the transport gap below the optical gap.

This also explained why DMFT calculations did not capture the full renormalization of the bandwidth.

Questions:

1.

Andrey Chubukov: Where in the Raman spectrum is the 2 magnon peak.

Answer: We think all the features of the Raman spectrum can be explained, but not due to a 2 magnon peak

2.

Unidentified interrogator: How large is J in the Heisenberg interaction?

Answer: It's about 7meV

3.

Piers Coleman: Has the Fe version of this material been made?

Answer: For the pnictides there is a similar [unspecified - ed]  material, but it is insulating, The Fe compounds are expected to be less strongly interacting

4.

Hide Takagi: Please say more about the FM phase?

Answer: In the FM phase nearest neighbor interactions are still AFM but there is no phase rigidity. [Note this should be consistent with the resistivity which showed no significant change between at the AFM/FM phase transition.]

5.

Natalia Perkins (chair)

Why is the renormalization so large?

Answer: DMFT finds some renormalization from the bare LDA, the remaining renormalization comes from strong correlations.

Aditi Mitra (New York University, NY)

Quantum quenches in one-dimension: A renormalization group approach

Blogged by Piers coleman

Aditi discusses the challenges of a "Quantum Quench". One of the most exciting areas for Quantum Quenches (QQ) is in cold atoms systems. These are highly tunable systems - one can realize model Hamiltonians and tune the interactions between the atoms.  Another method is the use of ultra-fast optical pump probe methods.  This allows one to probe time evolutions on femto-pico time scales, when the physics should be governed by quantum unitary time evolution.  One applicaion is work by Cavalieri et al. 

AM gives an outline:

Quenches in free theories - result - non equlibrium steady state.

What happens then if one adds a periodic potential.  Will study case of "irrelevant operators"  in eqn. SHow that they become relevant out of eqn.

Then consider interactions that are relevant in eqn.  This leads to a new kind of dynamical phase transition.    She considers a Luttinger liquid (spinless), and shows that in  a quench that suddenly changes the Luttinger constant K0-> K,  the power-laws for the density density and phase-phase correlation function acuquire a new exponent. Correlations always decay more rapidly than in equilibrium but with a new powerlaw.  Interestingly, the non-equilibrium state is not a Luttinger liquid because the new powerlaws are not the inverse of one-another. 

AM now explains the reasoning behind these results.  One looks at the bosonization the initial and final Hamiltonian's are non-interacting bosons.  The initial distribution is conserved, and the results can be understood in terms of a "Generalized Gibb's ensemble" rhoGGE.  

Now what happens with some non-linearities in the system.  Look at the effect of a periodic potential.  The final partition function is given by

Z = Lim Tr[U(t)rhogge U\dg(t)]

When the periodic potential is there with interactions, dissipation arise. Interestingly enough,  now the density density decays exponentially fast.  This is because of the generated noise.  More importantly,   The conductivity acuires a finite value (from an infinite one). 

Now AM considers a different quench protocole in which K is shifted and the lattice potential is simultaneously turned on.   In this case, the slow and fast modes separate out. Now the correlation function depends on both the relative time and the "center of mass"  time. At short times, power-aw in space with exponent K0, but at long times, plaw in space and time with exponent Kneq.  Teh crossover between these two times is governed by ...., which means that the scaling dimensions of the lattice depend on time. 


Aditi introduces the scaling equations, which he time-dependent scaling dimensions. Providing one is only interested in times tm < 1/eta.  The RG reduces to just three equations. One defines a g-eff = g Sqrt[IK(Tm)] which leads us to a Kostlitz phas transition. Four cases

a. periodic pot irrelevant at all times
b. perioidic potential relevant at all times.
c. PP relevant at short, irrelevant at long times
d. PP irrelevant at short times, relevant at long. 

Integrate the RG up to the point where g Cos(phi) = 1- gphi^2.  There is an exactly solvable point that can be used to check the results.Case b such that geff = epsilon (Tm*) There is a non-analytic behvior in the RG, corresponding to a dynamical phase transition. Even to leading order in the potential, multi-particle scattering processed. 

Now its the conclusions. 

Quantum quenches in Free Theories can lead ot interesting non-equilibrium behavior.

