arXiv subjects

Erez Berg

Publications and source records attributed to Erez Berg.

At least 55 records · Page 3Linked to original sources

arXiv2023

A Criterion for Strange Metallicity in the Lorenz Ratio

The Wiedemann-Franz (WF) law, stating that the Lorenz ratio $L = κ/(Tσ)$ between the thermal and electrical conductivities in a metal approaches a universal constant $L_0=π^2 k_B^2/ (3 e^2)$ at low temperatures, is often interpreted as a signature of fermionic Landau quasi-particles. In contrast, we show that various models of weakly disordered non-Fermi liquids also obey the WF law at $T \to 0$. Instead, we propose using the leading low-temperature correction to the WF law, $L(T)-L_0$ (proportional to the inelastic scattering rate), to distinguish different types of strange metals. As an example, we demonstrate that in a solvable model of a marginal Fermi liquid, $L(T)-L_0\propto -T$. Using the quantum Boltzmann equation (QBE) approach, we find analogous behavior in a class of marginal- and non-Fermi liquids with a weakly momentum-dependent inelastic scattering. In contrast, in a Fermi liquid, $L(T)-L_0$ is proportional to $-T^2$. This holds even when the resistivity grows linearly with $T$, due to $T-$linear quasi-elastic scattering (as in the case of electron-phonon scattering at temperatures above the Debye frequency). Finally, by exploiting the QBE approach, we demonstrate that the transverse Lorenz ratio, $L_{xy} = κ_{xy}/(Tσ_{xy})$, exhibits the same behavior.

cond-mat.str-el↗

arXiv2023

Intervalley coherence and intrinsic spin-orbit coupling in rhombohedral trilayer graphene

Rhombohedral graphene multilayers provide a clean and highly reproducible platform to explore the emergence of superconductivity and magnetism in a strongly interacting electron system. Here, we use electronic compressibility and local magnetometry to explore the phase diagram of this material class in unprecedented detail. We focus on rhombohedral trilayer in the quarter metal regime, where the electronic ground state is characterized by the occupation of a single spin and valley isospin flavor. Our measurements reveal a subtle competition between valley imbalanced (VI) orbital ferromagnets and intervalley coherent (IVC) states in which electron wave functions in the two momentum space valleys develop a macroscopically coherent relative phase. Contrasting the in-plane spin susceptibility of the IVC and VI phases reveals the influence of graphene's intrinsic spin-orbit coupling, which drives the emergence of a distinct correlated phase with hybrid VI and IVC character. Spin-orbit also suppresses the in-plane magnetic susceptibility of the VI phase, which allows us to extract the spin-orbit coupling strength of $λ\approx 50μ$eV for our hexagonal boron nitride-encapsulated graphene system. We discuss the implications of finite spin-orbit coupling on the spin-triplet superconductors observed in both rhombohedral and twisted graphene multilayers.

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arXiv2023

Tunable non-Fermi liquid phase from coupling to two-level systems

We study a controlled large-$N$ theory of electrons coupled to dynamical two-level systems (TLSs) via spatially-random interactions. Such a physical situation arises when electrons scatter off low-energy excitations in a metallic glass, such as a charge or stripe glass. Our theory is governed by a non-Gaussian saddle point, which maps to the celebrated spin-boson model. By tuning the coupling strength we find that the model crosses over from a Fermi liquid at weak coupling to an extended region of non-Fermi liquid behavior at strong coupling, and realizes a marginal Fermi liquid at the crossover. Beyond a critical coupling strength, the TLSs freeze and Fermi-liquid behavior is restored. Our results are valid for generic space dimensions $d>1$.

