arXiv subjects

Xiao-Liang Qi

Publications and source records attributed to Xiao-Liang Qi.

At least 127 records · Page 7Linked to original sources

arXiv2011

Topological field theory and thermal responses of interacting topological superconductors

We investigate the three-dimensional, time-reversal invariant topological superconductors with generic interaction by their response to external fields. The first description is a gravitational topological field theory, which gives a $Z_2$ classification of topological superconductors, and predicts a half-quantized thermal Hall effect on the surface. The second description introduces an s-wave proximity pairing field on the surface, and the associated topological defects give an integer $Z$ classification of the topological superconductors.

cond-mat.str-el↗

arXiv2011

Weakly-Coupled non-Abelian Anyons in Three Dimensions

We introduce a Hamiltonian coupling Majorana fermion degrees of freedom to a quantum dimer model. We argue that, in three dimensions, this model has deconfined quasiparticles supporting Majorana zero modes obeying nontrivial statistics. We introduce two effective field theory descriptions of this deconfined phase, in which the excitations have Coulomb interactions. A key feature of this system is the existence of topologically non-trivial fermionic excitations, called "Hopfions" because, in a suitable continuum limit of the dimer model, such excitations correspond to the Hopf map and are related to excitations identified in arXiv:1003.1964. We identify corresponding topological invariants of the quantum dimer model (with or without fermions) which are present even on lattices with trivial topology. The Hopfion energy gap depends upon the phase of the model. We briefly comment on the possibility of a phase with a gapped, deconfined $\mathbb{Z}_2$ gauge field, as may arise on the stacked triangular lattice.

cond-mat.str-el↗

arXiv2011

Spin polarization of the quantum spin Hall edge states

While the helical character of the edge channels responsible for charge transport in the quantum spin Hall regime of a two-dimensional topological insulator is by now well established, an experimental confirmation that the transport in the edge channels is spin-polarized is still outstanding. We report experiments on nanostructures fabricated from HgTe quantum wells with an inverted band structure, in which a split gate technique allows us to combine both quantum spin Hall and metallic spin Hall transport in a single device. In these devices, the quantum spin Hall effect can be used as a spin current injector and detector for the metallic spin Hall effect, and vice versa, allowing for an all-electrical detection of spin polarization.

cond-mat.mes-hall↗

arXiv2011

Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators

We propose a systematical approach to construct generic fractional quantum anomalous Hall (FQAH) states, which are generalizations of the fractional quantum Hall states to lattice models with zero net magnetic field and full lattice translation symmetry. Local and translationally invariant Hamiltonians can also be constructed, for which the proposed states are unique ground states. Our result demonstrates that generic chiral topologically ordered states can be realized in lattice models, without requiring magnetic translation symmetry and Landau level structure. We further generalize our approach to the time-reversal invariant analog of fractional quantum Hall states--fractional topological insulators, and provide the first explicit wavefunction description of fractional topological insulators in the absence of spin conservation.

cond-mat.str-el↗

arXiv2011

Topological insulators in filled skutterudites

We propose new topological insulators in cerium filled skutterudite (FS) compounds based on ab initio calculations. We find that two compounds CeOs4As12 and CeOs4Sb12 are zero gap materials with band inversion between Os-d and Ce-f orbitals, which are thus parent compounds of two and three-dimensional topological insulators just like bulk HgTe. At low temperature, both compounds become topological Kondo insulators, which are Kondo insulators in the bulk, but have robust Dirac surface states on the boundary. This new family of topological insulators has two advantages compared to previous ones. First, they can have good proximity effect with other superconducting FS compounds to realize Majarona fermions. Second, the antiferromagnetism of CeOs4Sb12 at low temperature provides a way to realize the massive Dirac fermion with novel topological phenomena.

cond-mat.mtrl-sci↗

arXiv2011

General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States

We consider (2+1)-dimensional topological quantum states which possess edge states described by a chiral (1+1)-dimensional Conformal Field Theory (CFT), such as e.g. a general quantum Hall state. We demonstrate that for such states the reduced density matrix of a finite spatial region of the gapped topological state is a thermal density matrix of the chiral edge state CFT which would appear at the spatial boundary of that region. We obtain this result by applying a physical instantaneous cut to the gapped system, and by viewing the cutting process as a sudden "quantum quench" into a CFT, using the tools of boundary conformal field theory. We thus provide a demonstration of the observation made by Li and Haldane about the relationship between the entanglement spectrum and the spectrum of a physical edge state.

cond-mat.mes-hall↗

arXiv2011

Confinement-deconfinement interplay in quantum phases of doped Mott insulators

It is generally accepted that doped Mott insulators can be well characterized by the t-J model. In the t-J model, the electron fractionalization is dictated by the phase string effect. We found that in the underdoped regime, the antiferromagnetic and superconducting phases are dual: in the former, holons are confined while spinons are deconfined, and {\it vice versa} in the latter. These two phases are separated by a novel phase, the so-called Bose-insulating phase, where both holons and spinons are deconfined. A pair of Wilson loops was found to constitute a complete set of order parameters determining this zero-temperature phase diagram. The quantum phase transitions between these phases are suggested to be of non-Landau-Ginzburg-Wilson type.

