








Classical chaotic systems exhibit exponential divergence of initially infinitesimally close trajectories, which is characterized by the Lyapunov exponent. This sensitivity to initial conditions is popularly known as the "butterfly effect." Of great recent interest has been to understand how/if the butterfly effect and Lyapunov exponents generalize to quantum mechanics, where the notion of a trajectory does not exist. In this talk, I will introduce the measure of quantum chaoticity – a socalled outoftimeordered fourpoint correlator (whose semiclassical limit reproduces classical Lyapunov growth), and use it to describe quantum chaotic dynamics and its eventual disappearance in the standard models of classical and quantum chaos – Bunimovich stadium billiard and standard map or kicked rotor [1]. I will describe our recent results on the quantum Lyapunov exponent in these singleparticle models as well as results in interacting manybody systems, such as disordered metals [2]. The latter manybody model exhibits an interactioninduced transition from quantum chaotic to nonchaotic dynamics, which may manifest itself in a sharp change of the distribution of energy levels from WignerDyson to Poisson statistics. I will conclude by formulating a manybody analogue of the BohigasGiannoniSchmit conjecture.



















Anyons, quasiparticles with exotic statistics, are one of the most intriguing possibilities that exist in condensed matter systems. Their novelty from the fundamental physics point of view notwithstanding, much recent attention has been drawn to their potential applications for quantum information processing. NonAbelian anyons are theoretically expected to be found only in a few special fractional quantum Hall states with very stringent material and experimental requirements. In an exciting development, it was realized that engineering an effective Hamiltonian at the interface of a superconductorsemiconductor could lead to creation of nonAbelian quasiparticles. We briefly discuss our approach in realization of these quasiparticles first on induced superconductivity in quantum Hall regime. Then we present data on Shapiro steps that appear in the IV characteristic of a junction under microwave irradiation. We observe a missing first Shapiro step below 6 GHz that may point to a 4π component in the currentphase relation of those junctions. That missing step can be recovered at higher frequencies. Such features have been observed in HgTe (in topological regime) based junctions but were unexpected in our InAs based devices.


















The initial theoretical proposal for the realization of Majorana bounds states in a condensed matter setup requires three simple ingredients: superconductivity, spinorbit coupling and magnetic field. While this proposal is simple, the experiments are not, as they involve material science, fabrication steps, cooling, electrostatic control and actual measurements. The results of experiments are not unambiguous and allow for multiple interpretation by simple theoretical models. In order to bridge the gap one has to include peculiarities of experimental setup and engineer the modelling of systems supporting Majorana zero modes. In this talk I will show how the next generation of numerical models captures the effects of electric fields, disorder, orbital effects and how it can feedback and guide the ongoin experimental effort in the field.


















The combination of spinorbit coupling and magnetic field produces an interesting bandstructure with a coexisting Dirac point and Fermi points. In the first part of my talk I will briefly review how proximityinduced superconductivity is expected to lead to topological superconductivity. I will discuss then discuss how Coulomb blockade physics in these systems can lead to the detection of such topological superconductivity.
In the second part we discuss strongly interacting Bosons subject to the same Hamiltonian, which would be the Tonks gas version of the spinorbit coupled gases realized in experiments. We use the effective Lagrangian formalism for classifying nonrelativistic NambuGoldstone modes due to derive the existance of an Ising transition between two gapless phases that can be thought of as a superfluid minimally coupled to an Ising gauge field. This coupling between the Ising model and the superfluid turns out to modify the dynamical critical exponent from Lorentzlike (z~1) to Lifshitzlike (z~2). We find these predictions to be consistent with DMRG simulations.
























Superconductors of the transition metal dichalcogenide (TMD) family have seen a revival of interest subsequent to developments in device fabrication by mechanical exfoliation. Recent studies1 show that at the ultrathin limit, NbSe2 and similar TMDs can sustain superconductivity at very high inplane magnetic fields, well beyond the Pauli limit2. This apparent stability is associated with Ising spinorbit coupling, which keeps spins oriented out of the sample plane, thereby providing strong protection against depairing. In my talk, I will report our recent spectroscopy measurements of NbSe2 using vdW tunnel devices3. Our devices are fabricated by placing insulating barriers on top of exfoliated NbSe2 using the mechanical transfer technique. The resulting tunnel junctions exhibit extremely stable currents, and are characterized by a hard gap. At miliKelvin temperatures, the tunneling spectra exhibit a wellresolved separation into a twogap structure. We show that by applying inplane magnetic fields to bulk devices (2050 nm thick), it is possible to distinguish between the kinematics of quasiparticles which belong to different gaps. When probing ultrathin devices (34 layers), we find the larger energy gap to be almost fully protected to depairing, an effect consistent with transport studies. Finally, I will discuss the implications of our technique to vortexbound state spectroscopy.


















