arXiv subjects

Erez Berg

Publications and source records attributed to Erez Berg.

At least 145 records · Page 8Linked to original sources

arXiv2016

Edge--Entanglement correspondence for gapped topological phases with symmetry

The correspondence between the edge theory and the entanglement spectrum is firmly established for the chiral topological phases. We study gapped, topologically ordered, non-chiral states with a conserved $U(1)$ charge and show that the entanglement Hamiltonian contains not only the information about topologically distinct edges such phases may admit, but also which of them will be realized in the presence of symmetry breaking/conserving perturbations. We introduce an exactly solvable, charge conserving lattice model of a $\mathbb{Z}_2$ spin liquid and derive its edge theory and the entanglement Hamiltonian, also in the presence of perturbations. We construct a field theory of the edge and study its RG flow. We show the precise extent of the correspondence between the information contained in the entanglement Hamiltonian and the edge theory.

cond-mat.str-el↗

arXiv2016

No-go theorem for a time-reversal invariant topological phase in noninteracting systems coupled to conventional superconductors

We prove that a system of non-interacting electrons proximity coupled to a conventional s-wave superconductor cannot realize a time reversal invariant topological phase. This is done by showing that for such a system, in either one or two dimensions, the topological invariant of the corresponding symmetry class (DIII) is always trivial. Our results suggest that the pursuit of Majorana bound states in time-reversal invariant systems should be aimed at interacting systems or at proximity to unconventional superconductors.

cond-mat.mes-hall↗

arXiv2016

Topological Superconductivity in a Planar Josephson Junction

We consider a two-dimensional electron gas with strong spin-orbit coupling contacted by two superconducting leads, forming a Josephson junction. We show that in the presence of an in-plane Zeeman field the quasi-one-dimensional region between the two superconductors can support a topological superconducting phase hosting Majorana bound states at its ends. We study the phase diagram of the system as a function of the Zeeman field and the phase difference between the two superconductors (treated as an externally controlled parameter). Remarkably, at a phase difference of $π$, the topological phase is obtained for almost any value of the Zeeman field and chemical potential. In a setup where the phase is not controlled externally, we find that the system undergoes a first-order topological phase transition when the Zeeman field is varied. At the transition, the phase difference in the ground state changes abruptly from a value close to zero, at which the system is trivial, to a value close to $π$, at which the system is topological. The critical current through the junction exhibits a sharp minimum at the critical Zeeman field, and is therefore a natural diagnostic of the transition. We point out that in presence of a symmetry under a modified mirror reflection followed by time reversal, the system belongs to a higher symmetry class and the phase diagram as a function of the phase difference and the Zeeman field becomes richer.

cond-mat.mes-hall↗

arXiv2016

Quantum critical properties of a metallic spin density wave transition

We report on numerically exact determinantal quantum Monte Carlo simulations of the onset of spin-density wave (SDW) order in itinerant electron systems captured by a sign-problem-free two-dimensional lattice model. Extensive measurements of the SDW correlations in the vicinity of the phase transition reveal that the critical dynamics of the bosonic order parameter are well described by a dynamical critical exponent z = 2, consistent with Hertz-Millis theory, but are found to follow a finite-temperature dependence that does not fit the predicted behavior of the same theory. The presence of critical SDW fluctuations is found to have a strong impact on the fermionic quasiparticles, giving rise to a dome-shaped superconducting phase near the quantum critical point. In the superconducting state we find a gap function that has an opposite sign between the two bands of the model and is nearly constant along the Fermi surface of each band. Above the superconducting $T_c$ our numerical simulations reveal a nearly temperature and frequency independent self energy causing a strong suppression of the low-energy quasiparticle spectral weight in the vicinity of the hot spots on the Fermi surface. This indicates a clear breakdown of Fermi liquid theory around these points.

cond-mat.str-el↗

arXiv2016

Spin density wave order, topological order, and Fermi surface reconstruction

In the conventional theory of density wave ordering in metals, the onset of spin density wave (SDW) order co-incides with the reconstruction of the Fermi surfaces into small 'pockets'. We present models which display this transition, while also displaying an alternative route between these phases via an intermediate phase with topological order, no broken symmetry, and pocket Fermi surfaces. The models involve coupling emergent gauge fields to a fractionalized SDW order, but retain the canonical electron operator in the underlying Hamiltonian. We establish an intimate connection between the suppression of certain defects in the SDW order, and the presence of Fermi surface sizes distinct from the Luttinger value in Fermi liquids. We discuss the relevance of such models to the physics of the hole-doped cuprates near optimal doping.

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arXiv2016

Interaction-driven topological superconductivity in one dimension

We study one-dimensional topological superconductivity in the presence of time-reversal symmetry. This phase is characterized by having a bulk gap, while supporting a Kramers' pair of zero-energy Majorana bound states at each of its ends. We present a general simple model which is driven into this topological phase in the presence of repulsive electron-electron interactions. We further propose two experimental setups and show that they realize this model at low energies. The first setup is a narrow two-dimensional topological insulator partially covered by a conventional s-wave superconductor, and the second is a semiconductor wire in proximity to an s-wave superconductor. These systems can therefore be used to realize and probe the time-reversal invariant topological superconducting phase. The effect of interactions is studied using both a mean-field approach and a renormalization group analysis.

