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Samuel Lederer

Publications and source records attributed to Samuel Lederer.

18 recordsLinked to original sources
arXiv2022

Unsupervised learning of two-component nematicity from STM data on magic angle bilayer graphene

Moir\'e materials such as magic angle twisted bilayer graphene (MATBG) exhibit remarkable phenomenology, but present significant challenges for certain experimental methods, particularly scanning probes such as scanning tunneling microscopy (STM). Typical STM studies that can image tens of thousands of atomic unit cells can image roughly ten moir\'e cells, making data analysis statistically fraught. Here, we propose a method to mitigate this problem by aggregating STM conductance data from several bias voltages, and then using the unsupervised machine learning method of gaussian mixture model clustering to draw maximal insight from the resulting dataset. We apply this method, using as input coarse-grained bond variables respecting the point group symmetry, to investigate nematic ordering tendencies in MATBG for both charge neutral and hole-doped samples. For the charge-neutral dataset, the clustering reveals the surprising coexistence of multiple types of nematicity that are unrelated by symmetry, and therefore generically nondegenerate. By contrast, the clustering in the hole doped data is consistent with long range order of a single type. Beyond its value in analyzing nematicity in MATBG, our method has the potential to enhance understanding of symmetry breaking and its spatial variation in a variety of moir\'e materials.

cond-mat.str-el↗
arXiv2021

Quantum critical fluctuations in an Fe-based superconductor

Quantum critical fluctuations may prove to play an instrumental role in the formation of unconventional superconductivity. Here, we show that the characteristic scaling of a marginal Fermi liquid is present in inelastic light scattering data of an Fe-based superconductor tuned through a quantum critical point (QCP) by chemical substitution or doping. From the doping dependence of the imaginary time dynamics we are able to distinguish regions dominated by quantum critical behavior from those having classical critical responses. This dichotomy reveals a connection between the marginal Fermi liquid behavior and quantum criticality. In particular, the overlap between regions of high superconducting transition temperatures and quantum critical scaling suggests a contribution from quantum fluctuations to the formation of superconductivity.

cond-mat.supr-con↗
arXiv2021

Hamiltonian reconstruction as metric for variational studies

Variational approaches are among the most powerful modern techniques to approximately solve quantum many-body problems. These encompass both variational states based on tensor or neural networks, and parameterized quantum circuits in variational quantum eigensolvers. However, self-consistent evaluation of the quality of variational wavefunctions is a notoriously hard task. Using a recently developed Hamiltonian reconstruction method, we propose a multi-faceted approach to evaluating the quality of neural-network based wavefunctions. Specifically, we consider convolutional neural network (CNN) and restricted Boltzmann machine (RBM) states trained on a square lattice spin-1/2 $J_1$-$J_2$ Heisenberg model. We find that the reconstructed Hamiltonians are typically less frustrated, and have easy-axis anisotropy near the high frustration point. Furthermore, the reconstructed Hamiltonians suppress quantum fluctuations in the large $J_2$ limit. Our results highlight the critical importance of the wavefunction's symmetry. Moreover, the multi-faceted insight from the Hamiltonian reconstruction reveals that a variational wave function can fail to capture the true ground state through suppression of quantum fluctuations.

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arXiv2020

Observation of non-Fermi liquid physics in a quantum critical metal via quantum loop topography

Non-Fermi liquid physics is a ubiquitous feature in strongly correlated metals, manifesting itself in anomalous transport properties, such as a $T$-linear resistivity in experiments. However, its theoretical understanding in terms of microscopic models is lacking despite decades of conceptual work and attempted numerical simulations. Here we demonstrate that a combination of sign problem-free quantum Monte Carlo sampling and quantum loop topography, a physics-inspired machine learning approach, can map out the emergence of non-Fermi liquid physics in the vicinity of a quantum critical point with little prior knowledge. Using only three parameter points for training the underlying neural network, we are able to reproducibly identify a stable non-Fermi liquid regime tracing the fan of a metallic quantum critical points at the onset of both spin-density wave and nematic order. Our study thereby provides an important proof-of-principle example that new physics can be detected via unbiased machine-learning approaches.

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arXiv2019

Quantum aspects of "hydrodynamic" transport from weak electron-impurity scattering

Recent experimental observations of apparently hydrodynamic electronic transport have generated much excitement. However, the understanding of the observed non-local transport (whirlpool) effects and parabolic (Poiseuille-like) current profiles has largely been motivated by a phenomenological analogy to classical fluids. This is due to difficulty in incorporating strong correlations in quantum mechanical calculation of transport, which has been the primary angle for interpreting the apparently hydrodynamic transport. Here we demonstrate that even free fermion systems, in the presence of (inevitable) disorder, exhibit non-local conductivity effects such as those observed in experiment because of the fermionic system's long-range entangled nature. On the basis of explicit calculations of the conductivity at finite wavevector, $\sigma({\bf q})$, for selected weakly disordered free fermion systems, we propose experimental strategies for demonstrating distinctive quantum effects in non-local transport at odds with the expectations of classical kinetic theory. Our results imply that the observation of whirlpools or other "hydrodynamic" effects does not guarantee the dominance of electron-electron scattering over electron-impurity scattering.

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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.

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arXiv2018

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.

