Enrico Rossi Condensed Matter Theory GroupHome Group Publications CM seminars Briefcase |
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**Biao Lian**

We propose a quantum model of fermions simulating the electrical breakdown process of dielectrics. The model consists of M sites with N fermion modes per site, and has a conserved charge Q. It has an on-site chemical potential μ with disorder W, and an interaction of strength J restricting each fermion to excite two more fermions when moving forward by one site. We show the N=3 model with disorder W=0 show a Hilbert space fragmentation and is exactly solvable except for very few Krylov subspaces. The analytical solution shows that the N=3 model exhibits many-body localization (MBL) as M→∞, which is stable against W>0 as our exact diagonalization (ED) shows. At N>3, our ED suggests a MBL to quantum chaos crossover at small W as M/N decreases across 1, and persistent MBL at large W. At W=0, an exactly solvable many-body scar flat band exists in many charge Q sectors, which has a nonzero measure in the thermodynamic limit. We further calculate the time evolution of a fermion added to the particle vacuum, which shows a breakdown (dielectric) phase when μ/J<1/2 (μ/J>1/2) if W≪J, and no breakdown if W≫J.

Reference:

https://arxiv.org/abs/2208.10509

**Zhenghan Wang**

Brief introduction to approaches to classify topological quantum field theories.

**Victor Galitski**

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 so-called out-of-time-ordered four-point 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 single-particle models as well as results in interacting many-body systems, such as disordered metals [2]. The latter many-body model exhibits an interaction-induced transition from quantum chaotic to non-chaotic dynamics, which may manifest itself in a sharp change of the distribution of energy levels from Wigner-Dyson to Poisson statistics. I will conclude by formulating a many-body analogue of the Bohigas-Giannoni-Schmit conjecture.

References:

[1] "Lyapunov exponent and out-of-time-ordered correlator's growth rate in a chaotic system," E. Rozenbaum, S. Ganeshan, and V. Galitski, Physical Review Letters 118, 086801 (2017)

[2] "Non-linear sigma model approach to many-body quantum chaos," Y. Liao and and V. Galitski, arXiv:1807.09799

**Javad Shabani**

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. Non-Abelian 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 superconductor-semiconductor could lead to creation of non-Abelian 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 current-phase 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.

**Andrey Antipov**

The initial theoretical proposal for the realization of Majorana bounds states in a condensed matter setup requires three simple ingredients: superconductivity, spin-orbit 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.

**Jay Deep Sau**

The combination of spin-orbit coupling and magnetic field produces an interesting bandstructure with a co-existing Dirac point and Fermi points. In the first part of my talk I will briefly review how proximity-induced 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 spin-orbit coupled gases realized in experiments. We use the effective Lagrangian formalism for classifying non-relativistic Nambu-Goldstone 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 Lorentz-like (z~1) to Lifshitz-like (z~2). We find these predictions to be consistent with DMRG simulations.

**Hadar Steinberg**

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 in-plane magnetic fields, well beyond the Pauli limit2. This apparent stability is associated with Ising spin-orbit 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 mili-Kelvin temperatures, the tunneling spectra exhibit a well-resolved separation into a two-gap structure. We show that by applying in-plane magnetic fields to bulk devices (20-50 nm thick), it is possible to distinguish between the kinematics of quasiparticles which belong to different gaps. When probing ultra-thin devices (3-4 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 vortex-bound state spectroscopy.

References:

[1] X. Xi, Z. Wang, W. Zhao, J.-H. Park, K. T. Law, H. Berger, L. ForrÃ³, J. Shan & K. F. Mak. Ising pairing in superconducting NbSe2 atomic layers. Nature Physics 12, 139-143 (2016).

[2] J. M. Lu, O. Zheliuk, I. Leermakers, N. F. Q. Yuan, U. Zeitler, K. T. Law & J. T. Ye. Evidence for two-dimensional Ising superconductivity in gated MoS2. Science 350, 1353-1357 (2015).

[3] T. Dvir, F. Massee, L. Attias, M. Khodas, M. Aprili, C.H.L. Quay, H. Steinberg. Spectroscopy of bulk and few-layer superconducting NbSe2 with van der Waals tunnel junctions. Preprint: arXiv:1711.09615

**Mikhail Katsnelson**

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 two-dimensional systems (which can be probed in experiments with ultracold gases in optical lattices) [2] and spin-polaron 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 single-site 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], charge-density-wave instability in extended Hubbard model [8], and ultracold molecular gases with dipole-dipole interactions in optical lattices [9,10]. These examples show that DB, in particular, provides a prospective way to treat strongly correlated systems with long-range interactions.

