arXiv subjects

Charles L. Kane

Publications and source records attributed to Charles L. Kane.

At least 19 recordsLinked to original sources

arXiv2026

Observation of magnetically switchable quantum geometric photocurrents

In non-centrosymmetric materials, light can be rectified into two types of DC photocurrents, known as injection and shift currents, through the bulk photovoltaic effect. Recent theory has uncovered their deep relation with the two-state quantum geometry of resonant transitions: In non-magnetic crystals, where these currents have been routinely observed, the injection current responds to circular light and probes the Berry curvature, while the shift current responds to linear light and probes the geometric connection. Magnetic crystals have been predicted to show a new set of hitherto unobserved magnetically switchable photocurrents, with the roles of linear and circular light interchanged: A linear injection current, which probes the quantum metric, and a circular shift current, which probes the geometric torsion. In this work, we demonstrate the existence of such currents for the first time, demonstrating the switching of the current by flipping the Néel vector in a van der Waals antiferromagnet. Furthermore, their specific frequency and temperature dependence confirm the assignment of circular shift and linear injection currents. Our work demonstrates a new way to control photocurrents in magnets that are directly tied to geometry and have promising applications in antiferromagnetic spintronics and light harvesting.

cond-mat.mtrl-sci↗

arXiv2026

Singular three-point density correlations in two-dimensional Fermi liquids

We characterize a singularity in the equal-time three-point density correlations that is generic to two-dimensional interacting Fermi liquids. In momentum space where the three-point correlation is determined by two wavevectors $\mathbf{q}_1$ and $\mathbf{q}_2$, the singularity takes the form $|\mathbf{q}_1\times\mathbf{q}_2|$. We explain how this singularity is sharply defined in a long-wavelength collinear limit. For a non-interacting Fermi gas, the coefficient of this singularity is given by the quantized Euler characteristic of the Fermi sea, and it implies a long-range real space correlation favoring collinear configurations. We show that this singularity persists in interacting Fermi liquids, and express the renormalization of the coefficient of singularity in terms of Landau parameters, for both spinless and spinful Fermi liquids. Implications for quantum gas experiments are discussed.

cond-mat.str-el↗

arXiv2025

Probing the Fermi Sea Topology in a Quantum Gas

Pauli's exclusion principle forces fermions to occupy distinct quantum states, creating a filled region of momentum space at low temperature, the Fermi sea, whose topology governs the system's response to perturbations and the nature of its correlation functions. Recent theory predicts that for non-interacting fermions, the Euler characteristic of a $D$-dimensional Fermi sea -- the topological invariant that describes its shape -- is encoded in its ($D$+1)-point density correlations. Here we experimentally demonstrate this connection in a two-dimensional degenerate gas of neutral $^{6}$Li atoms using single-atom-resolved imaging. By measuring three- and four-point connected density correlations in real space, we directly extract topological invariants of the underlying Fermi sea, including the Euler characteristic. Our results are in remarkable agreement with ideal-gas predictions, despite the presence of sizeable interactions, and establish a new pathway for probing many-body topology through correlation measurements.

cond-mat.quant-gas↗

arXiv2023

Topological Density Correlations in a Fermi Gas

A Fermi gas of non-interacting electrons, or ultra-cold fermionic atoms, has a quantum ground state defined by a region of occupancy in momentum space known as the Fermi sea. The Euler characteristic $χ_F$ of the Fermi sea serves to topologically classify these gapless fermionic states. The topology of a $D$ dimensional Fermi sea is physically encoded in the $D+1$ point equal time density correlation function. In this work, we first present a simple proof of this fact by showing that the evaluation of the correlation function can be formulated in terms of a triangulation of the Fermi sea with a collection of points, links and triangles and their higher dimensional analogs. We then make use of the topological $D+1$ point density correlation to reveal universal structures of the more general $M$ point density correlation functions in a $D$ dimensional Fermi gas. Two experimental methods are proposed for observing these correlations in $D=2$. In cold atomic gases imaged by quantum gas microscopy, our analysis supports the feasibility of measuring the third order density correlation, from which $χ_F$ can be reliably extracted in systems with as few as around 100 atoms. For solid-state electron gases, we propose measuring correlations in the speckle pattern of intensity fluctuations in nonlinear X-ray scattering experiments.

