arXiv subjects

Taylor L. Hughes

Publications and source records attributed to Taylor L. Hughes.

At least 109 records · Page 6Linked to original sources

arXiv2018

Observation of the topological Anderson insulator in disordered atomic wires

Topology and disorder have deep connections and a rich combined influence on quantum transport. In order to probe these connections, we synthesized one-dimensional chiral symmetric wires with controllable disorder via spectroscopic Hamiltonian engineering, based on the laser-driven coupling of discrete momentum states of ultracold atoms. We characterize the system's topology through measurement of the mean chiral displacement of the bulk density extracted from quench dynamics. We find evidence for the topological Anderson insulator phase, in which the band structure of an otherwise trivial wire is driven topological by the presence of added disorder. In addition, we observed the robustness of topological wires to weak disorder and measured the transition to a trivial phase in the presence of strong disorder. Atomic interactions in this quantum simulation platform will enable future realizations of strongly interacting topological fluids.

cond-mat.quant-gas↗

arXiv2017

Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states

The modern theory of electric polarization in crystals associates the dipole moment of an insulator with a Berry phase of its electronic ground state [1, 2]. This concept constituted a breakthrough that not only solved the long-standing puzzle of how to calculate dipole moments in crystals, but also lies at the core of the theory of topological band structures in insulators and superconductors, including the quantum anomalous Hall insulator [3, 4] and the quantum spin Hall insulator [5-7], as well as quantized adiabatic pumping processes [8-10]. A recent theoretical proposal extended the Berry phase framework to account for higher electric multipole moments [11], revealing the existence of topological phases that have not previously been observed. Here we demonstrate the first member of this predicted class -a quantized quadrupole topological insulator- experimentally produced using a GHz-frequency reconfigurable microwave circuit. We confirm the non-trivial topological phase through both spectroscopic measurements, as well as with the identification of corner states that are manifested as a result of the bulk topology. We additionally test a critical prediction that these corner states are protected by the topology of the bulk, and not due to surface artifacts, by deforming the edge between the topological and trivial regimes. Our results provide conclusive evidence of a unique form of robustness which has never previously been observed.

cond-mat.mes-hall↗

arXiv2017

Perturbative and global anomalies in bosonic analogues of integer quantum Hall and topological insulator phases

We study perturbative and global anomalies at the boundaries of bosonic analogues of integer quantum Hall (BIQH) and topological insulator (BTI) phases using a description of the boundaries of these phases in terms of a nonlinear sigma model (NLSM) with Wess-Zumino term. One of the main results of the paper is that these anomalies are robust against arbitrary smooth deformations of the target space of the NLSM which describes the phase, provided that the deformations also respect the symmetry of the phase. In the first part of the paper we discuss the perturbative $U(1)$ anomaly at the boundary of BIQH states in all odd (spacetime) dimensions. In the second part we study global anomalies at the boundary of BTI states in even dimensions. In a previous work [Phys. Rev. B 95, 035149 (2017)] we argued that the boundary of the BTI phase exhibits a global anomaly which is an analogue of the parity anomaly of Dirac fermions in three dimensions. Here we elevate this argument to a proof for the boundary of the two-dimensional BTI state by explicitly computing the partition function of the gauged NLSM describing the boundary. We then use the powerful equivariant localization technique to show that this global anomaly is robust against all smooth deformations of the target space of the NLSM which preserve the $U(1)\rtimes\mathbb{Z}_2$ symmetry of the BTI state. We also comment on the difficulties of generalizing this latter proof to higher dimensions. Finally, we discuss the expected low energy behavior of the boundary theories studied in this paper when the coupling constants are allowed to flow under the renormalization group.

cond-mat.str-el↗

arXiv2017

Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators

We extend the theory of dipole moments in crystalline insulators to higher multipole moments. In this paper, we expand in great detail the theory presented in Ref. 1, and extend it to cover associated topological pumping phenomena, and a novel class of 3D insulator with chiral hinge states. In quantum-mechanical crystalline insulators, higher multipole bulk moments manifest themselves by the presence of boundary-localized moments of lower dimension, in exact correspondence with the electromagnetic theory of classical continuous dielectrics. In the presence of certain symmetries, these moments are quantized, and their boundary signatures are fractionalized. These multipole moments then correspond to new SPT phases. The topological structure of these phases is described by "nested" Wilson loops, which reflect the bulk-boundary correspondence in a way that makes evident a hierarchical classification of the multipole moments. Just as a varying dipole generates charge pumping, a varying quadrupole generates dipole pumping, and a varying octupole generates quadrupole pumping. For non-trivial adiabatic cycles, the transport of these moments is quantized. An analysis of these interconnected phenomena leads to the conclusion that a new kind of Chern-type insulator exists, which has chiral, hinge-localized modes in 3D. We provide the minimal models for the quantized multipole moments, the non-trivial pumping processes and the hinge Chern insulator, and describe the topological invariants that protect them.