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arXiv2016

Signatures of topological Josephson junctions

Quasiparticle poisoning and diabatic transitions may significantly narrow the window for the experimental observation of the $4π$-periodic $dc$ Josephson effect predicted for topological Josephson junctions. Here, we show that switching current measurements provide accessible and robust signatures for topological superconductivity which persist in the presence of quasiparticle poisoning processes. Such measurements provide access to the phase-dependent subgap spectrum and Josephson currents of the topological junction when incorporating it into an asymmetric SQUID together with a conventional Josephson junction with large critical current. We also argue that pump-probe experiments with multiple current pulses can be used to measure the quasiparticle poisoning rates of the topological junction. The proposed signatures are particularly robust, even in the presence of Zeeman fields and spin-orbit coupling, when focusing on short Josephson junctions. Finally, we also consider microwave excitations of short topological Josephson junctions which may complement switching current measurements.

cond-mat.mes-hall↗

arXiv2016

Non-quasiparticle transport and resistivity saturation: A view from the large-N limit

The electron dynamics in metals are usually well described by the semiclassical approximation for long-lived quasiparticles. However, in some metals, the scattering rate of the electrons at elevated temperatures becomes comparable to the Fermi energy; then, this approximation breaks down, and the full quantum-mechanical nature of the electrons must be considered. In this work, we study a solvable, large-$N$ electron-phonon model, which at high temperatures enters the non-quasiparticle regime. In this regime, the model exhibits "resistivity saturation" to a temperature-independent value of the order of the quantum of resistivity - the first analytically tractable model to do so. The saturation is not due to a fundamental limit on the electron lifetime, but rather to the appearance of a second conductivity channel. This is suggestive of the phenomenological "parallel resistor formula", known to describe the resistivity of a variety of saturating metals.

cond-mat.str-el↗

arXiv2016

Ising nematic quantum critical point in a metal: a Monte Carlo study

The Ising nematic quantum critical point (QCP) associated with the zero temperature transition from a symmetric to a nematic {\it metal} is an exemplar of metallic quantum criticality. We have carried out a minus sign-free quantum Monte Carlo study of this QCP for a two dimensional lattice model with sizes up to $24\times 24$ sites. The system remains non-superconducting down to the lowest accessible temperatures. The results exhibit critical scaling behavior over the accessible ranges of temperature, (imaginary) time, and distance. This scaling behavior has remarkable similarities with recently measured properties of the Fe-based superconductors proximate to their putative nematic QCP.

cond-mat.supr-con↗

arXiv2016

Effects of order parameter self-consistency in a $s_\pm$-s junction

The properties of Josephson tunneling between a single band s-wave superconductor and a two band $s_\pm$ superconductor are studied, in relation to recent experiments involving iron-based superconductors. We study a single junction and tune the order parameter (OP) phase difference across the junction. We find a variety of behaviors which are characterized by their energy-phase difference relation. The system is modeled on a lattice and treated in self-consistent mean field approximation. We also study a loop structure made with s-wave and $s_\pm$ parts with two junctions between the parts. The phase of the order parameter is then controlled by a magnetic flux threading the loop. Our analysis suggests four types of junction behaviors which are characterized by the dependence of the junction energy on the phase difference between the s-wave and the $s_\pm$ superconductors. The energy vs. phase difference curve has either one minimum at $Δϕ= 0,π$ or somewhere in between, or a double minimum structure. This leads to four different behaviors in a loop structure as a function of the flux threaded through the loop.

cond-mat.supr-con↗

arXiv2016

Fluctuation and strain effects in a chiral $p$-wave superconductor

For a tetragonal material, order parameters of $p_x$ and $p_y$ symmetry are related by rotation and hence have the same $T_{\rm c}$ at a mean-field level. This degeneracy can be lifted by a symmetry-breaking field, like (uniaxial) in-plane strain, such that at $T_{\rm c}$, the order parameter is only of $p_x$ or $p_y$ symmetry. Only at a lower temperature also the respective other order parameter condenses to form a chiral $p$-wave state. At the mean-field level, the derivative of $T_{\rm c}$ with strain is discontinuous at zero strain. We analyze consequences of (thermal) fluctuations on the strain-temperature phase diagram within a Ginzburg-Landau approach. We find that the order-parameter fluctuations can drive the transition to be weakly first order, rounding off this discontinuity. We discuss the possibility of a second-order transition into a non-superconducting time-reversal-symmetry-breaking phase and consequences for the spin-triplet superconductor Sr$_2$RuO$_4$.

cond-mat.supr-con↗

arXiv2016

The Mott-Ioffe-Regel limit and resistivity crossover in a tractable electron-phonon model

