arXiv subjects

Jeffrey C. Y. Teo

Publications and source records attributed to Jeffrey C. Y. Teo.

At least 37 records · Page 2Linked to original sources

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

Topological Phases on Non-orientable Surfaces: Twisting by Parity Symmetry

We discuss (2+1)D topological phases on non-orientable spatial surfaces, such as Möbius strip, real projective plane and Klein bottle, etc., which are obtained by twisting the parent topological phases by their underlying pairty symmetries through introducing parity defects. We construct the ground states on arbitrary non-orientable closed manifolds and calculate the ground state degeneracy. Such degeneracy is shown to be robust against continuous deformation of the underlying manifold. We also study the action of the mapping class group on the multiplet of ground states on the Klein bottle. The physical properties of the topological states on non-orientable surfaces are deeply related to the parity symmetric anyons which do not have a notion of orientation in their statistics. The number of ground states on the projective plane equals the root of the number of distinguishable parity symmetric anyons, while the ground state degeneracy on the Klein bottle equals the total number of parity symmetric anyons; In deforming the Klein bottle, the Dehn twist encodes the topological spins whereas the Y-homeomorphism tells the particle-hole relation of the parity symmetric anyons.

cond-mat.str-el↗

arXiv2015

Globally symmetric topological phase: from anyonic symmetry to twist defect

Topological phases in two dimensions support anyonic quasiparticle excitations that obey neither bosonic nor fermionic statistics. These anyon structures often carry global symmetries that relate distinct anyons with similar fusion and statistical properties. Anyonic symmetries associate topological defects or fluxes in topological phases. As the symmetries are global and static, these extrinsic defects are semiclassical objects that behave disparately from conventional quantum anyons. Remarkably, even when the topological states supporting them are Abelian, they are generically non-Abelian and powerful enough for topological quantum computation. In this article, I review the most recent theoretical developments on symmetries and defects in topological phases.

cond-mat.str-el↗

arXiv2015

Coupled wire model of symmetric Majorana surfaces of topological superconductors

Time reversal symmetric topological superconductors in three spatial dimensions carry gapless surface Majorana fermions. They are robust against any time reversal symmetric single-body perturbation weaker than the bulk energy gap. We mimic the massless surface Majorana's by coupled wire models in two spatial dimensions. We introduce explicit many-body interwire interactions that preserve time reversal symmetry and give energy gaps to all low energy degrees of freedom. We show the gapped models generically carry non-trivial topological order and support anyonic excitations.

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

Topologically Induced Fermion Parity Flips in Superconductor Vortices

A highlighting feature of Majorana bound states in two-dimensional topological superconductors is that they gain a phase factor of $π$ upon being orbited by a vortex. This work focuses on the vortex degree of freedom itself and demonstrates that the change in the Majorana state is accompanied by a fermion parity change within the vortex. Such a parity flip is interpreted as a higher dimensional analog of the fermion parity pump mechanism in superconducting wires as well as through general topological arguments. It is demonstrated in terms of level crossings in three different situations - in i) spin-triplet paired superconductors, and in proximity-induced superconducting systems involving ii) quantum spin Hall-ferromagnet hybrids and iii) Chern insulators.

cond-mat.str-el↗

arXiv2015

Effective response theory for zero energy Majorana bound states in three spatial dimensions

We propose a gravitational response theory for point defects (hedgehogs) binding Majorana zero modes in (3+1)-dimensional superconductors. Starting in 4+1 dimensions, where the point defect is extended into a line, a coupling of the bulk defect texture with the gravitational field is introduced. Diffeomorphism invariance then leads to an $SU(2)_2$ Kac-Moody current running along the defect line. The $SU(2)_2$ Kac-Moody algebra accounts for the non-Abelian nature of the zero modes in 3+1 dimensions. It is then shown to also encode the angular momentum density which permeates throughout the bulk between hedgehog-anti-hedgehog pairs.

cond-mat.other↗

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

Unconventional Fusion and Braiding of Topological Defects in a Lattice Model

We demonstrate the semiclassical nature of symmetry twist defects that differ from quantum deconfined anyons in a true topological phase by examining non-abelian crystalline defects in an abelian lattice model. An underlying non-dynamical ungauged S3-symmetry labels the quasi-extensive defects by group elements and gives rise to order dependent fusion. A central subgroup of local Wilson observables distinguishes defect-anyon composites by species, which can mutate through abelian anyon tunneling by tuning local defect phase parameters. We compute a complete consistent set of primitive basis transformations, or F-symbols, and study braiding and exchange between commuting defects. This suggests a modified spin-statistics theorem for defects and non-modular group structures unitarily represented by the braiding S and exchange T matrices. Non-abelian braiding operations in a closed system represent the sphere braid group projectively by a non-trivial central extension that relates the underlying symmetry.