cond-mat.str-el↗

arXiv2023

Heat Conductance of the Quantum Hall Bulk

The Quantum Hall Effect (QHE) is a prototypical realization of a topological state of matter. It emerges from a subtle interplay between topology, interactions, and disorder. The disorder enables the formation of localized states in the bulk that stabilize the quantum Hall states with respect to the magnetic field and carrier density. Still, the details of the localized states and their contribution to transport remain beyond the reach of most experimental techniques. Here, we describe an extensive study of the bulk's heat conductance. Using a novel 'multi-terminal' short device (on a scale of $10 μm$), we separate the longitudinal thermal conductance, $κ_{xx}T$ (due to bulk's contribution), from the topological transverse value $κ_{xy}T$, by eliminating the contribution of the edge modes. When the magnetic field is tuned away from the conductance plateau center, the localized states in the bulk conduct heat efficiently ($κ_{xx}T \propto T$), while the bulk remains electrically insulating. Fractional states in the first excited Landau level, such as the $ν=7/3$ and $ν=5/2$, conduct heat throughout the plateau with a finite $κ_{xx} T$. We propose a theoretical model that identifies the localized states as the cause of the finite heat conductance, agreeing qualitatively with our experimental findings.

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arXiv2023

$T-$linear resistivity from magneto-elastic scattering: application to PdCrO$_2$

An electronic solid with itinerant carriers and localized magnetic moments represents a paradigmatic strongly correlated system. The electrical transport properties associated with the itinerant carriers, as they scatter off these local moments, has been scrutinized across a number of materials. Here we analyze the transport characteristics associated with ultra-clean PdCrO$_2$ -- a quasi two-dimensional material consisting of alternating layers of itinerant Pd-electrons and Mott-insulating CrO$_2$ layers -- which shows a pronounced regime of $T-$linear resistivity over a wide-range of intermediate temperatures. By contrasting these observations to the transport properties in a closely related material PdCoO$_2$, where the CoO$_2$ layers are band-insulators, we can rule out the traditional electron-phonon interactions as being responsible for this interesting regime. We propose a previously ignored electron-magnetoelastic interaction between the Pd-electrons, the Cr local-moments and an out-of-plane phonon as the main scattering mechanism that leads to the significant enhancement of resistivity and a $T-$linear regime in PdCrO$_2$ at temperatures far in excess of the magnetic ordering temperature. We suggest a number of future experiments to confirm this picture in PdCrO$_2$, as well as other layered metallic/Mott-insulating materials.

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arXiv2023

Robust Fermi liquid instabilities in sign problem-free models

Determinant Quantum Monte Carlo (DQMC) is a powerful numerical technique to study many-body fermionic systems. In recent years, several classes of sign-free (SF) models have been discovered, where the notorious sign problem can be circumvented. However, it is not clear what are the inherent physical characteristics and limitations of SF models. In particular, which zero-temperature quantum phases of matter are accessible within such models, and which are fundamentally inaccessible? Here, we show that a model belonging to any of the known SF classes within DQMC cannot have a stable Fermi liquid ground state in spatial dimension $d\ge 2$, unless the anti-unitary symmetry that prevents the sign problem is spontaneously broken (for which there are currently no known examples in SF models). For SF models belonging to one of the symmetry classes (where the absence of the sign problem follows from a combination of non-unitary symmetries of the fermionic action), any putative Fermi liquid fixed point generically includes an attractive Cooper-like interaction that destabilizes it. In the recently discovered lower-symmetry classes of SF models, the Fermi surface is generically unstable even at the level of the quadratic action. Our results suggest a fundamental link between Fermi liquids and the fermion sign problem. Interestingly, our results do not rule out a non-Fermi liquid ground state with a Fermi surface in a sign-free model.

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arXiv2023

Nematic metal in a multi-valley electron gas: Variational Monte Carlo analysis and application to AlAs

The two-dimensional electron gas is of fundamental importance in quantum many-body physics. We study a minimal extension of this model with $C_4$ (as opposed to full rotational) symmetry and an electronic dispersion with two valleys with anisotropic effective masses. Using variational Monte Carlo simulations, we find a broad intermediate range of densities with a metallic valley-polarized, spin-unpolarized ground-state. Our results are of direct relevance to the recently discovered ``nematic'' state in AlAs quantum wells. For the effective mass anisotropy relevant to this system, $m_x/m_y\approx 5.2$, we obtain a transition from an anisotropic metal to a valley-polarized metal at $r_s \approx 12$ (where $r_s$ is the dimensionless Wigner-Seitz radius). At still lower densities, we find a (possibly metastable) valley and spin-polarized state with a reduced electronic anisotropy.