In non-linearities, an analytic approach to study dynamics is presented that is valid in teh thermodynamic and long time limit where numerical studies are hard to do. 

Even when the periodic potential is irrelevan, its effect is no-trivial as it generates dissipation and noise.

When the PP is relevant a new kind of non-equilbrium dynamical phase transition takes place - a kind of non-equiibrium Kosterlitz Thouless transition.


Q: what happens when you include a cubic term? 
A: will give new results, but we have not done this yet. 

Q: Is there a quantum version of the Komogorov theorem. 
A: Now and you have to be very careful about this. 

 

Andrey Chubukov: Collective instabilities of doped graphene

Blogged by Rafael Fernandes

 Contrasting the talk given by Oscar Vafek, who looked at many-body instabilities in double-layer graphene, Andrey will talk about instabilities in (doped) single-layer graphene.  

 Glossary: SDW = spin-density wave; SC = superconductivity; CDW = charge-density wave; FS = Fermi surface; VHS = van Hove singularity; RG = renormalization group.

 Andrey explains that when the chemical potential of graphene is changed (via electron doping, for instance), the Fermi surface changes from two Dirac points to a hexagonal FS with three saddle points, corresponding to VHS. He mentions that experiments in doped graphene find a hexagonal FS, which is somewhat similar to the one expected theoretically. However, there is no consensus that this is really the VHS of the band structure.

 Andrey proposes to study the "ideal" situation of 3/8 doping. Besides the VHS, there are three nesting vectors connecting different sides of the hexagonal FS. He mentions that such a FS is stable even when one includes next-nearest neighbor hopping. Due to the presence of VHS, the particle-particle bubble acquires an extra log, and the SC instability becomes log^2. Furthermore, due to the presence of perfect nesting, the particle-hole bubble also acquires an extra log, and density wave instabilities also becomes log^2. Other exotic instabilities may also appear, but they do not have log^2. Thus, there are several many-body instabilities, and one needs to investigate in which channels there are small attractive interactions that can take advantage of the these log instabilities. Ultimately, Andrey wants to find which of the several instabilities is the leading one.

 To address this problem, he will use parquet RG, which treats particle-particle and particle-hole channels on equal footing. In the RPA level, the pairing interaction is repulsive, but SDW and CDW channels are attractive. However, these are the bare interactions, which become renormalized at low energies. Andrey now writes all the possible interactions between the low-energy fermions near the VHS in each of the three FS patches. There are four of them, including density-density interactions, pair-hopping, exchange, etc. Doing the one-loop parquet RG, these interactions are renormalized and change as higher energy modes are integrated out. The question Andrey wants to answer is which of these four coupling constants diverges, and which order it triggers. Formally, one has a set of coupled first-order differential equations. Andrey considers both the cases of perfect nesting and non-perfect nesting - the latter via an effective parameter.

 Q: is umklapp considered? A: sure, pair-hopping is an umklapp process.

 Andrey shows the solution of the flow equations - all couplings diverge at a certain energy scale, but one of them diverges first. By writing down the SC, SDW, and CDW vertices, and plugging in the renormalized couplings, he can identify which one diverges first. The two leading instabilities are the SDW (whose bare coupling was positive - attractive) and singlet SC (whose bare coupling was negative - repulsive). Eventually (i.e. at lowest energies), SC wins and becomes the leading instability. Several technical questions pop up, from the validity of the RG procedure for log^2 instability to the fate of the flow equations away from perfect nesting.

 Now the symmetry of the SC state is discussed. There are three gaps corresponding to the three VH points, and three possible eigenvectors/eigenvalues for the linearized gap equations. Two of these eigenvalues are actually degenerate - the other one, whose eigenvector corresponds to the s-wave solution, remains always negative, i.e. it is not realized. The two degenerate solutions have d-wave symmetry: d_xy and d_{x^2-y^2}. By performing a Ginzburg-Landau expansion, Andrey finds that the solution with lowest energy is actually a combination of these two symmetries: it is a (d+id) state, which breaks time-reveral symmetry. Interestingly, functional RG gives the same result.

 Conclusion: graphene doped to the saddle-point of the band structure displays as the leading instability a time-reversal (d+id) SC state!

