arXiv subjects

Erez Berg

Publications and source records attributed to Erez Berg.

At least 109 records · Page 6Linked to original sources

arXiv2020

Electronic Floquet Liquid Crystals

"Floquet engineering" - designing band structures "on-demand" through the application of coherent time-periodic drives - has recently emerged as a powerful tool for creating new topological and anomalous phases of matter. In this manuscript, we show that the same principle can be applied to create non-equilibrium correlated states with spontaneously broken symmetry in a lightly doped semiconductor. The periodic drive provides means for obtaining large electronic densities of states necessary for the broken symmetry phase. The phase transition occurs in the steady-state of the system achieved due to interplay between the coherent external drive, electron-electron interactions, and dissipative processes arising from the coupling to phonons and the electromagnetic environment. We obtain the phase diagram of the system using numerical calculations that match predictions obtained from a phenomenological treatment and discuss the conditions on the system and the external drive under which spontaneous symmetry breaking occurs. Our results imply that Floquet engineering of the density of states provides a new route for generating and controlling correlated states of electrons with external fields.

cond-mat.str-el↗

arXiv2020

The unreasonable effectiveness of Eliashberg theory for pairing of non-Fermi liquids

The paradigmatic Migdal-Eliashberg theory of the electron-phonon problem is central to the understanding of superconductivity in conventional metals. This powerful framework is justified by the smallness of the Debye frequency relative to the Fermi energy, and allows an enormous simplification of the full many-body problem. However, superconductivity is found also in many families of strongly-correlated materials, in which there is no {\it a priori} justification for the applicability of Eliashberg theory. In these systems, superconductivity emerges out of an anomalous metallic state, calling for a new theoretical framework to describe pairing out of a non-Fermi liquid. In this article, we review two model systems in which such behavior is found: a Fermi sea coupled to gapless bosonic fluctuations, and a system of fermions with local, strongly frustrated interactions. In both models, there is a well-defined limit in which the Eliashberg equations are asymptotically exact even in the strongly coupled regime. These models thus provide tractable examples of how superconductivity can emerge in the absence of coherent electronic quasiparticles; they also demonstrate the surprisingly wide applicability of the Eliashberg formalism, well beyond the conventional regime for which it was originally designed.

cond-mat.supr-con↗

arXiv2020

Superconductivity, pseudogap, and phase separation in topological flat bands: a quantum Monte Carlo study

We study a two-dimensional model of an isolated narrow topological band at partial filling with local attractive interactions. Numerically exact quantum Monte Carlo calculations show that the ground state is a superconductor with a critical temperature that scales nearly linearly with the interaction strength. We also find a broad pseudogap regime at temperatures above the superconducting phase that exhibits strong pairing fluctuations and a tendency towards electronic phase separation; introducing a small nearest neighbor attraction suppresses superconductivity entirely and results in phase separation. We discuss the possible relevance of superconductivity in this unusual regime to the physics of flat band moiré materials, and as a route to designing higher temperature superconductors.

cond-mat.str-el↗

arXiv2020

Floating topological phases

While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered quantum phases with an emergent 2+1 dimensional gauge symmetry can be asymptotically impervious to interplane couplings. We discuss the stability of such "floating topological phases", as well as their diagnosis by means of a non-local order parameter. Such a phase can produce a divergent ratio $ρ_{\perp}/ρ_{\parallel}$ of the inter-layer to intra-layer resistivity as $T\to 0$, even in an insulator where both $ρ_{\perp}$ and $ρ_\parallel$ individually diverge. Experimental observation of such a divergence would constitute proof of the existence of a topological (e.g. spin liquid) phase.

cond-mat.str-el↗

arXiv2020

Strongly coupled quantum phonon fluid in a solvable model

We study a model of a large number of strongly coupled phonons that can be viewed as a bosonic variant of the Sachdev-Ye-Kitaev model. We determine the phase diagram of the model which consists of a glass phase and a disordered phase, with a first-order phase transition separating them. We compute the specific heat of the disordered phase, with which we diagnose the high-temperature crossover to the classical limit. We further study the real-time dynamics of the disordered phase, where we identify three dynamical regimes as a function of temperature. Low temperatures are associated with a semiclassical regime, where the phonons can be described as long-lived normal modes. High temperatures are associated with the classical limit of the model. For a large region in parameter space, we identify an intermediate-temperatures regime, where the phonon lifetime is of the order of the Planckian time scale $\hbar/k_B T$.

cond-mat.str-el↗

arXiv2020

Exponentially long lifetime of universal quasi-steady states in topological Floquet pumps