Many metals display resistivity saturation - a substantial decrease in the slope of the resistivity as a function of temperature, that occurs when the electron scattering rate $τ^{-1}$ becomes comparable to the Fermi energy $E_F/\hbar$ (the Mott-Ioffe-Regel limit). At such temperatures, the usual description of a metal in terms of ballistically propagating quasiparticles is no longer valid. We present a tractable model of a large $N$ number of electronic bands coupled to $N^2$ optical phonon modes, which displays a crossover behavior in the resistivity at temperatures where $τ^{-1}\sim E_F/\hbar$. At low temperatures, the resistivity obeys the familiar linear form, while at high temperatures, the resistivity still increases linearly, but with a modified slope (that can be either lower or higher than the low-temperature slope, depending on the band structure). The high temperature non-Boltzmann regime is interpreted by considering the diffusion constant and the compressibility, both of which scale as the inverse square root of the temperature.

cond-mat.mes-hall↗

arXiv2015

Competing Orders in a Nearly Antiferromagnetic Metal

We study the onset of spin-density wave order in itinerant electron systems via a two-dimensional lattice model amenable to numerically exact, sign-problem-free determinantal quantum Monte Carlo simulations. The finite-temperature phase diagram of the model reveals a dome-shaped $d$-wave superconducting phase near the magnetic quantum phase transition. Above the critical superconducting temperature, we observe an extended fluctuation regime, which manifests itself in the opening of a gap in the electronic density of states and an enhanced diamagnetic response. While charge density wave fluctuations are moderately enhanced in the proximity of the magnetic quantum phase transition, they remain short-ranged. The striking similarity of our results to the phenomenology of many unconventional superconductors points a way to a microscopic understanding of such strongly coupled systems in a controlled manner.

cond-mat.supr-con↗

arXiv2015

Current Correlations in a Majorana Beam Splitter

We study current correlations in a $T$-junction composed of a grounded topological superconductor and of two normal-metal leads which are biased at a voltage $V$. We show that the existence of an isolated Majorana zero mode in the junction dictates a universal behavior for the cross correlation of the currents through the two normal-metal leads of the junction. The cross correlation is negative and approaches zero at high bias voltages as -1/$V$. This behavior is robust in the presence of disorder and multiple transverse channels, and persists at finite temperatures. In contrast, an accidental low-energy Andreev bound state gives rise to nonuniversal behavior of the cross correlation. We employ numerical transport simulations to corroborate our conclusions.

cond-mat.mes-hall↗

arXiv2015

Current at a distance and resonant transparency in Weyl semimetals

Surface Fermi arcs are the most prominent manifestation of the topological nature of Weyl semimetals. In the presence of a static magnetic field oriented perpendicular to the sample surface, their existence leads to unique inter-surface cyclotron orbits. We propose two experiments which directly probe the Fermi arcs: a magnetic field dependent non-local DC voltage and sharp resonances in the transmission of electromagnetic waves at frequencies controlled by the field. We show that these experiments do not rely on quantum mechanical phase coherence, which renders them far more robust and experimentally accessible than quantum effects. We also comment on the applicability of these ideas to Dirac semimetals.

cond-mat.mes-hall↗

arXiv2015

A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension

We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show that a sharply defined topological phase with protected, exponentially localized edge states exists. If one of the spin components is conserved, the protection of the edge modes can be understood as a consequence of the presence of a spin gap. In the more general case, the localization of the edge states arises from a gap to single particle excitations in the bulk. We consider specific microscopic models and demonstrate both analytically and numerically (using density matrix renormalization group calculations) that they can support the topologically non-trivial phase.

cond-mat.mes-hall↗

arXiv2015

The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump

Periodically driven quantum systems provide a novel and versatile platform for realizing topological phenomena. Among these are analogs of topological insulators and superconductors, attainable in static systems; however, some of these phenomena are unique to the periodically driven case. Here, we show that disordered, periodically driven systems admit an "anomalous" two dimensional phase, whose quasi-energy spectrum consists of chiral edge modes that coexist with a fully localized bulk - an impossibility for static Hamiltonians. This unique situation serves as the basis for a new topologically-protected non-equilibrium transport phenomenon: quantized non-adiabatic charge pumping. We identify the bulk topological invariant that characterizes the new phase (which we call the "anomalous Floquet Anderson Insulator", or AFAI). We provide explicit models which constitute a proof of principle for the existence of the new phase. Finally, we present evidence that the disorder-driven transition from the AFAI to a trivial, fully localized phase is in the same universality class as the quantum Hall plateau transition.

cond-mat.mes-hall↗

arXiv2015

Signatures of Majorana Zero Modes in Spin-Resolved Current Correlations

We consider a normal lead coupled to a Majorana bound state. We show that the spin-resolved current correlations exhibit unique features which distinguish Majorana bound states from other low-energy resonances. In particular, the spin-up and spin-down currents from a Majorana bound state are anti-correlated at low bias voltages, and become uncorrelated at higher voltages. This behavior is independent of the exact form of coupling to the lead, and of the direction of the spin polarization. In contrast, an ordinary low-energy Andreev bound state gives rise to a positive correlation between the spin-up and spin-down currents, and this spin-resolved current-current correlation approaches a non-zero constant at high bias voltages. We discuss experimental setups in which this effect can be measured.

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