arXiv subjects

Erez Berg

Publications and source records attributed to Erez Berg.

At least 127 records · Page 7Linked to original sources

arXiv2018

Signatures of fractionalization in spin liquids from interlayer thermal transport

Quantum spin liquids (QSLs) are intriguing phases of matter possessing fractionalized excitations. Several quasi-two dimensional materials have been proposed as candidate QSLs, but direct evidence for fractionalization in these systems is still lacking. In this paper, we show that the inter-plane thermal conductivity in layered QSLs carries a unique signature of fractionalization. We examine several types of gapless QSL phases - a $Z_2$ QSL with either a Dirac spectrum or a spinon Fermi surface, and a $U(1)$ QSL with a Fermi surface. In all cases, the in-plane and $c-$axis thermal conductivities have a different power law dependence on temperature, due to the different mechanisms of transport in the two directions: in the planes, the thermal current is carried by fractionalized excitations, whereas the inter-plane current is carried by integer (non-fractional) excitations. In layered $Z_2$ and $U(1)$ QSLs with a Fermi surface, the $c-$axis thermal conductivity is parametrically smaller than the in-plane one, but parametrically larger than the phonon contribution at low temperatures.

cond-mat.str-el↗

arXiv2018

Topologically protected braiding in a single wire using Floquet Majorana modes

Majorana zero modes are a promising platform for topologically protected quantum information processing. Their non-Abelian nature, which is key for performing quantum gates, is most prominently exhibited through braiding. While originally formulated for two-dimensional (2d) systems, it has been shown that braiding can also be realized using one-dimensional (1d) wires by forming an essentially two-dimensional network. Here, we show that in driven systems far from equilibrium, one can do away with the second spatial dimension altogether by instead using quasienergy as the second dimension. To realize this, we use a Floquet topological superconductor which can exhibit Majorana modes at two special eigenvalues of the evolution operator, 0 and pi, and thus can realize four Majorana modes in a single, driven quantum wire. We describe and numerically evaluate a protocol that realizes a topologically protected exchange of two Majorana zero modes in a single wire by adiabatically modulating the Floquet drive and using the pi modes as auxiliary degrees of freedom.

cond-mat.str-el↗

arXiv2018

Fractional Josephson Vortices and Braiding of Majorana Zero Modes in Planar Superconductor-Semiconductor Heterostructures

We consider the one-dimensional (1D) topological superconductor that may form in a planar superconductor-metal-superconductor Josephson junction in which the metal is is subjected to spin orbit coupling and to an in-plane magnetic field. This 1D topological superconductor has been the subject of recent theoretical and experimental attention. We examine the effect of perpendicular magnetic field and a supercurrent driven across the junction on the position and structure of the Majorana zero modes that are associated with the topological superconductor. In particular, we show that under certain conditions the Josephson vortices fractionalize to half-vortices, each carrying half of the superconducting flux quantum and a single Majorana zero mode. Furthemore, we show that the system allows for a current-controlled braiding of Majorana zero modes.

cond-mat.supr-con↗

arXiv2018

Evidence of topological superconductivity in planar Josephson junctions

Majorana zero modes are quasiparticle states localized at the boundaries of topological superconductors that are expected to be ideal building blocks for fault-tolerant quantum computing. Several observations of zero-bias conductance peaks measured in tunneling spectroscopy above a critical magnetic field have been reported as experimental indications of Majorana zero modes in superconductor/semiconductor nanowires. On the other hand, two dimensional systems offer the alternative approach to confine Ma jorana channels within planar Josephson junctions, in which the phase difference ϕ between the superconducting leads represents an additional tuning knob predicted to drive the system into the topological phase at lower magnetic fields. Here, we report the observation of phase-dependent zero-bias conductance peaks measured by tunneling spectroscopy at the end of Josephson junctions realized on a InAs/Al heterostructure. Biasing the junction to ϕ ~ π significantly reduces the critical field at which the zero-bias peak appears, with respect to ϕ = 0. The phase and magnetic field dependence of the zero-energy states is consistent with a model of Majorana zero modes in finite-size Josephson junctions. Besides providing experimental evidence of phase-tuned topological superconductivity, our devices are compatible with superconducting quantum electrodynamics architectures and scalable to complex geometries needed for topological quantum computing.