References:

[1] A. N. Rubtsov, M. I. Katsnelson, and A. I. Lichtenstein, Phys. Rev. B 77, 033101 (2008).

[2] D. Yudin, D. Hirschmeier, H. Hafermann, O. Eriksson, A. I. Lichtenstein, and M. I. Katsnelson, Phys. Rev. Lett.112, 070403 (2014).

[3] A. Wilhelm, F. Lechermann, H. Hafermann, M. I. Katsnelson, and A. I. Lichtenstein, Phys. Rev. B 91, 155114 (2015).

[4] A. N. Rubtsov, M. I. Katsnelson, and A. I. Lichtenstein, Ann. Phys. (NY) 327, 1320 (2012).

[5] H. Hafermann, E. G. C. P. van Loon, M. I. Katsnelson, A. I. Lichtenstein, and O. Parcollet, Phys. Rev. B 90, 235105 (2014).

[6] E. A. Stepanov, E. G. C. P. van Loon, A. A. Katanin, A. I. Lichtenstein, M. I. Katsnelson, and A. N. Rubtsov, Phys. Rev. B 93, 045107 (2016).

[7] E. G. C. P. van Loon, H. Hafermann, A. I. Lichtenstein, A. N. Rubtsov, and M. I. Katsnelson, Phys. Rev. Lett. 113, 246407 (2014).

[8] E. G. C. P. van Loon, A. I. Lichtenstein, M. I. Katsnelson, O. Parcollet, and H. Hafermann, Phys. Rev. B 90, 235135 (2014).

[9] E. G. C. P. van Loon, M. I. Katsnelson, and M. Lemeshko, Phys. Rev. B 92, 081106(R) (2015).

[10] E. G. C. P. van Loon, M. I. Katsnelson, L. Chomaz, and M. Lemeshko, Phys. Rev. B 93, 195145 (2016).

**Hitesh J. Changlani**

Strongly correlated systems provide a fertile ground for discovering exotic states of matter, for example, those with topologically non-trivial 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 near-ideal realizations in several materials. First, I present a study of the spin-1 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 spin-1/2 XXZ model in a magnetic field, equivalent to a hard-core bosonic problem with density-density 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.

**Alessandro Principi**

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 thin-film plane, but its direction changes periodically, forming an alternating spin-up and spin-down stripe pattern. The latter is stabilized by the competition between the ferromagnetic coupling and dipole-dipole interactions, and disappears when a moderate in-plane magnetic field is applied. It has been suggested that such a behavior may be understood in terms of a self-induced stripe glassiness. In this talk I will show that such a scenario is compatible with the experimental findings. The strong out-of-plane magnetic anisotropy of the film is found to be beneficial for the formation of both the stripe-ordered and glassy phases. At zero magnetic field the system can form a glass only in a narrow interval of fairly large temperatures. An in-plane 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 in-plane magnetic field of the order of 50 mT can lead to the formation of defects in the stripe pattern.

References:

[1] A. Principi, M.I. Katsnelson, Phys. Rev. B 93, 054410

**David Abergel**

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 two-dimensional 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 one-dimensional systems, a concept which appears to be excluded by the Mermin-Wagner theorem. However, we show that the inclusion of an inter-layer single particle hopping process breaks the conditions for the theorem and allows off-diagonal long range order in the condensate channel.

References:

[1] D.S.L. Abergel, E. Rossi, and S. Das Sarma, Phys. Rev. B 86, 155447 (2012)

[2] D.S.L. Abergel, M. Rodriguez-Vega, E. Rossi, and S. Das Sarma, Phys. Rev. B 88, 235402 (2013)

[3] D.S.L. Abergel, Appl. Phys. Lett. 106, 213103 (2015)

**Matej Komelj**

Motivated by experimental activities, recent ab-initio calculations within the framework of the density-functional theory predict the Im-3m 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 exchange-correlation functional, which is a combination of the exact Hartree-Fock term and the generalized-gradient approximation (GGA), demonstrate a non-negligible influence on the equation of state and on the phonon dispersion, obtained by applying the frozen-phonon approximation. This method does not make it possible to determine the electron-phonon coupling coefficient, which is the essential quantity in the Allen-Dynes equation. Therefore we calculate the respective GGA coupling coefficients on the basis of the linear-response theory and estimate the hybrid values by analyzing the details in the corresponding electronic band structures. The enhancement of the of the calculated electron-phonon coupling coefficient by more than 20%, and consequently of the Tc, proves an importance of the correlation effects in the investigated material.