Collective excitations and nonlocal correlations play an important role in strongly correlated electron systems, especially in low dimensions. Dynamical Mean Field Theory (DMFT), nowadays the standard approximation for correlated electronic systems, cannot capture these strongly nonlocal effects. The Dual Fermion (DF) theory [1] reformulates the perturbation theory for the Hubbard model starting with the DMFT as zeroths order approximation which allows us to consider nonlocal correlation effects in a systematic way for both weakly and strongly correlated limits. As examples of these nonlocal correlations I will consider formation of flat bands near Van Hove singularities in twodimensional systems (which can be probed in experiments with ultracold gases in optical lattices) [2] and spinpolaron effects in NaxCoO2 [3]. The Dual Boson (DB) theory [4] was designed to treat the nonlocal interactions (that is, interactions beyond the Hubbard model) correctly, starting from a singlesite reference problem. I will discuss both formal aspects of this method such as charge conservation in ladder DB approximation [5,6] and applications to various physical problems, including plasmons in strongly correlated systems [7], chargedensitywave instability in extended Hubbard model [8], and ultracold molecular gases with dipoledipole interactions in optical lattices [9,10]. These examples show that DB, in particular, provides a prospective way to treat strongly correlated systems with longrange interactions.


















Strongly correlated systems provide a fertile ground for discovering exotic states of matter, for example, those with topologically nontrivial properties. Among these are frustrated magnets, where the lattice geometry prevents spins from ordering even at very low temperatures, thereby leading to "spin liquid" phases. Since their excitations involve quasiparticles with "fractional" anyonic statistics which are potentially useful for topological quantum computation, spin liquids have generated a lot of research activity on both theoretical and experimental fronts. The findings have also highlighted the need for accurate advanced numerical techniques to understand the quantum many body problem.
I will present two of our theoretical works in this area, both focusing on the kagome geometry which has nearideal realizations in several materials. First, I present a study of the spin1 Heisenberg antiferromagnet, where contrary to previous theoretical proposals, our calculations indicate that the ground state is a valence bond (simplex) solid with a spin gap that is consistent with experimental findings. In the second part, I consider the spin1/2 XXZ model in a magnetic field, equivalent to a hardcore bosonic problem with densitydensity interactions at finite filling fraction. Motivated by previous field theoretical studies, I focus my attention to understanding the XY limit for the 2/3 magnetization plateau (i.e. 1/6 filling of bosons). We perform exact computations to search for the predicted "chiral spin liquid" and based on energetics and the determination of minimally entangled states and the associated modular matrices, provide evidence for this phase.


















Domain walls in magnetic multilayered systems can exhibit a very complex and fascinating behavior. The magnetization of thin films of hard magnetic materials is in general perpendicular to the thinfilm plane, but its direction changes periodically, forming an alternating spinup and spindown stripe pattern. The latter is stabilized by the competition between the ferromagnetic coupling and dipoledipole interactions, and disappears when a moderate inplane magnetic field is applied. It has been suggested that such a behavior may be understood in terms of a selfinduced stripe glassiness. In this talk I will show that such a scenario is compatible with the experimental findings. The strong outofplane magnetic anisotropy of the film is found to be beneficial for the formation of both the stripeordered and glassy phases. At zero magnetic field the system can form a glass only in a narrow interval of fairly large temperatures. An inplane magnetic field, however, shifts the glass transition towards lower temperatures, therefore enabling it at or below room temperature. In good qualitative agreement with the experimental findings, we show that a moderate inplane magnetic field of the order of 50 mT can lead to the formation of defects in the stripe pattern.


















Dipolar excitons are bosons consisting of a paired state of electrons and holes which are spatially separated from each other and interact only via the Coulomb interaction. It has long been predicted that under appropriate conditions they can form a macroscopic condensate, and this has been observed for twodimensional electron gases in a strong magnetic field. However, this phenomenon has never been observed at zero field. In this talk, we begin with an introduction to the field of dipolar excitons and then describe how charged impurity disorder impacts the formation of such a condensate in double graphene layer systems. We then examine exciton condensation in onedimensional systems, a concept which appears to be excluded by the MerminWagner theorem. However, we show that the inclusion of an interlayer single particle hopping process breaks the conditions for the theorem and allows offdiagonal long range order in the condensate channel.


















Motivated by experimental activities, recent abinitio calculations within the framework of the densityfunctional theory predict the Im3m structure as the stable superconducting phase of the H3S stoichiometry at the pressure of 200 GPa with the high Tc of about 200 K. The results of our calculation with the hybrid exchangecorrelation functional, which is a combination of the exact HartreeFock term and the generalizedgradient approximation (GGA), demonstrate a nonnegligible influence on the equation of state and on the phonon dispersion, obtained by applying the frozenphonon approximation. This method does not make it possible to determine the electronphonon coupling coefficient, which is the essential quantity in the AllenDynes equation. Therefore we calculate the respective GGA coupling coefficients on the basis of the linearresponse theory and estimate the hybrid values by analyzing the details in the corresponding electronic band structures. The enhancement of the of the calculated electronphonon coupling coefficient by more than 20%, and consequently of the Tc, proves an importance of the correlation effects in the investigated material. 

