We investigate a mechanism to transiently stabilize topological phenomena in long-lived quasi-steady states of isolated quantum many-body systems driven at low frequencies. We obtain an analytical bound for the lifetime of the quasi-steady states which is exponentially large in the inverse driving frequency. Within this lifetime, the quasi-steady state is characterized by maximum entropy subject to the constraint of fixed number of particles in the system's Floquet-Bloch bands. In such a state, all the non-universal properties of these bands are washed out, hence only the topological properties persist.

cond-mat.stat-mech↗

arXiv2020

Theory of the Strange Metal Sr$_3$Ru$_2$O$_7$

The bilayer perovskite Sr$_3$Ru$_2$O$_7$ has been widely studied as a canonical strange metal. It exhibits $T$-linear resistivity and a $T\log(1/T)$ electronic specific heat in a field-tuned quantum critical fan. Criticality is known to occur in `hot' Fermi pockets with a high density of states close to the Fermi energy. We show that while these hot pockets occupy a small fraction of the Brillouin zone, they are responsible for the anomalous transport and thermodynamics of the material. Specifically, a scattering process in which two electrons from the large, `cold' Fermi surfaces scatter into one hot and one cold electron renders the ostensibly non-critical cold fermions a marginal Fermi liquid. From this fact the transport and thermodynamic phase diagram is reproduced in detail. Finally, we show that the same scattering mechanism into hot electrons that are instead localized near a two-dimensional van Hove singularity explains the anomalous transport observed in strained Sr$_2$RuO$_4$.

cond-mat.str-el↗

arXiv2020

Normal state properties of quantum critical metals at finite temperature

We study the effects of finite temperature on normal state properties of a metal near a quantum critical point to an antiferromagnetic or Ising-nematic state. At $T = 0$ bosonic and fermionic self-energies are traditionally computed within Eliashberg theory and obey scaling relations with characteristic power-laws. Quantum Monte Carlo (QMC) simulations have shown strong systematic deviations from these predictions, casting doubt on the validity of the theoretical analysis. We extend Eliashberg theory to finite $T$ and argue that for the $T$ range accessible in the QMC simulations, the scaling forms for both fermionic and bosonic self energies are quite different from those at $T = 0$. We compare finite $T$ results with QMC data and find good agreement for both systems. This, we argue, resolves the key apparent contradiction between the theory and the QMC simulations.

cond-mat.str-el↗

arXiv2020

Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: a Monte Carlo study

We present numerically exact results from sign-problem free quantum Monte Carlo simulations for a spin-fermion model near an $O(3)$ symmetric antiferromagnetic (AFM) quantum critical point. We find a hierarchy of energy scales that emerges near the quantum critical point. At high energy scales, there is a broad regime characterized by Landau-damped order parameter dynamics with dynamical critical exponent $z=2$, while the fermionic excitations remain coherent. The quantum critical magnetic fluctuations are well described by Hertz-Millis theory, except for a $T^{-2}$ divergence of the static AFM susceptibility. This regime persists down to a lower energy scale, where the fermions become overdamped and concomitantly, a transition into a $d-$wave superconducting state occurs. These findings resemble earlier results for a spin-fermion model with easy-plane AFM fluctuations of an $O(2)$ SDW order parameter, despite noticeable differences in the perturbative structure of the two theories. In the $O(3)$ case, perturbative corrections to the spin-fermion vertex are expected to dominate at an additional energy scale, below which the $z=2$ behavior breaks down, leading to a novel $z=1$ fixed point with emergent local nesting at the hot spots [Schlief et al., PRX 7, 021010 (2017)]. Motivated by this prediction, we also consider a variant of the model where the hot spots are nearly locally nested. Within the available temperature range in our study ($T\ge E_F/200$), we find substantial deviations from the $z=2$ Hertz-Millis behavior, but no evidence for the predicted $z=1$ criticality.

cond-mat.str-el↗

arXiv2020

Signatures of Topological Superconductivity and Parafermion Zero Modes in Fractional Quantum Hall Edges

Parafermion zero modes are exotic emergent excitations that can be considered as $\mathbb{Z}_n$ generalizations of Majorana fermions. Present in fractional quantum Hall-superconductor hybrid systems, among others, they can serve as potential building blocks in fault-tolerant topological quantum computing. We propose a system that reveals noise and current signatures indicative of parafermion zero modes. The system is comprised of the edge excitations ("quasi-particles") of a fractional quantum Hall bulk at filling factor $ν= 1/m$ (for odd integer $m$) incident upon the interface of a superconductor, and in the presence of back-scattering. Using perturbative calculations, we derive the current that propagates away from this structure, and its corresponding noise correlation function. Renormalization group analysis reveals a flow from a UV fixed point of perfect normal reflection towards an IR fixed point of perfect Andreev reflection. The power law dependence of the differential conductance near these fixed points is determined by $m$. We find that behavior at these two limits is physically distinguishable; whereas near perfect Andreev reflection, the system deviates from equilibrium via tunneling of Cooper pairs between the two edges, near perfect Normal reflection this is done via tunneling of a single quasi-particle to an emergent parafermion zero mode at the superconductor interface. These results are fortified by an exact solution.