cond-mat.quant-gas↗

arXiv2023

Topological Andreev Rectification

We develop the theory of an Andreev junction, which provides a method to probe the intrinsic topology of the Fermi sea of a two-dimensional electron gas (2DEG). An Andreev junction is a Josephson $π$ junction proximitizing a ballistic 2DEG, and exhibits low-energy Andreev bound states that propagate $\textit{along}$ the junction. It has been shown that measuring the nonlocal Landauer conductance due to these Andreev modes in a narrow linear junction leads to a topological Andreev rectification (TAR) effect characterized by a quantized conductance that is sensitive to the Euler characteristic $χ_F$ of the 2DEG Fermi sea. Here we expand on that analysis and consider more realistic device geometries that go beyond the narrow linear junction and fully adiabatic limits considered earlier. Wider junctions exhibit additional Andreev modes that contribute to the transport and degrade the quantization of the conductance. Nonetheless, we show that an appropriately defined $\textit{rectified conductance}$ remains robustly quantized provided large momentum scattering is suppressed. We verify and demonstrate these predictions by performing extensive numerical simulations of realistic device geometries. We introduce a simple model system that demonstrates the robustness of the rectified conductance for wide linear junctions as well as point contacts, even when the nonlocal conductance is not quantized. Motivated by recent experimental advances, we model devices in specific materials, including InAs quantum wells, as well as monolayer and bilayer graphene. These studies indicate that for sufficiently ballistic samples observation of the TAR effect should be within experimental reach.

cond-mat.mes-hall↗

arXiv2023

Probing Fermi sea topology by Andreev state transport

We show that the topology of the Fermi sea of a two-dimensional electron gas (2DEG) is reflected in the ballistic Landauer transport along a long and narrow Josephson $π$-junction that proximitizes the 2DEG. The low-energy Andreev states bound to the junction are shown to exhibit a dispersion that is sensitive to the Euler characteristic of the Fermi sea ($χ_F$). We highlight two important relations: one connects the electron/hole nature of Andreev states to the convex/concave nature of Fermi surface critical points, and one relates these critical points to $χ_F$. We then argue that the transport of Andreev states leads to a quantized conductance that probes $χ_F$. An experiment is proposed to measure this effect, from which we predict an $I$-$V$ characteristic that not only captures the topology of Fermi sea in metals, but also resembles the rectification effect in diodes. Finally, we evaluate the feasibility of measuring this quantized response in graphene, InAs and HgTe 2DEGs.

cond-mat.mes-hall↗

arXiv2023

Observation of the superconducting proximity effect from surface states in SmB$_6$/YB$_6$ thin film heterostructures via terahertz spectroscopy

The AC conduction of epitaxially-grown SmB$_6$ thin films and superconducting heterostructures of SmB$_6$/YB$_6$ are investigated via time domain terahertz spectroscopy. A two-channel model of thickness-dependent bulk states and thickness-independent surface states accurately describes the measured conductance of bare SmB$_6$ thin films, demonstrating the presence of surface states in SmB$_6$. While the observed reductions in the simultaneously-measured superconducting gap, transition temperature, and superfluid density of SmB$_6$/YB$_6$ heterostructures relative to bare YB$_6$ indicate the penetration of proximity-induced superconductivity into the SmB$_6$ overlayer; the corresponding SmB$_6$-thickness independence between different heterostructures indicates that the induced superconductivity is predominantly confined to the interface surface state of the SmB$_6$. This study demonstrates the ability of terahertz spectroscopy to probe proximity-induced superconductivity at an interface buried within a heterostructure, and our results show that SmB$_6$ behaves as a predominantly insulating bulk surrounded by conducting surface states in both the normal and induced-superconducting states in both terahertz and DC responses, which is consistent with the topological Kondo insulator picture.