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↗

arXiv2013

Braiding Statistics and Congruent Invariance of Twist Defects in Bosonic Bilayer Fractional Quantum Hall States

We describe the braiding statistics of topological twist defects in abelian bosonic bilayer (mmn) fractional quantum Hall (FQH) states, which reduce to the Z_n toric code when m=0. Twist defects carry non-abelian fractional Majorana-like characteristics. We propose local statistical measurements that distinguish the fractional charge, or species, of a defect-quasiparticle composite. Degenerate ground states and basis transformations of a multi-defect system are characterized by a consistent set of fusion properties. Non-abelian unitary exchange operations are determined using half braids between defects, and projectively represent the sphere braid group in a closed system. Defect spin statistics are modified by equating exchange with 4πrotation. The braiding S matrix is identified with a Dehn twist (instead of a π/2 rotation) on a torus decorated with a non-trivial twofold branch cut, and represents the congruent subgroup Γ_0(2) of modular transformations.

cond-mat.str-el↗

arXiv2013

Topological phase states of the SU(3) QCD

We consider the topologically nontrivial phase states and the corresponding topological defects in the SU(3) d-dimensional quantum chromodynamics (QCD). The homotopy groups for topological classes of such defects are calculated explicitly. We have shown that the three nontrivial groups are pi_3 SU(3)=Z, pi_5 SU(3)=Z, and pi_6 SU(3)=Z_6 if 3 < d < 6. The latter result means that we are dealing exactly with six topologically different phase states. The topological invariants for d=3,5,6 are described in detail.

hep-th↗

arXiv2013

Disclination classes, fractional excitations, and the melting of quantum liquid crystals

We consider how fractional excitations bound to a dislocation evolve as the dislocation is separated into a pair of disclinations. We show that some dislocation-bound excitations (such as Majorana modes and half-quantum vortices) are possible only if the elementary dislocation consists of two inequivalent disclinations, as is the case for stripes or square lattices but not for triangular lattices. The existence of multiple inequivalent disclination classes governs the two-dimensional melting of quantum liquid crystals (i.e., nematics and hexatics), determining whether superfluidity and orientational order can simultaneously vanish at a continuous transition.

cond-mat.quant-gas↗

arXiv2012

Majorana Fermions and Disclinations in Topological Crystalline Superconductors

We prove a topological criterion for the existence of zero-energy Majorana bound-state on a disclination, a rotation symmetry breaking point defect, in 4-fold symmetric topological crystalline superconductors (TCS). We first establish a complete topological classification of TCS using the Chern invariant and three integral rotation invariants. By analytically and numerically studying disclinations, we algebraically deduce a Z_2-index that identifies the parity of the number of Majorana zero-modes at a disclination. Surprisingly, we also find weakly-protected Majorana fermions bound at the corners of superconductors with trivial Chern and weak invariants.

cond-mat.mes-hall↗

arXiv2011

From Luttinger liquid to non-Abelian quantum Hall states

We formulate a theory of non-Abelian fractional quantum Hall states by considering an anisotropic system consisting of coupled, interacting one dimensional wires. We show that Abelian bosonization provides a simple framework for characterizing the Moore Read state, as well as the more general Read Rezayi sequence. This coupled wire construction provides a solvable Hamiltonian formulated in terms of electronic degrees of freedom, and provides a direct route to characterizing the quasiparticles and edge states in terms of conformal field theory. This construction leads to a simple interpretation of the coset construction of conformal field theory, which is a powerful method for describing non Abelian states. In the present context, the coset construction arises when the original chiral modes are fractionalized into coset sectors, and the different sectors acquire energy gaps due to coupling in "different directions". The coupled wire construction can also can be used to describe anisotropic lattice systems, and provides a starting point for models of fractional and non-Abelian Chern insulators. This paper also includes an extended introduction to the coupled wire construction for Abelian quantum Hall states, which was introduced earlier.

cond-mat.mes-hall↗

arXiv2010

Topological Defects and Gapless Modes in Insulators and Superconductors

We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians H(k,r) that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified, and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions and helical Majorana fermions, as well as zero dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes.

cond-mat.mes-hall↗

arXiv2010

Majorana Fermions and Non-Abelian Statistics in Three Dimensions

We show that three dimensional superconductors, described within a Bogoliubov de Gennes framework can have zero energy bound states associated with pointlike topological defects. The Majorana fermions associated with these modes have non-Abelian exchange statistics, despite the fact that the braid group is trivial in three dimensions. This can occur because the defects are associated with an orientation that can undergo topologically nontrivial rotations. A new feature of three dimensional systems is that there are "braidless" operations in which it is possible to manipulate the groundstate associated with a set of defects without moving or measuring them. To illustrate these effects we analyze specific architectures involving topological insulators and superconductors.

cond-mat.mes-hall↗

arXiv2009

Critical Behavior of a Point Contact in a Quantum Spin Hall Insulator

We study a quantum point contact in a quantum spin Hall insulator. It has recently been shown that the Luttinger liquid theory of such a structure maps to the theory of a weak link in a Luttinger liquid with spin with Luttinger liquid parameters g_ρ= 1/g_σ= g < 1. We show that for 1/2<g<1, the pinch-off of the point contact as a function of gate voltage is controlled by a novel quantum critical point, related to a nontrivial intermediate fixed point found previously in the Luttinger liquid model. We predict that the dependence of the conductance on gate voltage and temperature near the pinch-off transition collapses onto a universal curve described by a crossover scaling function. We compute the conductance, the critical exponents and the scaling function in solvable limits, which include g=1-ε, g=1/2+εand g=1/\sqrt{3}. These results, along with a general scaling analysis provide an overall picture of the critical behavior as a function of g. In addition, we analyze the structure of the four terminal conductance of the point contact in the weak tunneling and weak backscattering limits. We find that different components of the conductance can have different temperature dependence. We identify a skew conductance G_{XY}, which we predict vanishes as T^γwith γ\ge 2. This behavior is a direct consequence of the unique edge state structure of the quantum spin Hall insulator. Finally, we show that for g<1/2 the presence of spin non conserving spin orbit interactions leads to a novel time reversal symmetry breaking insulating phase. In this phase, the transport is carried by spinless chargons and chargeless spinons. These lead to nontrivial correlations in the low frequency shot noise. Implications for experiments on HgCdTe quantum well structures will be discussed.

cond-mat.mes-hall↗