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arXiv2023

Multiband mean-field theory of the $d+ig$ superconductivity scenario in Sr$_2$RuO$_4$

Many seemingly contradictory experimental findings concerning the superconducting state in Sr$_2$RuO$_4$ can be accounted for on the basis of a conjectured accidental degeneracy between two patterns of pairing that are unrelated to each other under the $(D_{4h})$ symmetry of the crystal: a $d_{x^2-y^2}$-wave $(B_{1g})$ and a $g_{xy(x^2-y^2)}$-wave $(A_{2g})$ superconducting state. In this paper, we propose a generic multi-band model in which the $g$-wave pairing involving the $xz$ and $yz$ orbitals arises from second-nearest-neighbor interactions. Even if time-reversal symmetry is broken in a $d+ig$ state, such a superconductor remains gapless with a Bogoliubov Fermi surface that approximates a (vertical) line node. The model gives rise to a strain-dependent splitting between the critical temperature $T_c$ and the time-reversal symmetry-breaking temperature $T_\text{trsb}$ that is qualitatively similar to some of the experimental observations in Sr$_2$RuO$_4$.

cond-mat.supr-con↗

arXiv2023

Probing the order parameter symmetry of two-dimensional superconductors by twisted Josephson interferometry

Probing the superconducting order parameter symmetry is a crucial step towards understanding the pairing mechanism in unconventional superconductors. Inspired by the recent discoveries of superconductivity in various van der Waals materials, and the availability of the relative twist angle as a continuous tuning knob in these systems, we propose a general setup for probing the order parameter symmetry of two-dimensional superconductors in twisted Josephson junctions. The junction is composed of an anisotropic s-wave superconductor as a probe and another superconductor with an unknown order parameter symmetry. Assuming momentum-resolved tunneling, we investigate signatures of different order parameter symmetries in the twist angle dependence of the critical current, the current-phase relations, and magnetic field dependence. As a concrete example, we study a twisted Josephson junction between NbSe2 and magic angle twisted bilayer graphene.

cond-mat.supr-con↗

arXiv2023

Inhomogeneity-Induced Time-Reversal Symmetry Breaking in Cuprate Twist-Junctions

The lowest order Josephson coupling, $J_1(θ)\cos(ϕ)$, between two d-wave superconductors with phase-difference $ϕ$ across the junction vanishes when their relative orientation is rotated by $θ=π/4$. However, in the presence of inhomogeneity, $J_{1}(\mathbf{r})$ is non-zero locally, with a sign that fluctuates in space. We show that such a random $J_1$ generates a global second-harmonic Josephson coupling, $J_2\cos(2ϕ)$, with a sign that favors $ϕ= \pm π/2$, i.e., spontaneous breaking of time reversal symmetry. The magnitude of $J_2$ is substantially enhanced if the spatial correlations of $J_1(\mathbf{r})$ extend over large distances, such as would be expected in the presence of large amplitude twist-angle angle disorder or significant local electronic nematicity. We argue that this effect likely accounts for the recent observations in twisted Josephson junctions between high temperature superconductors.

cond-mat.supr-con↗

arXiv2023

Superconductivity, charge density wave, and supersolidity in flat bands with tunable quantum metric

Predicting the fate of an interacting system in the limit where the electronic bandwidth is quenched is often highly non-trivial. The complex interplay between interactions and quantum fluctuations driven by the band geometry can drive competition between various ground states, such as charge density wave order and superconductivity. In this work, we study an electronic model of topologically-trivial flat bands with a continuously tunable Fubini-Study metric in the presence of on-site attraction and nearest-neighbor repulsion, using numerically exact quantum Monte Carlo simulations. By varying the electron filling and the minimal spatial extent of the localized flat-band Wannier wavefunctions, we obtain a number of intertwined orders. These include a phase with coexisting charge density wave (CDW) order and superconductivity, i.e., a supersolid. In spite of the non-perturbative nature of the problem, we identify an analytically tractable limit associated with a 'small' spatial extent of the Wannier functions and derive a low-energy effective Hamiltonian that can well describe our numerical results. We also provide unambiguous evidence for the violation of any putative lower bound on the zero-temperature superfluid stiffness in geometrically non-trivial flat bands.

