arXiv subjects

Taylor L. Hughes

Publications and source records attributed to Taylor L. Hughes.

At least 127 records · Page 7Linked to original sources

arXiv2016

Response Properties of Axion Insulators and Weyl Semimetals Driven by Screw Dislocations and Dynamical Axion Strings

In this paper, we investigate the theory of dynamical axion string emerging from chiral symmetry breaking in three-dimensional Weyl semimetals. The chiral symmetry is spontaneously broken by a charge density wave (CDW) order which opens an energy gap and converts the Weyl semimetal into an axion insulator. Indeed, the phase fluctuations of the CDW order parameter act as a dynamical axion field $θ({\vec{x}},t)$ and couples to electromagnetic field via $\mathcal{L}_θ=\frac{θ(\vec{x},t)}{32π^2} ε^{στνμ} F_{στ} F_{νμ}.$ Additionally, when the axion insulator is coupled to the background geometry/strain fields via torsional defects, i.e., screw dislocations, there is a novel interplay between the crystal dislocations and dynamical axion strings (i.e., vortices of the CDW order parameter). For example, the screw dislocation traps axial charge, and there is a Berry phase accumulation when an axion string is braided with a screw dislocation. In addition, a cubic coupling between the axial current and the geometry fields is non-vanishing and indicates a Berry phase accumulation during a particular three-loop braiding procedure where a dislocation loop is braided with another dislocation and they are both threaded by an axion string. We also observe a chiral magnetic effect induced by a screw dislocation density in the absence of chemical potential imbalance between Weyl points and describe an additional chiral geometric effect and a geometric Witten effect.

cond-mat.str-el↗

arXiv2016

Topological superconducting phases from inversion symmetry breaking order in spin-orbit-coupled systems

We analyze the superconducting instabilities in the vicinity of the quantum-critical point of an inversion symmetry breaking order. We first show that the fluctuations of the inversion symmetry breaking order lead to two degenerate superconducting (SC) instabilities, one in the $s$-wave channel, and the other in a time-reversal invariant odd-parity pairing channel (the simplest case being the same as the of $^3$He-B phase). Remarkably, we find that unlike many well-known examples, the selection of the pairing symmetry of the condensate is independent of the momentum-space structure of the collective mode that mediates the pairing interaction. We found that this degeneracy is a result of the existence of a conserved fermionic helicity, $χ$, and the two degenerate channels correspond to even and odd combinations of SC order parameters with $χ=\pm1$. As a result, the system has an enlarged symmetry $U(1)\times U(1)$, with each $U(1)\times U(1)$ corresponding to one value of the helicity $χ$. Because of the enlarged symmetry, this system admits exotic topological defects such as a fractional quantum vortex, which we show has a Majorana zero mode bound at its core. We discuss how the enlarged symmetry can be lifted by small perturbations, such as the Coulomb interaction or Fermi surface splitting in the presence of broken inversion symmetry, and we show that the resulting superconducting state can be topological or trivial depending on parameters. The $U(1)\times U(1)$ symmetry is restored at the phase boundary between the topological and trivial SC states, and allows for a transition between topologically distinct SC phases without the vanishing of the order parameter. We present a global phase diagram of the superconducting states and discuss possible experimental implications.

cond-mat.str-el↗

arXiv2016

History-dependent dissipative vortex dynamics in superconducting arrays

We perform current(I)-voltage(V) measurements on low resistance superconductor-normal-superconductor arrays in finite magnetic fields, focusing on the dilute vortex population regime. We observe significant deviations from predicted behavior, notably the absence of a differential resistance peak near the vortex de-pinning current, and a broad linear I-V region with an extrapolated I intercept equal to the de-pinning current. Comparing these results to an overdamped molecular vortex model, we find that this behavior can be explained by the presence of a history dependent dissipative force. This approach has not been considered previously, yet is crucial for obtaining a correct description of the vortex dynamics in superconducting arrays.