cond-mat.mes-hall↗

arXiv2019

Cascade of Phase Transitions and Dirac Revivals in Magic Angle Graphene

Twisted bilayer graphene near the magic angle exhibits remarkably rich electron correlation physics, displaying insulating, magnetic, and superconducting phases. Here, using measurements of the local electronic compressibility, we reveal that these phases originate from a high-energy state with an unusual sequence of band populations. As carriers are added to the system, rather than filling all the four spin and valley flavors equally, we find that the population occurs through a sequence of sharp phase transitions, which appear as strong asymmetric jumps of the electronic compressibility near integer fillings of the moire lattice. At each transition, a single spin/valley flavor takes all the carriers from its partially filled peers, "resetting" them back to the vicinity of the charge neutrality point. As a result, the Dirac-like character observed near the charge neutrality reappears after each integer filling. Measurement of the in-plane magnetic field dependence of the chemical potential near filling factor one reveals a large spontaneous magnetization, further substantiating this picture of a cascade of symmetry breakings. The sequence of phase transitions and Dirac revivals is observed at temperatures well above the onset of the superconducting and correlated insulating states. This indicates that the state we reveal here, with its strongly broken electronic flavor symmetry and revived Dirac-like electronic character, is a key player in the physics of magic angle graphene, forming the parent state out of which the more fragile superconducting and correlated insulating ground states emerge.

cond-mat.mes-hall↗

arXiv2019

Quantized large-bias current in the anomalous Floquet-Anderson insulator

We study two-terminal transport through two-dimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We focus on the Anomalous Floquet-Anderson Insulator (AFAI) phase, a topologically-nontrivial phase within this class, which hosts topologically protected chiral edge modes coexisting with its fully localized bulk. We show that the unique properties of the AFAI yield remarkable far-from-equilibrium transport signatures: for a large bias between leads, a quantized amount of charge is transported through the system each driving period. Upon increasing the bias, the chiral Floquet edge mode connecting source to drain becomes fully occupied and the current rapidly approaches its quantized value.

cond-mat.mes-hall↗

arXiv2019

Tests of nematic-mediated superconductivity applied to Ba$_{1-x}$Sr$_x$Ni$_2$As$_2$

In many unconventional superconductors, nematic quantum fluctuations are strongest where the critical temperature is highest, inviting the conjecture that nematicity plays an important role in the pairing mechanism. Recently, Ba$_{1-x}$Sr$_x$Ni$_2$As$_2$ has been identified as a tunable nematic system that provides an ideal testing ground for this proposition. We therefore propose several sharp empirical tests, supported by quantitative calculations in a simple model of Ba$_{1-x}$Sr$_x$Ni$_2$As$_2$. The most stringent predictions concern experiments under uniaxial strain, which has recently emerged as a powerful tuning parameter in the study of correlated materials. Since uniaxial strain so precisely targets nematic fluctuations, such experiments may provide compelling evidence for nematic-mediated pairing, analogous to the isotope effect in conventional superconductors.

cond-mat.str-el↗

arXiv2019

Intrinsic superconducting instabilities of a solvable model for an incoherent metal

We construct a family of translationally invariant lattice models with a large number ($N$) of orbitals at every site coupled together via single electron tunneling. By tuning the relative strength of the electronic bandwidth and on-site interactions, that have a modified Sachdev-Ye-Kitaev (SYK) form, we demonstrate a number of unusual features at strong coupling and in the large$-N$ limit. We find examples of (i) an intrinsic non-BCS superconducting instability arising out of an incoherent non-Fermi liquid metal, and, (ii) an instability of an incipient heavy Fermi liquid metal to superconductivity with transition temperatures comparable to its renormalized bandwidth. At strong-coupling, these solvable models display pairing instabilities that are not driven by any special "nesting" properties associated with an underlying Fermi surface.

cond-mat.str-el↗

arXiv2019

Topological superconductivity in planar Josephson junctions: Narrowing down to the nanowire limit