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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 $\phi$, which undergoes a continuous transition towards nematic order with $d-$wave form-factor. We consider two cases: (a) when $\phi$ 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 $\Pi (q, \Omega)$ remains finite even at $q=0$. The polarization $\Pi (0, \Omega)$ has similar behavior in the two cases, but the relations between $\Pi (0, \Omega)$ and the bosonic susceptibility $\chi (0, \Omega)$ are different, leading to different forms of $\chi^{\prime \prime} (0, \Omega)$, 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

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: $\Pi(\mathbf{q} = 0,\Omega_m) \neq 0$. 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 $\Pi (\mathbf{q} = 0,\Omega_m) \neq 0$ over a parametrically broad range of frequencies where the fermionic self-energy $\Sigma (\omega)$ is irrelevant, and use Eliashberg theory to compute $\Pi (\mathbf{q} = 0,\Omega_m)$ in the non-Fermi liquid regime at smaller frequencies, where $\Sigma (\omega) > \omega$. We find that $\Pi(\mathbf{q}=0,\Omega)$ is a constant, plus a frequency dependent correction that goes as $|\Omega|$ at high frequencies, crossing over to $|\Omega|^{1/3}$ at lower frequencies. The $|\Omega|^{1/3}$ scaling holds also in a non-Fermi liquid regime. The non-vanishing of $\Pi (\mathbf{q}=0, \Omega)$ gives rise to additional structure in the imaginary part of the nematic susceptibility $\chi^{''} (\mathbf{q}, \Omega)$ at $\Omega > v_F q$, 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.

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arXiv2017

Theory of anomalous magnetotransport from mass anisotropy

In underdoped YBa$_2$Cu$_3$O$_{6+x}$, there is evidence of a small Fermi surface pocket subject to substantial mass enhancement in the doping regime $ 0.12<p<0.16$. This mass enhancement may vary substantially over the Fermi surface, due to "hot spot" or other relevant physics. We therefore examine the magnetotransport of an electron-like Fermi pocket with large effective mass anisotropy. Within the relaxation time approximation, we show that even for a pocket with a fixed shape, the magnitude and sign of the Hall effect may change as the mass anisotropy changes (except at very large, likely inaccessible magnetic fields). We discuss implications for recent Hall measurements in near optimally doped cuprates in high fields. In addition we identify a novel intermediate asymptotic regime of magnetic field, characterized by B-linear magnetoresistance. Similar phenomena should occur in a variety of other experimental systems with anisotropic mass enhancement

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arXiv2016

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.

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arXiv2015

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↗
arXiv2014

Non-topological nature of the edge current in a chiral p-wave superconductor

The edges of time reversal symmetry breaking topological superconductors support chiral Majorana bound states as well as spontaneous charge currents. The Majorana modes are a robust, topological property, but the charge currents are non-topological--and therefore sensitive to microscopic details--even if we neglect Meissner screening. We give insight into the non-topological nature of edge currents in chiral p-wave superconductors using a variety of theoretical techniques, including lattice Bogoliubov-de Gennes equations, the quasiclassical approximation, and the gradient expansion, and describe those special cases where edge currents do have a topological character. While edge currents are not quantized, they are generically large, but can be substantially reduced for a sufficiently anisotropic gap function, a scenario of possible relevance for the putative chiral p-wave superconductor Sr$_2$RuO$_4$.

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arXiv2014

Enhancement of superconductivity near a nematic quantum critical point

We consider a low $T_c$ metallic superconductor weakly coupled to the soft fluctuations associated with proximity to a nematic quantum critical point (NQCP). We show that: 1) a BCS-Eliashberg treatment remains valid outside of a parametrically narrow interval about the NQCP; 2) the symmetry of the superconducting state (d-wave, s-wave, p-wave) is typically determined by the non-critical interactions, but $T_c$ is enhanced by the nematic fluctuations in all channels; 3) in 2D, this enhancement grows upon approach to criticality up to the point at which the weak coupling approach breaks-down, but in 3D the enhancement is much weaker.

cond-mat.supr-con↗
arXiv2014

Suppression of spontaneous currents in Sr$_2$RuO$_4$ by surface disorder

A major challenge to the chiral $p$-wave hypothesis for the pairing symmetry of the unconventional superconductor Sr$_2$RuO$_4$ is the null result of sensitive scanning magnetometry experiments designed to detect the expected spontaneous charge currents. Motivated by junction tunneling conductance measurements which indicate the quenching of superconductivity at the surfaces of even high-purity samples, we examine the spontaneous currents in a chiral $p$-wave superconductor near a normal metal / superconductor interface using the lattice Bogoliubov-de Gennes equations and Ginzburg-Landau theory, and find that the edge current is suppressed by more than an order of magnitude compared to previous estimates. These calculations demonstrate that interface details can have a quantitatively meaningful effect on the expectations for magnetometry experiments.

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arXiv2012

Theory of `hidden' quasi-1D superconductivity in Sr$_2$RuO$_4$

Is the mechanism of unconventional superconductivity in Sr$_2$RuO$_4$ closer in spirit to superfluid $^3$He, or to the cuprates, pnictides, and organic superconductors? We challenge prevailing assumptions in this field and using well-controlled perturbative renormalization group calculations, we suggest that superconductivity in Sr$_2$RuO$_4$ resembles more closely the quasi-one dimensional organic superconductors. Our theory has certain phenomenological consequences that are consistent with the experimentally observed phenomena.

cond-mat.supr-con↗
arXiv2011

Observable NMR signal from circulating current order in YBCO

Assuming, as suggested by recent neutron scattering experiments, that a broken symmetry state with orbital current order occurs in the pseudo-gap phase of the cuprate superconductors, we show that there must be associated equilibrium magnetic fields at various atomic sites in the unit cell, which should be detectable by NMR experiments.

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