cond-mat.str-el↗

arXiv2023

Weakly damped bosons and precursor gap in the vicinity of an antiferromagnetic metallic transition

We study the electronic spectral function of a metal in the vicinity of an antiferromagnetic (AFM) quantum critical point, focusing on a situation where the bare bandwidth of the spin fluctuations is significantly smaller than the Fermi energy. In this limit, we identify a range of energies where the fermionic quasiparticles near the "hot spots'' on the Fermi surface are strongly scattered by the quantum critical fluctuations, whereas the damping of the AFM fluctuations by the electrons is negligible. Within a one-loop approximation, there is a parameter range where the $T=0$ spectral function at the hot spots has a "precursor gap'' feature, with a local maximum at a finite frequency. However, the ratio of the bare spin wave velocity to the Fermi velocity required to obtain a precursor gap is probably too small to explain experiments in the electron-doped cuprate superconductors (He et al., Proc. Natl. Acad. Sci 116, 3449 (2019)). At lower frequencies, the Landau damping of the AFM fluctuations becomes important, and the electronic spectral function has the familiar $ω^{-1/2}$ singularity. Our one-loop perturbative results are supported by a numerical Monte Carlo simulation of electrons coupled to an undamped, nearly-critical AFM mode.

cond-mat.str-el↗

arXiv2023

Superconductivity and fermionic dissipation in quantum Hall edges

Proximity-induced superconductivity in fractional quantum Hall edges is a prerequisite to proposed realizations of parafermion zero-modes. A recent experimental work [Gül et al., Phys. Rev. X 12, 021057 (2022)] provided evidence for such coupling, in the form of a crossed Andreev reflection signal, in which electrons enter a superconductor from one chiral mode and are reflected as holes to another, counter-propagating chiral mode. Remarkably, while the probability for crossed Andreev reflection was small, it was stronger for $ν=1/3$ fractional quantum Hall edges than for integer ones. We theoretically explain these findings, including the relative strengths of the signals in the two cases and their qualitatively different temperature dependencies. An essential part of our model is the coupling of the edge modes to normal states in the cores of Abrikosov vortices induced by the magnetic field, which provide a fermionic bath. We find that the stronger crossed Andreev reflection in the fractional case originates from the suppression of electronic tunneling between the fermionic bath and the fractional quantum Hall edges. Our theory shows that the mere observation of crossed Andreev reflection signal does not necessarily imply the presence of localized parafermion zero-modes, and suggests ways to identify their presence from the behavior of this signal in the low temperature regime.

cond-mat.mes-hall↗

arXiv2023

Electron-phonon coupling and competing Kekulé orders in twisted bilayer graphene

Recent scanning tunneling microscopy experiments [K.P. Nuckolls et al., arXiv:2303.00024] have revealed the ubiquity of Kekulé charge-density wave order in magic-angle twisted bilayer graphene. Most samples are moderately strained and show `incommensurate Kekulé spiral' (IKS) order involving a graphene-scale charge density distortion uniaxially modulated on the scale of the moiré superlattice, in accord with theoretical predictions. However, ultra-low strain samples instead show graphene-scale Kekulé charge order that is uniform on the moiré scale. This order, especially prominent near filling factor $ν=-2$, is unanticipated by theory which predicts a time-reversal breaking Kekulé current order at low strain. We show that including the coupling of moiré electrons to graphene-scale optical zone-corner (ZC) phonons stabilizes a uniform Kekulé charge ordered state at $|ν|=2$ with a quantized topological (spin or anomalous Hall) response. Our work clarifies how this phonon-driven selection of electronic order emerges in the strong-coupling regime of moiré graphene.

cond-mat.str-el↗

arXiv2023

Magnetization Dynamics and Peierls Instability in Topological Josephson Structures