cond-mat.mtrl-sci↗

arXiv2022

Topological Multipartite Entanglement in a Fermi Liquid

We show that the topology of the Fermi sea of a $D$-dimensional Fermi gas is reflected in the multipartite entanglement characterizing $D+1$ regions that meet at a point. For odd $D$ we introduce the multipartite mutual information, and show that it exhibits a $\log^D L$ divergence as a function of system size $L$ with a universal coefficient that is proportional to the Euler characteristic $χ_F$ of the Fermi sea. This provides a generalization, for a Fermi gas, of the well-known result for $D=1$ that expresses the $\log L$ divergence of the bipartite entanglement entropy in terms of the central charge $c$ characterizing a conformal field theory. For even $D$ we introduce a charge-weighted entanglement entropy that is manifestly odd under a particle-hole transformation. We show that the corresponding charge-weighted mutual information exhibits a similar $\log^D L$ divergence proportional to $χ_F$. Our analysis relates the universal behavior of the multipartite mutual information in the absence of interactions to the $D+1$'th order equal-time density correlation function, which we show exhibits a universal behavior in the long wavelength limit proportional to $χ_F$. Our analytic results are based on the replica method. In addition we perform a numerical study of the charge-weighted mutual information for $D=2$ that confirms several aspects of the analytic theory. Finally, we consider the effect of interactions perturbatively within the replica theory. We show that for $D=3$ the $\log^3 L$ divergence of the topological mutual information is not perturbed by weak short-ranged interactions, though for $D=2$ the charge-weighted mutual information is perturbed. Thus, for $D=3$ the multipartite mutual information provides a robust classification that distinguishes distinct topological Fermi liquid phases.

cond-mat.mes-hall↗

arXiv2022

Translation symmetry-enriched toric code insulator

We introduce a two-dimensional electronic insulator that possesses a toric code topological order enriched by translation symmetry. This state can be realized from disordering a weak topological superconductor by double-vortex condensation. It is termed the toric code insulator, whose anyonic excitations consist of a charge-$e$ chargon, a neutral fermion and two types of visons. There are two types of visons because they have constrained motion as a consequence of the fractional Josephson effect of one-dimensional topological superconductor. Importantly, these two types of visons are related by a discrete translation symmetry and have a mutual semionic braiding statistics, leading to a symmetry-enrichment akin to the type in Wen's plaquette model and Kitaev's honeycomb model. We construct this state using a three-fluid coupled-wire model, and analyze the anyon spectrum and braiding statistics in detail to unveil the nature of symmetry-enrichment due to translation. We also discuss potential material realizations and present a band-theoretic understanding of the state, fitting it into a general framework for studying fractionalizaton in strongly-interacting weak topological phases.

cond-mat.str-el↗

arXiv2021

Direct imaging of antiferromagnetic domains and anomalous layer-dependent mirror symmetry breaking in atomically thin MnPS$_3$

We have developed a sensitive cryogenic second-harmonic generation microscopy to study a van der Waals antiferromagnet MnPS$_3$. We find that long-range Néel antiferromagnetic order develops from the bulk crystal down to the bilayer, while it is absent in the monolayer. Before entering the long-range antiferromagnetic ordered phase in all samples, an upturn of the second harmonic generation below 200 K indicates the formation of the short-range order and magneto-elastic coupling. We also directly image the two antiphase (180$^{\circ}$) antiferromagnetic domains and thermally-induced domain switching down to bilayer. An anomalous mirror symmetry breaking shows up in samples thinner than ten layers for the temperature both above and below the Néel temperature, which indicates a structural change in few-layer samples. Minimal change of the second harmonic generation polar patterns in strain tuning experiments indicate that the symmetry crossover at ten layers is most likely an intrinsic property of MnPS$_3$ instead of an extrinsic origin of substrate-induced strain. Our results show that second harmonic generation microscopy is a direct tool for studying antiferromagnetic domains in atomically thin materials, and opens a new way to study two-dimensional antiferromagnets.

cond-mat.mtrl-sci↗

arXiv2021

Non-diagonal anisotropic quantum Hall states

We propose a family of Abelian quantum Hall states termed the non-diagonal states, which arise at filling factors $ν=p/2q$ for bosonic systems and $ν=p/(p+2q)$ for fermionic systems, with $p$ and $q$ being two coprime integers. Non-diagonal quantum Hall states are constructed in a coupled wire model, which shows an intimate relation to the non-diagonal conformal field theory and has a constrained pattern of motion for bulk quasiparticles, featuring a non-trivial interplay between charge symmetry and translation symmetry. The non-diagonal state is established as a distinctive symmetry-enriched topological order. Aside from the usual $U(1)$ charge sector, there is an additional symmetry-enriched neutral sector described by the quantum double model $\mathcal{D}(\mathbb{Z}_p)$, which relies on the presence of both the $U(1)$ charge symmetry and the $\mathbb{Z}$ translation symmetry of the wire model. Translation symmetry distinguishes non-diagonal states from Laughlin states, in a way similar to how it distinguishes weak topological insulators from trivial band insulators. Moreover, the translation symmetry in non-diagonal states can be associated to the $\mathbf{e}\leftrightarrow\mathbf{m}$ anyonic symmetry in $\mathcal{D}(\mathbb{Z}_p)$, implying the role of dislocations as two-fold twist-defects. The boundary theory of non-diagonal states is derived microscopically. For the edge perpendicular to the direction of wires, the effective Hamiltonian has two components: a chiral Luttinger liquid and a generalized $p$-state clock model. Importantly, translation symmetry in the bulk is realized as self-duality on the edge. The symmetric edge is thus either gapless or gapped with spontaneously broken symmetry. For $p=2,3$, the respective electron tunneling exponents are predicted for experimental probes.