cond-mat.mes-hall↗

arXiv2017

Topological Quadrupolar Semimetals

In this work we predict several new types of topological semimetals that exhibit a bulk quadrupole moment. These semimetals are modeled with a 3D extension of the 2D quadrupole topological insulator. One type of semimetal has bulk nodes and gapped, topological surfaces. A second type, which we may call a higher order topological semimetal, has a gapped bulk, but harbors a Dirac semimetal with an even number of nodes on one or more surfaces. The final type has a gapped bulk, but harbors half of a Dirac semimetal on multiple surfaces. Each of these semimetals gives rise to mid-gap hinge states and hinge charge, as well as surface polarization, which are all consequences of a bulk quadrupole moment. We show how the bulk quadrupole moments of these systems can be calculated from the momentum-locations of bulk or surface nodes in the energy spectrum. Finally, we illustrate that in some cases it is useful to examine nodes in the Wannier bands, instead of the energy bands, to extract the bulk quadrupole moment.

cond-mat.mes-hall↗

arXiv2017

Observation of domain wall motion in a polycrystalline vortex lattice

We present measurements showing how disorder determines the dynamics of a vortex lattice. Using superconductor-normal-superconductor (SNS) arrays placed in finite magnetic fields, disorder is introduced by shifting the field away from values where the vortex lattice is commensurate with the SNS array. By applying a current to drive vortex motion, we observe a two-step transition at incommensurate fields: first from pinned vortices to lattice defect motion, and then from individual defect to bulk vortex lattice flow. This behavior is consistent with a polycrystalline vortex structure where defects form on the edges of crystalline domains. This demonstrates that a disordered, interacting vortex system can favor interface physics rather than a quasiperiodic regime.

cond-mat.supr-con↗

arXiv2017

Hall Viscosity and the Acoustic Faraday Effect

For more than 20 years, observation of the non-dissipative Hall viscosity in the quantum Hall effect has been impeded by the difficulty to probe directly the momentum of the two-dimensional electron gas. However, in three-dimensional systems such as superfluid ${}^{3}\mathrm{He}\!\!-\!\!\mathrm{B}$, the momentum density is readily probed through transverse acoustic waves. We show that in a three-dimensional elastic medium supporting transverse waves, a non-vanishing Hall viscosity induces circular birefringence. Such an effect has been observed in ${}^{3}\mathrm{He}\!\!-\!\!\mathrm{B}$ in the presence of a weak magnetic field, and is known as the acoustic Faraday effect. The acoustic Faraday effect has been understood in terms of the Zeeman splitting of the excited order parameter modes which support the transverse wave propagation in the superfluid. We show that the Zeeman effect can generically lead to a non-zero Hall viscosity coefficient, and confirm this prediction using a simple phenomenological model for the ${}^{3}\mathrm{He}\!\!-\!\!\mathrm{B}$ collective modes. Therefore, we claim that the observation of the acoustic Faraday effect can be leveraged to make a direct observation of the Hall viscosity in superfluid ${}^{3}\mathrm{He}\!\!-\!\!\mathrm{B}$ in a magnetic field and other systems such as the crystalline $\mathrm{Tb}_{3}\mathrm{Ga}_{5}\mathrm{O}_{12}$ material.

cond-mat.other↗

arXiv2017

Interface Contributions to Topological Entanglement in Abelian Chern-Simons Theory

We study the entanglement entropy between (possibly distinct) topological phases across an interface using an Abelian Chern-Simons description with topological boundary conditions (TBCs) at the interface. From a microscopic point of view, these TBCs correspond to turning on particular gapping interactions between the edge modes across the interface. However, in studying entanglement in the continuum Chern-Simons description, we must confront the problem of non-factorization of the Hilbert space, which is a standard property of gauge theories. We carefully define the entanglement entropy by using an extended Hilbert space construction directly in the continuum theory. We show how a given TBC isolates a corresponding gauge invariant state in the extended Hilbert space, and hence compute the resulting entanglement entropy. We find that the sub-leading correction to the area law remains universal, but depends on the choice of topological boundary conditions. This agrees with the microscopic calculation of \cite{Cano:2014pya}. Additionally, we provide a replica path integral calculation for the entropy. In the case when the topological phases across the interface are taken to be identical, our construction gives a novel explanation of the equivalence between the left-right entanglement of (1+1)d Ishibashi states and the spatial entanglement of (2+1)d topological phases.