We study a long topological Josephson junction with a ferromagnetic strip between two superconductors. The low-energy theory exhibits a non-local in time and space interaction between chiral Majorana fermions, mediated by the magnonic excitations in the ferromagnet. While short ranged interactions turn out to be irrelevant by power counting, we show that sufficiently strong and long-ranged interactions may induce a $\mathbb{Z}_2$-symmetry breaking. This spontaneous breaking leads to a tilting of the magnetization perpendicular to the Majorana propagation direction and the opening of a fermionic gap (Majorana mass). It is analogous to the Peierls instability in the commensurate Fröhlich model and reflects the nontrivial interplay between Majorana modes and magnetization dynamics. Within a Gaussian fluctuation analysis, we estimate critical values for the temporal and spatial non-locality of the interaction, beyond which the symmetry breaking is stable at zero temperature -- despite the effective one-dimensionality of the model. We conclude that non-locality, i.e., the stiffness of the magnetization in space and time, stabilizes the symmetry breaking. In the stabilized regime, we expect the current-phase relation to exhibit an experimentally accessible discontinuous jump. At nonzero temperatures, as usual in the 1D Ising model, the long-range order is destroyed by solitonic excitations, which in our case carry each a Majorana zero mode. In order to estimate the correlation length, we investigate the solitons within a self-consistent mean-field approach.

cond-mat.mes-hall↗

arXiv2023

Investigation of Planckian behavior in a high-conductivity oxide: PdCrO$_2$

The layered delafossite metal PdCrO$_2$ is a natural heterostructure of highly conductive Pd layers Kondo coupled to localized spins in the adjacent Mott insulating CrO$_2$ layers. At high temperatures $T$ it has a $T$-linear resistivity which is not seen in the isostructural but non-magnetic PdCoO$_2$. The strength of the Kondo coupling is known, as-grown crystals are extremely high purity and the Fermi surface is both very simple and experimentally known. It is therefore an ideal material platform in which to investigate 'Planckian metal' physics. We do this by means of controlled introduction of point disorder, measurement of the thermal conductivity and Lorenz ratio and studying the sources of its high temperature entropy. The $T$-linear resistivity is seen to be due mainly to elastic scattering and to arise from a sum of several scattering mechanisms. Remarkably, this sum leads to a scattering rate within 10$\%$ of the Planckian value of $k_BT/$$\hbar$.

cond-mat.str-el↗

arXiv2023

Free energy and specific heat near a quantum critical point of a metal

We analyze free energy and specific heat for fermions interacting with gapless bosons at a quantum-critical point (QCP) in a metal. We use the Luttinger-Ward-Eliashberg formula for the free energy in the normal state, which includes contributions from bosons, fermions, and their interaction, all expressed via fully dressed fermionic and bosonic propagators. The sum of the last two contributions is the free energy $F_γ$ of an effective low-energy model of fermions with boson-mediated dynamical 4-fermion interaction $V (Ω_m) \propto 1/|Ω_m|^γ$ (the $γ-$model). This purely electronic model has been used to analyze the interplay between non-Fermi liquid (non-FL) behavior and pairing near a QCP, which are both independent of the upper energy cutoff $Λ$. However, the specific heat $C_γ(T)$, obtained from $F_γ$, does depend on $Λ$. We argue that this dependence is spurious and cancels out, once we include the contribution from bosons. We compare our $C(T)$ with the one obtained within the $γ-$model using recently proposed regularization of $F_γ$. We argue that for $γ<1$, the full $C(T)$ and the regularized $C_γ(T)$ differ by a $γ-$dependent prefactor, while for $γ>1$, the full $C(T)$ is the sum of $ C_γ(T)$ and the specific heat of free bosons with fully dressed mass. For these $γ$, $C_γ(T)$ is negative. The authors of Ref. [1] argued that a negative $ C_γ(T)$ implies that the normal state becomes unstable at some distance to a QCP. In our calculation, both terms in $C(T)$ come from the same source, and $ C_γ(T)$ is smaller as long as vertex corrections can be safely neglected. We then argue that the normal state remains stable even at a QCP.

cond-mat.str-el↗

arXiv2022

Strange-metal behavior in a Fermi liquid with strange scatterers

A variety of low-temperature, normal-state properties of optimally and overdoped cuprate superconductors, including the DC and optical transport responses, are sufficiently anomalous that they might seem to be inconsistent with any quasiparticle description. However, we show by explicit construction that the most salient phenomena can be accounted for in a system with localized "strange scatterers" embedded into a Fermi liquid with a conventional quasiparticle description. Such scatterers could originate from "two-level systems" associated with an electronic glassy state with short-range charge-order correlations.

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