cond-mat.supr-con↗

arXiv2016

Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases

In this paper we consider a layered heterostructure of an Abelian topologically ordered state (TO), such as a fractional Chern insulator/quantum Hall state with an s-wave superconductor in order to explore the existence of non-Abelian defects. In order to uncover such defects we must augment the original TO by a $\mathbb{Z}_2$ gauge theory sector coming from the s-wave SC. We first determine the extended TO for a wide variety of fractional quantum Hall or fractional Chern insulator heterostructures. We prove the existence of a general anyon permutation symmetry (AS) that exists in any fermionic Abelian TO state in contact with an s-wave superconductor. Physically this permutation corresponds to adding a fermion to an odd flux vortices (in units of $h/2e$) as they travel around the associated topological (twist) defect. As such, we call it a fermion parity flip AS. We consider twist defects which mutate anyons according to the fermion parity flip symmetry and show that they can be realized at domain walls between distinct gapped edges or interfaces of the TO superconducting state. We analyze the properties of such defects and show that fermion parity flip twist defects are always associated with Majorana zero modes. Our formalism also reproduces known results such as Majorana/parafermionic bound states at superconducting domain walls of topological/Fractional Chern insulators when twist defects are constructed based on charge conjugation symmetry. Finally, we briefly describe more exotic twist liquid phases obtained by gauging the AS where the twist defects become deconfined anyonic excitations.

cond-mat.str-el↗

arXiv2016

Phase diagrams of disordered Weyl semimetals

Weyl semimetals are gapless quasi-topological materials with a set of isolated nodal points forming their Fermi surface. They manifest their quasi-topological character in a series of topological electromagnetic responses including the anomalous Hall effect. Here we study the effect of disorder on Weyl semimetals while monitoring both their nodal/semi-metallic and topological properties through computations of the localization length and the Hall conductivity. We examine three different lattice tight-binding models which realize the Weyl semimetal in part of their phase diagram and look for universal features that are common to all of the models, and interesting distinguishing features of each model. We present detailed phase diagrams of these models for large system sizes and we find that weak disorder preserves the nodal points up to the diffusive limit, but does affect the Hall conductivity. We show that the trend of the Hall conductivity is consistent with an effective picture in which disorder causes the Weyl nodes move within the Brillouin zone along a specific direction that depends deterministically on the properties of the model and the neighboring phases to the Weyl semimetal phase. We also uncover an unusual (non-quantized) anomalous Hall insulator phase which can only exist in the presence of disorder.

cond-mat.mes-hall↗

arXiv2016

Charge density waves in disordered media circumventing the Imry-Ma argument

Two powerful theoretical predictions, Anderson localization and the Imry-Ma argument, impose significant restrictions on the phases of matter that can exist in the presence of even the smallest amount of disorder in one-dimensional systems. These predictions forbid conducting states and ordered states respectively. It was thus remarkable that a mechanism to circumvent Anderson localization relying on the presence of correlated disorder was found, that is also realized in certain biomolecular systems. In a similar manner, we show that the Imry-Ma argument can be circumvented resulting in the formation of stable ordered states with discrete broken symmetries in disordered one dimensional systems. Specifically, we simulate a family of Hamiltonians of spinless fermions with correlated disorder and interactions, where we find that a charge density wave is stable up to a finite critical disorder strength. Having circumvented the Imry-Ma mechanism, we then investigate other mechanisms by which disorder can destroy an ordered state.

cond-mat.dis-nn↗

arXiv2015

Viscoelastic response of topological tight-binding models in two and three dimensions

The topological response to external perturbations is an effective probe to characterize different topological phases of matter. Besides the Hall conductance, the Hall viscosity is another example of such a response that measures how electronic wave functions respond to changes in the underlying geometry. Topological (Chern) insulators are known to have a quantized Hall conductance. A natural question is how the Hall viscosity behaves for these materials. So far, most of studies on the Hall viscosity of Chern insulators have focused on the continuum limit. The presence of lattice breaks the continuous translational symmetry to a discrete group and this causes two complications: it introduces a new length scale associated with the lattice constant, and makes the momentum periodic. We develop two different methods of how to implement a lattice deformation: (1) a lattice distortion is encoded as a shift in the lattice momentum, and (2) a lattice deformation is treated microscopically in the gradient expansion of the hopping matrix elements. After establishing the method of deformation we can compute the Hall viscosity through a linear response (Kubo) formula. We examine these methods for three models: the Hofstadter model, the Chern insulator, and the surface of a 3D topological insulator. Our results in certain regimes of parameters, where the continuum limit is relevant, are in agreement with previous calculations. We also provide possible experimental signatures of the Hall viscosity by studying the phononic properties of a single crystal 3D topological insulator.