cond-mat.str-el↗

arXiv2017

Canonical quantization of nonlinear sigma models with theta term, with applications to symmetry-protected topological phases

We canonically quantize $O(D+2)$ nonlinear sigma models (NLSMs) with theta term on arbitrary smooth, closed, connected, oriented $D$-dimensional spatial manifolds $\mathcal{M}$, with the goal of proving the suitability of these models for describing symmetry-protected topological (SPT) phases of bosons in $D$ spatial dimensions. We show that in the disordered phase of the NLSM, and when the coefficient $θ$ of the theta term is an integer multiple of $2π$, the theory on $\mathcal{M}$ has a unique ground state and a finite energy gap to all excitations. We also construct the ground state wave functional of the NLSM in this parameter regime, and we show that it is independent of the metric on $\mathcal{M}$ and given by the exponential of a Wess-Zumino term for the NLSM field, in agreement with previous results on flat space. Our results show that the NLSM in the disordered phase and at $θ=2πk$, $k\in\mathbb{Z}$, has a symmetry-preserving ground state but no topological order (i.e., no topology-dependent ground state degeneracy), making it an ideal model for describing SPT phases of bosons. Thus, our work places previous results on SPT phases derived using NLSMs on solid theoretical ground. To canonically quantize the NLSM on $\mathcal{M}$ we use Dirac's method for the quantization of systems with second class constraints, suitably modified to account for the curvature of space. In a series of four appendices we provide the technical background needed to follow the discussion in the main sections of the paper.

cond-mat.str-el↗

arXiv2017

Parafermionic wires at the interface of chiral topological states

We explore a scenario where local interactions form one-dimensional gapped interfaces between a pair of distinct chiral two-dimensional topological states - referred to as phases 1 and 2 - such that each gapped region terminates at a domain wall separating the chiral gapless edge states of these phases. We show that this type of T-junction supports point-like fractionalized excitations obeying parafermion statistics, thus implying that the one-dimensional gapped interface forms an effective topological parafermionic wire possessing a non-trivial ground state degeneracy. The physical properties of the anyon condensate that gives rise to the gapped interface are investigated. Remarkably, this condensate causes the gapped interface to behave as a type of anyon "Andreev reflector" in the bulk, whereby anyons from one phase, upon hitting the interface, can be transformed into a combination of reflected anyons and outgoing anyons from the other phase. Thus, we conclude that while different topological orders can be connected via gapped interfaces, the interfaces are themselves topological.

cond-mat.str-el↗

arXiv2017

Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations

We classify discrete-rotation symmetric topological crystalline superconductors (TCS) in two dimensions and provide the criteria for a zero energy Majorana bound state (MBS) to be present at composite defects made from magnetic flux, dislocations, and disclinations. In addition to the Chern number that encodes chirality, discrete rotation symmetry further divides TCS into distinct stable topological classes according to the rotation eigenspectrum of Bogoliubov-de Gennes quasi-particles. Conical crystalline defects are shown to be able to accommodate robust MBS when a certain combination of these bulk topological invariants is non-trivial as dictated by the index theorems proved within. The number parity of MBS is counted by a $\mathbb{Z}_2$-valued index that solely depends on the disclination and the topological class of the TCS. We also discuss the implications for corner-bound Majorana modes on the boundary of topological crystalline superconductors.

cond-mat.supr-con↗

arXiv2017

Quantized Electric Multipole Insulators

In this article we extend the celebrated Berry-phase formulation of electric polarization in crystals to higher electric multipole moments. We determine the necessary conditions under which, and minimal models in which, the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they manifest topologically protected corner states carrying fractional charge, i.e., fractionalization at the boundary of the boundary. To characterize these new insulating phases of matter, we introduce a new paradigm whereby `nested' Wilson loops give rise to a large number of new topological invariants that have been previously overlooked. We propose three realistic experimental implementations of this new topological behavior that can be immediately tested.