**Georg Schwiete**

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 metal-insulator transition in two-dimensional 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 Wiedemann-Franz law remains valid even in the presence of quantum corrections caused by the interplay of diffusion modes and the electron-electron interaction. For the disordered electron liquid we additionally analyze inelastic processes induced by the Coulomb interaction at sub-temperature 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 Wiedemann-Franz law.

References:

[1] G. Schwiete and A. M. Finkelstein, Renormalization group analysis of thermal transport in the disordered Fermi liquid, Phys. Rev. B 90, 155441 (2014)

[2] G. Schwiete and A. M. Finkelstein, Thermal transport and the Wiedemann Franz law in the disordered Fermi liquid, Phys. Rev. B 90, 060201(R) (2014)

[3] G. Schwiete and A. M. Finkelstein, Keldysh approach to the renormalization group analysis of the disordered electron liquid, Phys. Rev. B 89, 075437 (2014)

**Lianyi He**

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 long-sought 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 two-particle virial contributions from the scattering continuum to all orders in the fugacity. By further adopting a nonperturbative large-N expansion approach, we determine a finite-temperature phase diagram for the Stoner instability of a quasirepulsive Fermi gas near resonance. Our results agree well with the known quantum Monte-Carlo 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.

**Driss Badiane**

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 three-terminal Josephson junctions. Majorana fermions have been introduced in 1937 by E. Majorana as real solutions of the relativistic Dirac equation. Even if their existence remains hypothetic in high energy physics, recent developments in condensed matter physics suggest their presence as emergent excitations in solid state devices. During the last decade, they have attracted a lot of interest due to their non-Abelian statistics, allowing promising applications in fault-tolerant quantum computing. For instance, Majorana fermions appears at the boundaries of topological superconductors. When two topological superconductors are connected, zero-energy Majorana bound states localized on either side of the junction form an Andreev bound state. As this current carrying state is 4pi-periodic in the superconducting phase difference, it was speculated that, at finite dc bias voltage, the junction exhibits a fractional Josephson effect. We will show that any finite phase velocity induce a dynamic coupling between the bound state and the continuum of states above the superconducting gap amplitude. This intrinsic coupling provides unavoidable mechanism that alter the fractional Josephson effect. We will discuss, in terms of the circuit parameters, signatures of the fractional Josephson effect that could be relevant for current experimental investigations: the even-odd effect in Shapiro steps and the emergence of a peak at fractional Josephson frequency in the current noise spectrum. Furthermore, other manifestations of the Majorana bound states forming at the edges will be discussed. In addition, substantial part of the talk will be devoted to quantum entanglement in three terminal Josephson junctions. Quantum entanglement is a crucial ingredient in modern quantum communication proposals. A quantitative test of entanglement is provided by the Bell inequalities which were successfully measured in quantum optics. However, in condensed matter physics, the question is still open. In solid state devices, the current is the natural observable and Bell inequalities are expressed via current-current correlation functions. Moreover, superconductivity offers a natural playground for the search of entangled particles: Cooper pairs are singlet states which are naturally entangled in spin space. We will show that, current-current cross correlations can be positive and amplified in coherent three terminal Josephson junctions. This finding opens the possibility for further investigations on quantum entanglement in those systems..

**Alessandro Principi**

The Wiedemann-Franz law, connecting the electronic thermal conductivity to the electrical conductivity of a disordered metal, is generally found to be well satisfied even when electron-electron (e-e) interactions are strong. In ultra-clean conductors, however, large deviations from the standard form of the law are expected, due to the fact that e-e interactions affect the two conductivities in radically different ways. Thus, the standard Wiedemann-Franz ratio between the thermal and the electric conductivity is reduced by a factor

**Marco Polini**

Dirac plasmons are self-sustained 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 two-dimensional parabolic-band 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 electron-electron, electron-impurity, and electron-phonon collisions.

**Jens Bardarson**

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 non-trivial 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 spin-rotation 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 inter-valley scattering.