The main subject of this talk is thermal transport in the disordered
Fermi and electron liquids at low temperatures. I plan to
start with a brief introduction to the physics of quantum
corrections to conductivity in disordered systems and the
phenomenology of the metalinsulator transition in
twodimensional electron systems. Then, I will contrast
approaches to the calculation of electric and thermal
transport. A principle difficulty for the description of
thermal transport is that temperature is an internal
parameter, and a temperature gradient does not correspond to
an external "mechanical" force like a the one originating from
an electric potential. We use Luttinger's gravitational
potentials as sources for finding the heat density and its
correlation function. For a comprehensive study, we extend the
RG analysis developed for electric transport by including the
gravitational potentials into the RG scheme. The analysis
reveals that for the disordered Fermi liquid the
WiedemannFranz law remains valid even in the presence of
quantum corrections caused by the interplay of diffusion modes
and the electronelectron interaction. For the disordered
electron liquid we additionally analyze inelastic processes
induced by the Coulomb interaction at subtemperature
energies. While the general form of the correlation function
has to be compatible with energy conservation, these inelastic
processes are at the origin of logarithmic corrections
violating the WiedemannFranz law.


















Recent advances in rapidly quenched ultracold atomic Fermi gases near a Feshbach resonance arise a number of interesting problems, in the context of observing the longsought Stoner ferromagnetic phase transition. The possibility of experimentally obtaining a "quasirepulsive" regime in the upper branch of the energy spectrum due to the rapid quench is currently debated and theoretically, the Stoner transition has mainly been investigated by using perturbation theory or at high polarization, due to the limited theoretical approaches in the strongly repulsive regime. In this work, we present an appropriate prescription for the quasirepulsive branch and prove it by resumming the twoparticle virial contributions from the scattering continuum to all orders in the fugacity. By further adopting a nonperturbative largeN expansion approach, we determine a finitetemperature phase diagram for the Stoner instability of a quasirepulsive Fermi gas near resonance. Our results agree well with the known quantum MonteCarlo simulations at zero temperature and recover the known virial expansion prediction at high temperature for arbitrary interaction strengths. At resonance, we find that the unitary Fermi gas undergoes the Stoner transition at about one and a half Fermi temperature, around which the pair formation rate becomes vanishingly small. This suggests a feasible way to observe Stoner ferromagnetism. We also apply the same prescription to study the strongly interacting Bose gases near unitary. 

















This seminar consists of two parts: i) on signatures of Majorana fermions in topological Josephson junctions, and ii) on the possibility to generate entangled quasiparticles in threeterminal Josephson junctions.


















The WiedemannFranz law, connecting the electronic thermal conductivity to the electrical conductivity of a disordered metal, is generally found to be well satisfied even when electronelectron (ee) interactions are strong. In ultraclean conductors, however, large deviations from the standard form of the law are expected, due to the fact that ee interactions affect the two conductivities in radically different ways. Thus, the standard WiedemannFranz ratio between the thermal and the electric conductivity is reduced by a factor $1+\tau/\tau_{\rm th}^{\rm ee}$, where $1/\tau$ is the momentum relaxation rate, and $1/\tau_{\rm th}^{\rm ee}$ is the relaxation time of the thermal current due to ee collisions. Here we study the density and temperature dependence of $1/\tau_{\rm th}^{\rm ee}$ in the important case of doped, clean single layers of graphene, which exhibit recordhigh thermal conductivities. We show that at low temperature $1/\tau_{\rm th}^{\rm ee}$ is $8/5$ of the quasiparticle decay rate. We also show that the manybody renormalization of the thermal Drude weight coincides with that of the Fermi velocity. 

















Dirac plasmons are selfsustained density oscillations that occur in a doped graphene sheet. These collective modes have recently attracted enormous experimental interest for their potential use in plasmonic circuits. In this talk I will discuss the two most important figures of merit of "graphene plasmonics", namely the ratio between the Dirac plasmon wavelength and the illumination wavelength, and the Dirac plasmon damping rate. More precisely, I will first discuss about the fundamental properties of the Dirac plasmon dispersion, highlighting the main differences with respect to plasmons in ordinary twodimensional parabolicband electron liquids. I will then emphasize the subtle difference between plasmon lifetime and Drude transport scattering time. Finally, I will present a theoretical framework that allows to calculate in a fully microscopic fashion Dirac plasmon damping rates due to electronelectron, electronimpurity, and electronphonon collisions. 

















In this talk I will give an introduction to the physics of disorder in the surface states of topological insulators  bulk insulators with topologically protected surface states. In particular, I will explore the intriguing connection between the possibility of realizing nontrivial topological states in certain symmetry classes and the absence of Anderson localization in the corresponding surface theory. After some general overview, I will focus on the symplectic class (AII) which is obtained in materials with time reversal symmetry, but broken spinrotation symmetry. In the simplest case, such as in Bi_2Se_3, a single Dirac Fermion is realized at the surface. Another relevant system is graphene in the absence of intervalley scattering. 