cond-mat.str-el↗

arXiv2016

A Bosonic Analog of a Topological Dirac Semi-Metal: Effective Theory, Neighboring Phases, and Wire Construction

We construct a bosonic analog of a two-dimensional topological Dirac Semi-Metal (DSM). The low-energy description of the most basic 2D DSM model consists of two Dirac cones at positions $\pm\mathbf{k}_0$ in momentum space. The local stability of the Dirac cones is guaranteed by a composite symmetry $Z_2^{\mathcal{TI}}$, where $\mathcal{T}$ is time-reversal and $\mathcal{I}$ is inversion. This model also exhibits interesting time-reversal and inversion symmetry breaking electromagnetic responses. In this work we construct a bosonic version by replacing each Dirac cone with a copy of the $O(4)$ Nonlinear Sigma Model (NLSM) with topological theta term and theta angle $θ=\pm π$. One copy of this NLSM also describes the gapless surface termination of the 3D Bosonic Topological Insulator (BTI). We compute the time-reversal and inversion symmetry breaking electromagnetic responses for our model and show that they are twice the value one gets in the DSM case matching what one might expect from, for example, a bosonic Chern insulator. We also investigate the stability of the BSM model and find that the composite $Z_2^{\mathcal{TI}}$ symmetry again plays an important role. Along the way we clarify many aspects of the surface theory of the BTI including the electromagnetic response, the charges and statistics of vortex excitations, and the stability to symmetry-allowed perturbations. We briefly comment on the relation between the various descriptions of the $O(4)$ NLSM with $θ=π$ used in this paper (a dual vortex description and a description in terms of four massless fermions) and the recently proposed dual description of the BTI surface in terms of $2+1$ dimensional Quantum Electrodynamics with two flavors of fermion ($N=2$ QED$_3$). In a set of four Appendixes we review some of the tools used in the paper, and also derive some of the more technical results.

cond-mat.str-el↗

arXiv2016

Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions

We calculate the topological part of the electromagnetic response of Bosonic Integer Quantum Hall (BIQH) phases in odd (spacetime) dimensions, and Bosonic Topological Insulator (BTI) and Bosonic chiral semi-metal (BCSM) phases in even dimensions. To do this we use the Nonlinear Sigma Model (NLSM) description of bosonic symmetry-protected topological (SPT) phases, and the method of gauged Wess-Zumino (WZ) actions. We find the surprising result that for BIQH states in dimension $2m-1$ ($m=1,2,\dots$), the bulk response to an electromagnetic field $A_μ$ is characterized by a Chern-Simons term for $A_μ$ with a level quantized in integer multiples of $m!$ (factorial). We also show that BTI states (which have an extra $\mathbb{Z}_2$ symmetry) can exhibit a $\mathbb{Z}_2$ breaking Quantum Hall effect on their boundaries, with this boundary Quantum Hall effect described by a Chern-Simons term at level $\frac{m!}{2}$. We show that the factor of $m!$ can be understood by requiring gauge invariance of the exponential of the Chern-Simons term on a general Euclidean manifold, and we also use this argument to characterize the electromagnetic and gravitational responses of fermionic SPT phases with $U(1)$ symmetry in all odd dimensions. We then use our gauged boundary actions for the BIQH and BTI states to (i) construct a bosonic analogue of a chiral semi-metal (BCSM) in even dimensions, (ii) show that the boundary of the BTI state exhibits a bosonic analogue of the parity anomaly of Dirac fermions in odd dimensions, and (iii) study anomaly inflow at domain walls on the boundary of BTI states. In a series of Appendices we derive important formulas and additional results. In particular, in Appendix A we use the connection between equivariant cohomology and gauged WZ actions to give a mathematical interpretation of the actions for the BIQH and BTI boundaries constructed in this paper.

cond-mat.str-el↗

arXiv2016

Topological protection of photonic mid-gap cavity modes

Defect modes in two-dimensional periodic photonic structures have found use in a highly diverse set of optical devices. For example, photonic crystal cavities confine optical modes to subwavelength volumes and can be used for Purcell enhancement of nonlinearity, lasing, and cavity quantum electrodynamics. Photonic crystal fiber defect cores allow for supercontinuum generation and endlessly-single-mode fibers with large cores. However, these modes are notoriously fragile: small changes in the structure can lead to significant detuning of resonance frequency and mode volume. Here, we show that a photonic topological crystalline insulator structure can be used to topologically protect the resonance frequency to be in the middle of the band gap, and therefore minimize the mode volume of a two-dimensional photonic defect mode. We experimentally demonstrate this in a femtosecond-laser-written waveguide array, a geometry akin to a photonic crystal fiber. The topological defect modes are determined by a topological invariant that protects zero-dimensional states (defect modes) embedded in a two-dimensional environment; a novel form of topological protection that has not been previously demonstrated.