cond-mat.mes-hall↗

arXiv2015

Bulk Topological Proximity Effect

Existing proximity effects stem from systems with a local order parameter, such as a local magnetic moment or a local superconducting pairing amplitude. Here, we demonstrate that despite lacking a local order parameter, topological phases also may give rise to a proximity effect of a distinctively inverted nature. We focus on a general construction in which a topological phase is extensively coupled to a second system, and we argue that in many cases, the inverse topological order will be induced on the second system. To support our arguments, we rigorously establish this "bulk topological proximity effect" for all gapped free fermion topological phases and representative integrable models of interacting topological phases. We present a terrace construction which illustrates the phenomenological consequences of this proximity effect. Finally, we discuss generalizations beyond our framework, including how intrinsic topological order may also exhibit this effect.

cond-mat.str-el↗

arXiv2015

Entanglement Entropy & Anomaly Inflow

We study entanglement entropy for parity-violating (time-reversal breaking) quantum field theories on $\mathbb{R}^{1,2}$ in the presence of a domain wall between two distinct parity-odd phases. The domain wall hosts a 1+1-dimensional conformal field theory (CFT) with non-trivial chiral central charge. Such a CFT possesses gravitational anomalies. It has been shown recently that, as a consequence, its intrinsic entanglement entropy is sensitive to Lorentz boosts around the entangling surface. Here, we show using various methods that the entanglement entropy of the three-dimensional bulk theory is also sensitive to such boosts owing to parity-violating effects, and that the bulk response to a Lorentz boost precisely cancels the contribution coming from the domain wall CFT. We argue that this can naturally be interpreted as entanglement inflow (i.e., inflow of entanglement entropy analogous to the familiar Callan-Harvey effect) between the bulk and the domain-wall, mediated by the low-lying states in the entanglement spectrum. These results can be generally applied to 2+1-d topological phases of matter that have edge theories with gravitational anomalies, and provide a precise connection between the gravitational anomaly of the physical edge theory and the low-lying spectrum of the entanglement Hamiltonian.

hep-th↗

arXiv2015

Quasi-Topological Electromagnetic Response of Line-node Semimetals

Topological semimetals are gapless states of matter which have robust surface states and interesting electromagnetic responses. In this paper, we consider the electromagnetic response of gapless phases in $3+1$-dimensions with line nodes. We show through a layering approach that an intrinsic $2$-form ${\cal{B}}_{μν}$ emerges in the effective response field theory that is determined by the geometry and energy-embedding of the nodal lines. This 2-form is shown to be simply related to the charge polarization and orbital magnetization of the sample. We conclude by discussing the relevance for recently proposed materials and heterostructures with line-node fermi-surfaces.

cond-mat.mes-hall↗

arXiv2015

Phase diagram of the $Z_3$ Parafermionic Chain with Chiral Interactions

Parafermions are exotic quasiparticles with non-Abelian fractional statistics that can be realized and stabilized in 1-dimensional models that are generalizations of the Kitaev p-wave wire. We study the simplest generalization, i.e. the $Z_3$ parafermionic chain. Using a Jordan-Wigner transform we focus on the equivalent three-state chiral clock model, and study its rich phase diagram using the density matrix renormalization group technique. We perform our analyses using quantum entanglement diagnostics which allow us to determine phase boundaries, and the nature of the phase transitions. In particular, we study the transition between the topological and trivial phases, as well as to an intervening incommensurate phase which appears in a wide region of the phase diagram. The phase diagram is predicted to contain a Lifshitz type transition which we confirm using entanglement measures. We also attempt to locate and characterize a putative tricritical point in the phase diagram where the three above mentioned phases meet at a single point.

cond-mat.str-el↗

arXiv2015

Theory of Twist Liquids: Gauging an Anyonic Symmetry

Topological phases in (2+1)-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric-magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static point-like objects that permute the labels of orbiting anyons. Gauging these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases referred as twist liquids, which are generically non-Abelian. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. We explicitly demonstrate the gauging of the $\mathbb{Z}_2$-symmetric toric code, $SO(2N)_1$ and $SU(3)_1$ state as well as the $S_3$-symmetric $SO(8)_1$ state and a non-Abelian chiral state we call the "4-Potts" state.

cond-mat.str-el↗

arXiv2015

Hall Viscosity and Momentum Transport in Lattice and Continuum Models of the Integer Quantum Hall Effect in Strong Magnetic Fields