We theoretically study topological planar Josephson junctions (JJs) formed from spin-orbit-coupled two-dimensional electron gases (2DEGs) proximitized by two superconductors and subjected to an in-plane magnetic field $B_\parallel$. Compared to previous studies of topological superconductivity in these junctions, here we consider the case where the superconducting leads are narrower than the superconducting coherence length. In this limit the system may be viewed as a proximitized multiband wire, with an additional knob being the phase difference $ϕ$ between the superconducting leads. A combination of mirror and time-reversal symmetry may put the system into the class BDI. Breaking this symmetry changes the symmetry class to class D. The class D phase diagram depends strongly on $B_{\parallel}$ and chemical potential, with a weaker dependence on $ϕ$ for JJs with narrower superconducting leads. In contrast, the BDI phase diagram depends strongly on both $B_\parallel$ and $ϕ$. Interestingly, the BDI phase diagram has a "fan"-shaped region with phase boundaries which move away from $ϕ= π$ linearly with $B_\parallel$. The number of distinct phases in the fan increases with increasing chemical potential. We study the dependence of the JJ's critical current on $B_\parallel$, and find that minima in the critical current indicate first-order phase transitions in the junction only when the spin-orbit coupling strength is small. In contrast to the case of a JJ with wide leads, in the narrow case these transitions are not accompanied by a change in the JJ's topological index. Our results, calculated using realistic experimental parameters, provide guidelines for present and future searches for topological superconductivity in JJs with narrow leads, and are particularly relevant to recent experiments [A. Fornieri et al., Nature (London) 569, 89 (2019)].

cond-mat.mes-hall↗

arXiv2019

Anomalous Floquet Insulators

We demonstrate the existence of a two-dimensional anomalous Floquet insulator (AFI) phase: an interacting (periodically-driven) non-equilibrium topological phase of matter with no counterpart in equilibrium. The AFI is characterized by a many-body localized bulk, exhibiting nontrivial micromotion within a driving period, and delocalized (thermalizing) chiral states at its boundaries. For a geometry without edges, we argue analytically that the bulk may be many-body localized in the presence of interactions, deriving conditions where stability is expected. We investigate the interplay between the thermalizing edge and the localized bulk via numerical simulations of an AFI in a geometry with edges. We find that non-uniform particle density profiles remain stable in the bulk up to the longest timescales that we can access, while the propagating edge states persist and thermalize, despite being coupled to the bulk. These findings open the possibility of observing quantized edge transport in interacting systems at high temperature. The analytical approach introduced in this paper can be used to study the stability of other anomalous Floquet phases.

cond-mat.mes-hall↗

arXiv2019

Monte Carlo Studies of Quantum Critical Metals

Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this article, we review the status of the understanding of metallic quantum criticality, and the recent progress made by QMC simulations. We focus on the cases of spin density wave and Ising nematic criticality. We describe the results obtained so far, and their implications for superconductivity, non-Fermi liquid behavior, and transport in the vicinity of metallic quantum critical points. Some of the outstanding puzzles and future directions are highlighted.

cond-mat.str-el↗

arXiv2019

Scattering mechanisms and electrical transport near an Ising nematic quantum critical point

Electrical transport properties near an electronic Ising-nematic quantum critical point in two dimensions are of both theoretical and experimental interest. In this work, we derive a kinetic equation valid in a broad regime near the quantum critical point using the memory matrix approach. The formalism is applied to study the effect of the critical fluctuations on the dc resistivity through different scattering mechanisms, including umklapp, impurity scattering, and electron-hole scattering in a compensated metal. We show that electrical transport in the quantum critical regime exhibits a rich behavior that depends sensitively on the scattering mechanism and the band structure. In the case of a single large Fermi surface, the resistivity due to umklapp scattering crosses over from $ρ\sim T^2$ at low temperature to sublinear at high temperature. The crossover temperature scales as $q_0^3$, where $q_0$ is the minimal wavevector for umklapp scattering. Impurity scattering leads to $ρ-ρ_0\sim T^α$ ($ρ_0$ being the residual resistivity), where $α$ is either larger than 2 if there is only a single Fermi sheet present, or 4/3 in the case of multiple Fermi sheets. Finally, in a perfectly compensated metal with an equal density of electrons and holes, the low temperature behavior depends strongly on the structure of "cold spots" on the Fermi surface, where the coupling between the quasiparticles and order parameter fluctuations vanishes by symmetry. In particular, for a system where cold spots are present on some (but not all) Fermi sheets, $ρ\sim T^{5/3}$. At higher temperatures there is a broad crossover regime where $ρ$ either saturates or $ρ\sim T$, depending on microscopic details. We discuss these results in the context of recent quantum Monte Carlo simulations of a metallic Ising nematic critical point, and experiments in certain iron-based superconductors.

cond-mat.str-el↗