cond-mat.mes-hall↗

arXiv2016

Competing Adiabatic Thouless Pumps in Enlarged Parameter Spaces

The transfer of conserved charges through insulating matter via smooth deformations of the Hamiltonian is known as quantum adiabatic, or Thouless, pumping. Central to this phenomenon are Hamiltonians whose insulating gap is controlled by a multi-dimensional (usually two-dimensional) parameter space in which paths can be defined for adiabatic changes in the Hamiltonian, i.e., without closing the gap. Here, we extend the concept of Thouless pumps of band insulators by considering a larger, three-dimensional parameter space. We show that the connectivity of this parameter space is crucial for defining quantum pumps, demonstrating that, as opposed to the conventional two-dimensional case, pumped quantities depend not only on the initial and final points of Hamiltonian evolution but also on the class of the chosen path and preserved symmetries. As such, we distinguish the scenarios of closed/open paths of Hamiltonian evolution, finding that different closed cycles can lead to the pumping of different quantum numbers, and that different open paths may point to distinct scenarios for surface physics. As explicit examples, we consider models similar to simple models used to describe topological insulators, but with doubled degrees of freedom compared to a minimal topological insulator model. The extra fermionic flavors from doubling allow for extra gapping terms/adiabatic parameters - besides the usual topological mass which preserves the topology-protecting discrete symmetries - generating an enlarged adiabatic parameter-space. We consider cases in one and three \emph{spatial} dimensions, and our results in three dimensions may be realized in the context of crystalline topological insulators, as we briefly discuss.

cond-mat.mes-hall↗

arXiv2016

Composite Particle Theory of Three-dimensional Gapped Fermionic Phases: Fractional Topological Insulators and Charge-Loop Excitation Symmetry

Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the low-energy theory of the two-dimensional (2D) toric code model (i.e. the deconfined phase of $\mathbb{Z}_2$ gauge theory) is a $U(1)\times U(1)$ Chern-Simons theory in which gauge charges (i.e., $e$ and $m$ particles) are deconfined and the gauge fields are gapped, while the confined phase is topologically trivial. In this paper, we point out a new route to constructing exotic 3D gapped fermionic phases in a confining phase of a gauge theory. Starting from a parton construction with strongly fluctuating compact $U(1)\times U(1)$ gauge fields, we construct gapped phases of interacting fermions by condensing two linearly independent bosonic composite particles consisting of partons and $U(1)\times U(1)$ magnetic monopoles. This can be regarded as a 3D generalization of the 2D Bais-Slingerland condensation mechanism. Charge fractionalization results from a Debye-Hückel-like screening cloud formed by the condensed composite particles. Within our general framework, we explore two aspects of symmetry-enriched 3D Abelian topological phases. First, we construct a new fermionic state of matter with time-reversal symmetry and $Θ\neq π$, the fractional topological insulator. Second, we generalize the notion of anyonic symmetry of 2D Abelian topological phases to the charge-loop excitation symmetry ($\mathsf{Charles}$) of 3D Abelian topological phases. We show that line twist defects, which realize $\mathsf{Charles}$ transformations, exhibit non-Abelian fusion properties.

cond-mat.str-el↗

arXiv2016

Electromagnetic Response of Three-dimensional Topological Crystalline Insulators

Topological crystalline insulators (TCI) are a new class of materials which have metallic surface states on select surfaces due to point group crystalline symmetries. In this letter, we consider a model for a three-dimensional (3D) topological crystalline insulator with Dirac nodes occurring on a surface that are protected by the mirror and time reversal symmetry. We demonstrate that the electromagnetic response for such a system is characterized by a $1$-form $b_μ$. $b_μ$ can be inferred from the locations of the surface Dirac nodes in energy-momentum space and couples to the surface Dirac nodes like a valley gauge field. From both the effective action and analytical band structure calculations, we show that the vortex core of $\vec b$ or a domain wall of a component of $\vec b$ can trap surface charges.

cond-mat.mes-hall↗