cond-mat.mes-hall↗

arXiv2018

Translationally invariant non-Fermi liquid metals with critical Fermi-surfaces: Solvable models

We construct examples of translationally invariant solvable models of strongly-correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi liquid behavior. In the marginal Fermi liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi-surfaces. The self energy has a singular frequency dependence, but lacks momentum dependence, reminiscent of a dynamical mean field theory-like behavior but in dimensions $d<\infty$. In the low temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi-surface in the non-Fermi liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse grained descriptions of a class of intermediate scale non-fermi liquid behavior in generic correlated metals.

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arXiv2018

From one-dimensional charge conserving superconductors to the gapless Haldane phase

We develop a framework to analyze one-dimensional topological superconductors with charge conservation. In particular, we consider models with $N$ flavors of fermions and $(\mathbb{Z}_2)^N$ symmetry, associated with the conservation of the fermionic parity of each flavor. For a single flavor, we recover the result that a distinct topological phase with exponentially localized zero modes does not exist due to absence of a gap to single particles in the bulk. For $N>1$, however, we show that the ends of the system can host low-energy, exponentially-localized modes. The analysis can readily be generalized to systems in other symmetry classes. To illustrate these ideas, we focus on lattice models with $SO\left(N\right)$ symmetric interactions, and study the phase transition between the trivial and the topological gapless phases using bosonization and a weak-coupling renormalization group analysis. As a concrete example, we study in detail the case of $N=3$. We show that in this case, the topologically non-trivial superconducting phase corresponds to a gapless analogue of the Haldane phase in spin-1 chains. In this phase, although the bulk is gapless to single particle excitations, the ends host spin-$1/2$ degrees of freedom which are exponentially localized and protected by the spin gap in the bulk. We obtain the full phase diagram of the model numerically, using density matrix renormalization group calculations. Within this model, we identify the self-dual line studied by Andrei and Destri [Nucl. Phys. B, 231(3), 445-480 (1984)], as a first-order transition line between the gapless Haldane phase and a trivial gapless phase. This allows us to identify the propagating spin-$1/2$ kinks in the Andrei-Destri model as the topological end-modes present at the domain walls between the two phases.

cond-mat.mes-hall↗

arXiv2017

Dynamical susceptibility of a near-critical non-conserved order parameter and B2g Raman response in Fe-based superconductors

We analyze the dynamical response of a two-dimensional system of itinerant fermions coupled to a scalar boson $ϕ$, which undergoes a continuous transition towards nematic order with $d-$wave form-factor. We consider two cases: (a) when $ϕ$ is a soft collective mode of fermions near a Pomeranchuk instability, and (b) when it is an independent critical degree of freedom, such as a composite spin order parameter near an Ising-nematic transition. In both cases, the order-parameter is not a conserved quantity and the $d-$wave fermionic polarization $Π(q, Ω)$ remains finite even at $q=0$. The polarization $Π(0, Ω)$ has similar behavior in the two cases, but the relations between $Π(0, Ω)$ and the bosonic susceptibility $χ(0, Ω)$ are different, leading to different forms of $χ^{\prime \prime} (0, Ω)$, as measured by Raman scattering. We compare our results with polarization-resolved Raman data for the Fe-based superconductors FeSe$_{1-x}$S$_x$, NaFe$_{1-x}$Co$_x$As and BaFe$_2$As$_2$. We argue that the data for FeSe$_{1-x}$S$_x$ are well described within Pomeranchuk scenario, while the data for NaFe$_{1-x}$Co$_x$As and BaFe$_2$As$_2$ are better described within the "independent" scenario involving a composite spin order.