cond-mat.str-el↗

arXiv2019

Coupled Wire Model of $Z_2 \times Z_2$ Orbifold Quantum Hall States

We construct a coupled wire model for a sequence of non-Abelian quantum Hall states occurring at filling factors $ν=2/(2M+q)$ with integers $M$ and even(odd) integers $q$ for fermionic(bosonic) states. They are termed $Z_2 \times Z_2$ orbifold states, which have a topological order with a neutral sector described by the $c=1$ orbifold conformal field theory (CFT) at radius $R_{\rm orbifold}=\sqrt{p/2}$ with even integers $p$. When $p=2$, the state can be viewed as two decoupled layers of Moore-Read (MR) state, whose neutral sector is described by the Ising $\times$ Ising CFT and contains a $Z_2 \times Z_2$ fusion subalgebra. We demonstrate that orbifold states with $p>2$, also containing a $Z_2 \times Z_2$ fusion algebra, can be obtained by coupling together an array of MR $\times$ MR wires through local interactions. The corresponding charge spectrum of quasiparticles is also examined. The orbifold states constructed here are complementary to the $Z_4$ orbifold states, whose neutral edge theory is described by orbifold CFT with odd integer $p$ and contains a $Z_4$ fusion algebra.

cond-mat.str-el↗

arXiv2018

Coupled Wire Model of Z4 Orbifold Quantum Hall States

We introduce a coupled wire model for a sequence of non-Abelian quantum Hall states that generalize the Z4 parafermion Read Rezayi state. The Z4 orbifold quantum Hall states occur at filling factors ν= 2/(2m-p) for odd integers $m$ and $p$, and have a topological order with a neutral sector characterized by the orbifold conformal field theory with central charge $c=1$ at radius $R=\sqrt{p/2}$. When $p=1$ the state is Abelian. The state with $p=3$ is the $Z_4$ Read Rezayi state, and the series of $p\ge 3$ defines a sequence of non-Abelian states that resembles the Laughlin sequence. Our model is based on clustering of electrons in groups of four, and is formulated as a two fluid model in which each wire exhibits two phases: a weak clustered phase, where charge $e$ electrons coexist with charge $4e$ bosons and a strong clustered phase where the electrons are strongly bound in groups of 4. The transition between these two phases on a wire is mapped to the critical point of the 4 state clock model, which in turn is described by the orbifold conformal field theory. For an array of wires coupled in the presence of a perpendicular magnetic field, strongly clustered wires form a charge $4e$ bosonic Laughlin state with a chiral charge mode at the edge, but no neutral mode and a gap for single electrons. Coupled wires near the critical state form quantum Hall states with a gapless neutral mode described by the orbifold theory. The coupled wire approach allows us to employ the Abelian bosonization technique to fully analyze the physics of single wire, and then to extract most topological properties of the resulting non-Abelian quantum Hall states. These include the list of quasiparticles, their fusion rules, the correspondence between bulk quasiparticles and edge topological sectors, and most of the phases associated with quasiparticles winding one another.

cond-mat.str-el↗

arXiv2018

Spatially dispersive circular photogalvanic effect in a Weyl semimetal

Weyl semimetals are gapless topological states of matter with broken inversion and/or time reversal symmetry, which can support unconventional responses to externally applied electrical, optical and magnetic fields. Here we report a new photogalvanic effect in type-II WSMs, MoTe2 and Mo0.9W0.1Te2, which are observed to support a circulating photocurrent when illuminated by circularly polarized light at normal incidence. This effect occurs exclusively in the inversion broken phase, where crucially we find that it is associated with a spatially varying beam profile via a new dispersive contribution to the circular photogalvanic effect (s-CPGE). The response functions derived for s-CPGE reveal the microscopic mechanism of this photocurrent, which are controlled by terms that are allowed in the absence of inversion symmetry, along with asymmetric carrier excitation and relaxation. By evaluating this response for a minimal model of a Weyl semimetal, we obtain the frequency dependent scaling behavior of this form of photocurrent. These results demonstrate opportunities for controlling photoresponse by patterning optical fields to store, manipulate and transmit information over a wide spectral range.