The Hall viscosity describes a non-dissipative response to strain in systems with broken time-reversal symmetry. We develop a new method for computing the Hall viscosity of lattice systems in strong magnetic fields based on momentum transport, which we compare to the method of momentum polarization used by Tu et al. [Phys. Rev. B 88 195412 (2013)] and Zaletel et al. [Phys. Rev. Lett. 110 236801 (2013)] for non-interacting systems. We compare the Hall viscosity of square-lattice tight-binding models in magnetic field to the continuum integer quantum Hall effect (IQHE) showing agreement when the magnetic length is much larger than the lattice constant, but deviation as the magnetic field strength increases. We also relate the Hall viscosity of relativistic electrons in magnetic field (the Dirac IQHE) to the conventional IQHE. The Hall viscosity of the lattice Dirac model in magnetic field agrees with the continuum Dirac Hall viscosity when the magnetic length is much larger than the lattice constant. We also show that the Hall viscosity of the lattice model deviates further from the continuum model if the $C_4$ symmetry of the square lattice is broken to $C_2$, but the deviation is again minimized as the magnetic length increases.

cond-mat.mes-hall↗

arXiv2015

Many-body mobility edge due to symmetry-constrained dynamics and strong interactions

We provide numerical evidence combined with an analytical understanding of the many-body mobility edge for the strongly anisotropic spin-1/2 XXZ model in a random magnetic field. The system dynamics can be understood in terms of symmetry-constrained excitations about parent states with ferromagnetic and anti-ferromagnetic short range order. These two regimes yield vastly different dynamics producing an observable, tunable many-body mobility edge. We compute a set of diagnostic quantities that verify the presence of the mobility edge and discuss how weakly correlated disorder can tune the mobility edge further.

cond-mat.dis-nn↗

arXiv2014

Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases

A given fractional quantum Hall state may admit multiple, distinct edge phases on its boundary. We explore the implications that multiple edge phases have for the entanglement spectrum and entropy of a given bulk state. We describe the precise manner in which the entanglement spectrum depends upon local (tunneling) interactions along an entanglement cut and throughout the bulk. The sensitivity to local conditions near the entanglement cut appears not only in gross features of the spectrum, but can also manifest itself in an additive, positive constant correction to the topological entanglement entropy, i.e., it increases its magnitude. A natural interpretation for this result is that the tunneling interactions across an entanglement cut can function as a barrier to certain types of quasiparticle transport across the cut, thereby, lowering the total entanglement between the two regions.

cond-mat.str-el↗

arXiv2014

Majorana zero modes in dislocations of Sr$_2$RuO$_4$

We study the topologically protected Majorana zero modes induced by lattice dislocations in chiral topological superconductors. Dislocations provide a new way to realize Majorana zero modes at zero magnetic field. In particular, we study several different types of dislocations in the candidate material ${\rm Sr_2RuO_4}.$ We also discuss the properties of linked dislocation lines and linked dislocation and flux lines. Various experimental consequences are predicted which provide a new approach to determine whether nature of the superconducting phase of ${\rm Sr_2RuO_4}.$

cond-mat.supr-con↗

arXiv2014

Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the $ADE$ Classification

We study symmetries and defects of a wide class of two dimensional Abelian topological phases characterized by Lie algebras. We formulate the symmetry group of all Abelian topological field theories. The symmetries relabel quasiparticles (or anyons) but leave exchange and braiding statistics unchanged. Within the class of $ADE$ phases in particular, these anyonic symmetries have a natural origin from the Lie algebra. We classify one dimensional gapped phases along the interface between identical topological states according to symmetries. This classification also applies to gapped edges of a wide range of fractional quantum spin Hall(QSH) states. We show that the edge states of the $ADE$ QSH systems can be gapped even in the presence of time reversal and charge conservation symmetry. We distinguish topological point defects according to anyonic symmetries and bound quasiparticles. Although in an Abelian system, they surprisingly exhibit non-Abelian fractional Majorana-like characteristics from their fusion behavior.

cond-mat.str-el↗

arXiv2014

Interaction Enabled Topological Crystalline Phases

In this article we provide a general mechanism for generating interaction-enabled fermionic topological phases. We illustrate the mechanism with crystalline symmetry-protected topological phases in 1D and 2D. These non-trivial phases require interactions for their existence and, in the cases we consider, the free-fermion classification yields only a trivial phase. Similar to the interpretation of the Kitaev Majorana wire as a mean-field p-wave superconductor Hamiltonian arising from an interacting model with quartic interactions, we show that our systems can be interpreted as "mean-field" charge-$4e$ superconductors arising, e.g., from an interacting model with eight-body interactions, or through another physical mechanism. The quartet superconducting nature allows for the teleportation of full Cooper pairs, and in 2D for interesting semiclassical crystalline defects with non-Abelian anyon boundstates.

cond-mat.str-el↗