cond-mat.str-el↗

arXiv2017

Quantized magnetization density in periodically driven systems

We study micromotion in two-dimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We show that this micromotion gives rise to a quantized time-averaged magnetization density when the system is filled with fermions. Furthermore we find that a quantized current flows around the boundary of any filled region of finite extent. The quantization has a topological origin: we relate the time-averaged magnetization density to the winding number characterizing the new phase identified in Phys. Rev. X 6, 021013 (2016). We thus establish that the winding number invariant can be accessed directly in bulk measurements, and propose an experimental protocol to do so using interferometry in cold atom based realizations.

cond-mat.mes-hall↗

arXiv2017

Is charge order induced near an antiferromagnetic quantum critical point?

We investigate the interplay between charge order and superconductivity near an antiferromagnetic quantum critical point using sign-problem-free Quantum Monte Carlo simulations. We establish that, when the electronic dispersion is particle-hole symmetric, the system has an emergent SU(2) symmetry that implies a degeneracy between $d$-wave superconductivity and charge order with $d$-wave form factor. Deviations from particle-hole symmetry, however, rapidly lift this degeneracy, despite the fact that the SU(2) symmetry is preserved at low energies. As a result, we find a strong suppression of charge order caused by the competing, leading superconducting instability. Across the antiferromagnetic phase transition, we also observe a shift in the charge order wave-vector from diagonal to axial. We discuss the implications of our results to the universal phase diagram of antiferromagnetic quantum-critical metals and to the elucidation of the charge order experimentally observed in the cuprates.

cond-mat.supr-con↗

arXiv2017

Topological transitions and fractional charges induced by strain and magnetic field in carbon nanotubes

We show that carbon nanotubes (CNT) can be driven through a topological phase transition using either strain or a magnetic field. This can naturally lead to Jackiw-Rebbi soliton states carrying fractionalized charges, similar to those found in a domain wall in the Su-Schrieffer-Heeger model, in a setup with a spatially inhomogeneous strain and an axial field. Two types of fractionalized states can be formed at the interface between regions with different strain: a spin-charge separated state with integer charge and spin zero (or zero charge and spin $\pm \hbar/2$), and a state with charge $\pm e/2$ and spin $\pm \hbar/4$. The latter state requires spin-orbit coupling in the CNT. We show that in our setup, the precise quantization of the fractionalized interface charges is a consequence of the symmetry of the CNT under a combination of a spatial rotation by $π$ and time reversal. Finally, we comment on the effects of many-body interaction on this phenomena.

cond-mat.mes-hall↗

arXiv2017

Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter

We study the dynamic response of a two-dimensional system of itinerant fermions in the vicinity of a uniform ($\mathbf{Q}=0$) Ising nematic quantum critical point of $d-$wave symmetry. The nematic order parameter is not a conserved quantity, and this permits a nonzero value of the fermionic polarization in the $d-$wave channel even for vanishing momentum and finite frequency: $Π(\mathbf{q} = 0,Ω_m) \neq 0$. For weak coupling between the fermions and the nematic order parameter (i.e. the coupling is small compared to the Fermi energy), we perturbatively compute $Π(\mathbf{q} = 0,Ω_m) \neq 0$ over a parametrically broad range of frequencies where the fermionic self-energy $Σ(ω)$ is irrelevant, and use Eliashberg theory to compute $Π(\mathbf{q} = 0,Ω_m)$ in the non-Fermi liquid regime at smaller frequencies, where $Σ(ω) > ω$. We find that $Π(\mathbf{q}=0,Ω)$ is a constant, plus a frequency dependent correction that goes as $|Ω|$ at high frequencies, crossing over to $|Ω|^{1/3}$ at lower frequencies. The $|Ω|^{1/3}$ scaling holds also in a non-Fermi liquid regime. The non-vanishing of $Π(\mathbf{q}=0, Ω)$ gives rise to additional structure in the imaginary part of the nematic susceptibility $χ^{''} (\mathbf{q}, Ω)$ at $Ω> v_F q$, in marked contrast to the behavior of the susceptibility for a conserved order parameter. This additional structure may be detected in Raman scattering experiments in the $d-$wave geometry.