Maxim Dzero: Topological Kondo Insulators

Your blogger today: Andy Schofield

OK well due to a blogging malfunction - this blog is starting half-way through the talk - no it seems to be the end of the talk!

Max has defined two types of Topological Insulators: weak or strong. A large N analysis has been done.

Ce-based Kondo Insulators expected to be weak and unstable to disorder.
Mixed valence systems are most likely to be the ones where strong TI insulators would be observed. Hybridization with the conduction electrons can create an infinite spin-orbit coupling.
These are adiabatilcally connected to topological band insulators: small bandwidth and infinite spin-orbit.
Question: Could a Hopf term be useful? Possibly.
Question: Why are all topological insulators cubic and does this impact your discussion? Not sure and the questioner does not know either.
Question: Your analysis looks like 2D - aren't the supposed to be 3D creating surface states? Sure - layers will create it.
Question: Why called Dirac point? Answer: the dispersion looks like a Dirac cone.
Question: Why do we need the notion of entanglement entropy? It provides a way of distinguishing between charge density wavesand topological insulators.
Question: Can all of this physics be deduced from the Green function? No you might need a 4 particle correlation.
Question: Why do you get band narrowing from spin orbit? It is nothing to do with spin orbit. Instead it is simply the usual Kondo lattice phenomenon.
Question: Where is this in the periodic table of the topological insulators? Yes - it is A1.

Serguei Borisenko: Fermiology and Order Parameter of Fe Based Superconductors

SVBorisenko(Institut fuer Festkorper Physik, Dresden, Germany)
Fermiology and Order  Parameter of Fe based superconductors (FeSC)

–      Blogged by Saurabh Maiti

Blogger’s notation-
SV Borisenko (SVB)

Superconductor (SC)

Anti Ferro Magnetism (AFM)

Spin Density Wave (SDW)

SVB starts by advertising 1-cubed ARPES that can reach to temperatures below 1K. He explains how low energy excitations can be angle resolved by rotating the sample. ARPES can be used to probe-

(*)Fermiology— get information abt:Fermi Surface (FS), band structure, reconstruction due to (e.g magnetic) ordering

(*)Self Energy- Get information abt: V_F renormalization, scattering, coupling const. (these last two are related to imaginary and real parts of the self energy respectively)

(*)Order Parameter (mostly talks abt extracting SC order parameter)

SVB mentions this was very useful for the cuprates in all the three above mentioned aspects [although Self energy study was a little involved because the bosonic mode was likely to be of electronic origin]. For the cuprate case it was clearly established that there was no 3D and the gap was d-wave in character with clear nodes – max gaps of 20-30mev.

SVB mentions then talks abt how comparing ARPES band structure  and LDA band structure can be used to measure correlations, velocity renormalizations…

Having mentioned the success in Cuprates, SVB now moves on to FeSC-specifically the pnictides. He reminds us that the photoemission data is a product of

<f|p.A|i> A(k,e)f(e) X R(k,E)---the last term is resolution

Explains step by step how the matrix elements, polarization, resolution convolutions are taken care of and finally we get A(k,e)*f(e) and then final division by the Fermi-function gives the electronic spectral function which is used to extract info abt self energy and gap structure.

SVB then talks about LiFeAs-mentions presence of one large hole pocket and two crossed elliptical electron pockets at (\pi,\pi) in the two iron unit cell Brilliouin zone. But what happens very close to \Gamma point its more involved [different results for different polarizations---resolved by scanning across kz---he concludes that in a particular region of kz there is hole pocket… kind of like cigar shaped. Points out the 3D nature of this material.]

SVB now talks abt Co-NaFeAs shows ARPES results- combines results from different polarizations and concludes presence of two crossed elliptical electron pockets and 3D small hole pocket at \Gamma point.

SVB now moves to K-BaFeAs

Three hole pockets at \Gamma point—for optimally doped material

But !! Result!!  At corner there are 4 hole barrels [blogger’s note- star shaped] with an electron band crossing in the centre.