cond-mat.mtrl-sci↗

arXiv2017

Pairing in Luttinger Liquids and Quantum Hall States

We study spinless electrons in a single channel quantum wire interacting through attractive interaction, and the quantum Hall states that may be constructed by an array of such wires. For a single wire the electrons may form two phases, the Luttinger liquid and the strongly paired phase. The Luttinger liquid is gapless to one- and two-electron excitations, while the strongly paired state is gapped to the former and gapless to the latter. In contrast to the case in which the wire is proximity-coupled to an external superconductor, for an isolated wire there is no separate phase of a topological, weakly paired, superconductor. Rather, this phase is adiabatically connected to the Luttinger liquid phase. The properties of the one dimensional topological superconductor emerge when the number of channels in the wire becomes large. The quantum Hall states that may be formed by an array of single-channel wires depend on the Landau level filling factors. For odd-denominator fillings $ν=1/(2n+1)$, wires at the Luttinger phase form Laughlin states while wires in the strongly paired phase form bosonic fractional quantum Hall state of strongly-bound pairs at a filling of $1/(8n+4)$. The transition between the two is of the universality class of Ising transitions in three dimensions. For even-denominator fractions $ν=1/2n$ the two single-wire phases translate into four quantum Hall states. Two of those states are bosonic fractional quantum Hall states of weakly- and strongly- bound pairs of electrons. The other two are non-Abelian quantum Hall states, which originate from coupling wires close to their critical point. One of these non-Abelian states is the Moore-Read state. The transition between all these states are of the universality class of Majorana transitions. We point out some of the properties that characterize the different phases and the phase transitions.

cond-mat.str-el↗

arXiv2016

Topological classification of crystalline insulators through band structure combinatorics

We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure. The algorithm applies to crystals with broken time-reversal, particle-hole, and chiral symmetries in any dimension. The presented results match the mathematical structure underlying the topological classification of these crystals in terms of K-theory, and therefore elucidate this abstract mathematical framework from a simple combinatorial perspective. Using a straightforward counting procedure, we classify the allowed topological phases in any possible two-dimensional crystal in class A. We also show how the same procedure can be used to classify the allowed phases for any three-dimensional space group. Employing these classifications, we study transitions between topological phases within class A that are driven by band inversions at high symmetry points in the first Brillouin zone. This enables us to list all possible types of phase transitions within a given crystal structure, and identify whether or not they give rise to intermediate Weyl semimetallic phases.

cond-mat.mes-hall↗

arXiv2016

Mechanical Graphene

We present a model of a mechanical system with a vibrational mode spectrum identical to the spectrum of electronic excitations in a tight-binding model of graphene. The model consists of point masses connected by elastic couplings, called "tri-bonds," that implement certain three-body interactions, which can be tuned by varying parameters that correspond to the relative hopping amplitudes on the different bond directions in graphene. In the mechanical model, this is accomplished by varying the location of a pivot point that determines the allowed rigid rotations of a single tri-bond. The infinite system constitutes a Maxwell lattice, with the number of degrees of freedom equal to the number of constraints imposed by the tri-bonds. We construct the equilibrium and compatibility matrices and analyze the model's phase diagram, which includes spectra with Weyl points for some placements of the pivot and topologically polarized phases for others. We then discuss the edge modes and associated states of self stress for strips cut from the periodic lattice. Finally, we suggest a physical realization of the tri-bond, which allows access to parameter regimes not available to experiments on (strained) graphene and may be used to create other two-dimensional mechanical metamaterials with different spectral features.

cond-mat.soft↗

arXiv2015

Dirac Semimetals in Two Dimensions

Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature Dirac cones at high-symmetry points that are \emph{not} gapped by spin-orbit interactions, and exhibit behavior distinct from both graphene and 3D Dirac semimetals. Using a two-site tight-binding model, we construct representatives of three possible distinct Dirac semimetal phases, and show that single symmetry-protected Dirac points are impossible in two dimensions. An essential role is played by the presence of non-symmorphic space group symmetries. We argue that these symmetries tune the system to the boundary between a 2D topological and trivial insulator. By breaking the symmetries we are able to access trivial and topological insulators as well as Weyl semimetal phases.

cond-mat.mtrl-sci↗