cond-mat.str-el↗

arXiv2017

Non-Fermi-liquid at (2+1)d ferromagnetic quantum critical point

We construct a two-dimensional lattice model of fermions coupled to Ising ferromagnetic critical fluctuations. Using extensive sign-problem-free quantum Monte Carlo simulations, we show that the model realizes a continuous itinerant quantum phase transition. In comparison with other similar itinerant quantum critical points (QCPs), our QCP shows much weaker superconductivity tendency with no superconducting state down to the lowest temperature investigated, hence making the system a good platform for the exploration of quantum critical fluctuations. Remarkably, clear signatures of non-Fermi-liquid behavior in the fermion propagators are observed at the QCP. The critical fluctuations at the QCP partially resemble Hertz-Millis-Moriya behavior. However, careful scaling analysis reveals that the QCP belongs to a different universality class, deviating from both (2+1)d Ising and Hertz-Millis-Moriya predictions.

cond-mat.str-el↗

arXiv2017

Fractional chiral superconductors

Two-dimensional $p_x+ip_y$ topological superconductors host gapless Majorana edge modes, as well as Majorana bound states at the core of $h/2e$ vortices. Here we construct a model realizing the fractional counterpart of this phase: a fractional chiral superconductor. Our model is composed of an array of coupled Rashba wires in the presence of strong interactions, Zeeman field, and proximity coupling to an $s$-wave superconductor. We define the filling factor as $ν=l_{\text{so}}n/4$, where $n$ is the electronic density and $l_{\text{so}}$ is the spin-orbit length. Focusing on filling $ν=1/m$, with $m$ being an odd integer, we obtain a tractable model which allows us to study the properties of the bulk and the edge. Using an $ε$-expansion with $m=2+ε$, we show that the bulk Hamiltonian is gapped and that the edge of the sample hosts a chiral $\mathbb{Z}_{2m}$ parafermion theory with central charge $c=\frac{2m-1}{m+1}$. The tunneling density of states associated with this edge theory exhibits an anomalous energy dependence of the form $ω^{m-1}$. Additionally, we show that $\mathbb{Z}_{2m}$ parafermionic bound states reside at the cores of $h/2e$ vortices. Upon constructing an appropriate Josephson junction in our system, we find that the current-phase relation displays a $4πm$ periodicity, reflecting the underlying non-abelian excitations.

cond-mat.mes-hall↗

arXiv2017

Superconductivity mediated by quantum critical antiferromagnetic fluctuations: The rise and fall of hot spots

In several unconventional superconductors, the highest superconducting transition temperature $T_{c}$ is found in a region of the phase diagram where the antiferromagnetic transition temperature extrapolates to zero, signaling a putative quantum critical point. The elucidation of the interplay between these two phenomena - high-$T_{c}$ superconductivity and magnetic quantum criticality - remains an important piece of the complex puzzle of unconventional superconductivity. In this paper, we combine sign-problem-free Quantum Monte Carlo simulations and field-theoretical analytical calculations to unveil the microscopic mechanism responsible for the superconducting instability of a general low-energy model, called spin-fermion model. In this approach, low-energy electronic states interact with each other via the exchange of quantum critical magnetic fluctuations. We find that even in the regime of moderately strong interactions, both the superconducting transition temperature and the pairing susceptibility are governed not by the properties of the entire Fermi surface, but instead by the properties of small portions of the Fermi surface called hot spots. Moreover, $T_{c}$ increases with increasing interaction strength, until it starts to saturate at the crossover from hot-spots dominated to Fermi-surface dominated pairing. Our work provides not only invaluable insights into the system parameters that most strongly affect $T_{c}$, but also important benchmarks to assess the origin of superconductivity in both microscopic models and actual materials.