KFeAs          

Same as above but no central electron band crossing; So three hole pockets  at \Gamma and 4 hole barrels at the corner —

Co-BaFeAs

Two crossed elliptical electron pockets

One clear hole pocket, but two other bands possibly cross the FS. Its complicated due to hybridization of xz /yz.

FeSe-

Very tiny two elliptical electron pocket

And very tiny hole pocket at \Gamma point of xz/yz character

Rb-FeSe

Rb expels iron and causes vacancy ordering but will not discuss this.

Want to discuss the metallic behavior of  RbFe2Se2

Tiny hole pocket and two large elliptical electron pockets

In this case the disordered vacancies give metallic regions.

Two electron pockets at corner and 3D ELECRON pocket at gamma point (does not cross for all Kz values)

MAIN MESSAGE is that the standard picture of 2 circular hole pockets and two circular electron pockets is never experimentally realized.

Also points out that conventional mapping of FS topology to phase diagram is not realized experimentally…[insert picture].

SVB now discusses probing order parameter.

Start with FeSe (T_c=8K)—remind yourself that it has tiny electron pockets and tiny hole pocket. Then moves on to K-BaFeAs

Message- the gaps are strongly orbital dependent and kz dependent.

Points out that---

-xy band is irrelevant (gaps are small and some times give large FS, sometimes small, etc)

-xz/yz are the important bands

-Wherever the xy content is present the gap has a minima---

-Absence of xy character—large gap

SVB returns to his favorite material  ‘LiFe As’ to discuss its order parameter—The important results is the anisotropy of the SC gap which was claimed to be isotropic before. [blogger’s note: The oscillations are conts+cos4(\theta) type as expected from the A1g symmetry]

Electron pockets—also anisotropic.

The tiny hole pockets; cannot probe for anisotropy. [but gap is large]

[blogger’s note—the pocket is of xz/yz character; the outer FS is of xy character and the gap structure anisotropic and weaker]

SVB believes that it is likely to be s++ gap. He tried the fitting with usual form factors for the s+- wave gap structure like cosKx + cosKy and cosKx*cosKy. The only consistency he finds is with the gap structure predicted by Kontani et al. which describes the in-phase oscillations of the electron pockets. And since this required phonon mechanism in the theory, it might well be that electron-phonon mechanism is likely in this material.

Nevertheless, SVB points out that it can also be explained by S+- picture (S. Maiti et al. PRB 85, 014511 (2012)).

SVB thus invites the theorists to investigate this material more thoroughly because the self energy is known, band structure is known orbital characters are known, gaps are known; and this should be enough to find the right theory for this material.

SVB stresses on the fact that \Gamma point has cigar like features of the hole/electron pocket and suggests it  be taken into account instead of simply considering cylindrical FS. Simply put 3D is very likely important for SC. Life becomes hard but needs to be dealt with.---

Thanks collaborators and restates conclusions—

Q. Did you observe gaps induced by SDW gap in your?

A. Yes. It is clearly seen. But involves a lot of work.

Q. Are there data below Tc which show change electronic spectrum above and below Tc

A. Yes. No problem. Can be provided.

Q. Can your Spectroscopy give insight into the local  quantum chemistry of these materials?

A. Ok. Periodic potential gives good qualitative picture.

Local picture needs special attention and seems to be theorist dependent that is why I am not using that picture. Band structure picture seems to have some universal results that most people are getting. If I get a more or less universal local picture I don’t mind using it.

Q. 11 sample  FS looks like 122 (FeAs based); why? Even though the latter is heavily electron doped.

A. They are not really same. FeSe has a HOLE like  also the pockets are very Tiny. Doping with electrons makes electron pockets bigger.

Q. Is the phase diagram applicable to all pnictides.? What abt LiFeAs? No AFM… where does it fall?

A. The phase diagram is really for 122. 111 is different.

Q. Laser v/s your method; comparison?

A. Prof. Shin has an excellent technique. We have the same resolution as there’s.

Disadvantage of Laser is cannot scan kz and matrix elements can play crucial role in those measurements.

Q. In Li-111 what are the bands/orbitals responsible for SC?

A. xz and yz character of the inner pocket, I think is most relevant.

Q. Is there any criticality associated with change in FS topology?

A. It is interesting question—the main problem is that we don’t have data for continuous doping to probe that feature.