cond-mat.supr-con↗

arXiv2017

Quantum chaos in an electron-phonon bad metal

We calculate the scrambling rate $λ_L$ and the butterfly velocity $v_B$ associated with the growth of quantum chaos for a solvable large-$N$ electron-phonon system. We study a temperature regime in which the electrical resistivity of this system exceeds the Mott-Ioffe-Regel limit and increases linearly with temperature - a sign that there are no long-lived charged quasiparticles - although the phonons remain well-defined quasiparticles. The long-lived phonons determine $λ_L$, rendering it parametrically smaller than the theoretical upper-bound $λ_L \ll λ_{max}=2πT/\hbar$. Significantly, the chaos properties seem to be intrinsic - $λ_L$ and $v_B$ are the same for electronic and phononic operators. We consider two models - one in which the phonons are dispersive, and one in which they are dispersionless. In either case, we find that $λ_L$ is proportional to the inverse phonon lifetime, and $v_B$ is proportional to the effective phonon velocity. The thermal and chaos diffusion constants, $D_E$ and $D_L\equiv v_B^2/λ_L$, are always comparable, $D_E \sim D_L$. In the dispersive phonon case, the charge diffusion constant $D_C$ satisfies $D_L\gg D_C$, while in the dispersionless case $D_L \ll D_C$.

cond-mat.str-el↗

arXiv2017

Transverse fields to tune an Ising-nematic quantum critical transition

The paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a quantum phase transition also depends on the dynamics. In the transverse field Ising model, the order parameter is not conserved and increasing the transverse field enhances quantum fluctuations until they become strong enough to restore the symmetry of the ground state. Ising pseudo-spins can represent the order parameter of any system with a two-fold degenerate broken-symmetry phase, including electronic nematic order associated with spontaneous point-group symmetry breaking. Here, we show for the representative example of orbital-nematic ordering of a non-Kramers doublet that an orthogonal strain or a perpendicular magnetic field plays the role of the transverse field, thereby providing a practical route for tuning appropriate materials to a quantum critical point. While the transverse fields are conjugate to seemingly unrelated order parameters, their non-trivial commutation relations with the nematic order parameter, which can be represented by a Berry-phase term in an effective field theory, intrinsically intertwines the different order parameters.

cond-mat.str-el↗

arXiv2017

Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point

Using determinantal quantum Monte Carlo, we compute the properties of a lattice model with spin $\frac 1 2$ itinerant electrons tuned through a quantum phase transition to an Ising nematic phase. The nematic fluctuations induce superconductivity with a broad dome in the superconducting $T_c$ enclosing the nematic quantum critical point. For temperatures above $T_c$, we see strikingly non-Fermi liquid behavior, including a "nodal - anti nodal dichotomy" reminiscent of that seen in several transition metal oxides. In addition, the critical fluctuations have a strong effect on the low frequency optical conductivity, resulting in behavior consistent with "bad metal" phenomenology.

cond-mat.str-el↗

arXiv2017

Fate of the one-dimensional Ising quantum critical point coupled to a gapless boson

The problem of a quantum Ising degree of freedom coupled to a gapless bosonic mode appears naturally in many one dimensional systems, yet surprisingly little is known how such a coupling affects the Ising quantum critical point. We investigate the fate of the critical point in a regime, where the weak coupling renormalization group (RG) indicates a flow toward strong coupling. Using a renormalization group analysis and numerical density matrix renormalization group (DMRG) calculations we show that, depending on the ratio of velocities of the gapless bosonic mode and the Ising critical fluctuations, the transition may remain continuous or become fluctuation-driven first order. The two regimes are separated by a tri-critical point of a novel type.

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