cond-mat.str-el↗

arXiv2011

Topological superconductivity and Majorana fermions in half-metal / superconductor heterostructure

As a half-metal is spin-polarized at its Fermi level by definition, it was conventionally thought to have little proximity effect to an s-wave superconductor. Here we show that, with interface spin-orbit coupling, $p_x +ip_y$ superconductivity without spin degeneracy is induced on the half-metal, and we give an estimate of its bulk energy gap. Therefore a single-band half-metal can give us a topological superconductor with a single chiral Majorana edge state. Our band calculation shows that two atomic layers of VTe or CrO$_2$ is a single-band half-metal for a wide range ($\sim$0.1eV) of Fermi energy and thus is a suitable candidate material.

cond-mat.supr-con↗

arXiv2011

Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field

Motivated by the recent experimental observation of a Mott insulating state for the layered Iridate Na2IrO3, we discuss possible ordering states of the effective Iridium moments in the presence of strong spin-orbit coupling and a magnetic field. For a field pointing in the [111] direction - perpendicular to the hexagonal lattice formed by the Iridium moments - we find that a combination of Heisenberg and Kitaev exchange interactions gives rise to a rich phase diagram with both symmetry breaking magnetically ordered phases as well as a topologically ordered phase that is stable over a small range of coupling parameters. Our numerical simulations further indicate two exotic multicritical points at the boundaries between these ordered phases.

cond-mat.str-el↗

arXiv2010

Symmetry fractional quantization in two dimensions

We introduce a solvable spin-rotational and time-reversal invariant spin-1 model in two dimensions. Depending on parameters, the ground state is an equal-weight superposition of all valence loops called "resonating valence loop" (RVL) or an equal-weight superposition of all valence bonds known as "resonating valence bond" (RVB). In RVL, ends of open loops are deconfined spinons of spin-1/2 that cannot be obtained by simple combinations of spin-1 -- a phenomenon of fractionalization; while in RVB, all quasiparticles carry an integer spin, hence no fractionalization. RVL and RVB are spin liquids with identical topological order but different spin-rotational and time-reversal symmetry quantum numbers of quasiparticles. We propose that quantized symmetry quantum number gives a systematic way to (partially) classify phases with identical topological order in dimensions greater than one.

cond-mat.str-el↗

arXiv2010

Topological Order Parameters for Interacting Topological Insulators

We propose a topological order parameter for interacting topological insulators, expressed in terms of the full Green's functions of the interacting system. We show that it is exactly quantized for a time reversal invariant topological insulator, and it can be experimentally measured through the topological magneto-electric effect. This topological order parameter can be applied to both interacting and disordered systems, and used for determining their phase diagrams.

cond-mat.str-el↗

arXiv2010

Fractional topological insulators in three dimensions

Topological insulators can be generally defined by a topological field theory with an axion angle theta of 0 or pi. In this work, we introduce the concept of fractional topological insulator defined by a fractional axion angle and show that it can be consistent with time reversal (T) invariance if ground state degeneracies are present. The fractional axion angle can be measured experimentally by the quantized fractional bulk magnetoelectric polarization P_3, and a `halved' fractional quantum Hall effect on the surface with Hall conductance of the form (p/q)(e^2/2h) with p,q odd. In the simplest of these states the electron behaves as a bound state of three fractionally charged `quarks' coupled to a deconfined non-Abelian SU(3) `color' gauge field, where the fractional charge of the quarks changes the quantization condition of P_3 and allows fractional values consistent with T-invariance.

cond-mat.str-el↗

arXiv2010

Topological quantization in units of the fine structure constant

Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant topological insulator in three dimensions exhibits a topological magnetoelectric effect quantized in units of the fine structure constant $α=e^2/\hbar c$. In this work, we propose an optical experiment to directly measure this topological quantization phenomenon, independent of material details. Our proposal also provides a way to measure the half-quantized Hall conductances on the two surfaces of the topological insulator independently of each other.

cond-mat.str-el↗

arXiv2010

Topological Insulators in Ternary Compounds with a Honeycomb Lattice

One of the most exciting subjects in solid state physics is a single layer of graphite which exhibits a variety of unconventional novel properties. The key feature of its electronic structure are linear dispersive bands which cross in a single point at the Fermi energy. This so-called Dirac cone is closely related to the surface states of the recently discovered topological insulators. The ternary compounds, such as LiAuSe and KHgSb with a honeycomb structure of their Au-Se and Hg-Sb layers feature band inversion very similar to HgTe which is a strong precondition for existence of the topological surface states. In contrast to graphene with two Dirac cones at K and K' points, these materials exhibit the surface states formed by only a single Dirac cone at the Γ-point together with the small direct band gap opened by a strong spin-orbit coupling (SOC) in the bulk. These materials are centro-symmetric, therefore, it is possible to determine the parity of their wave functions, and hence, their topological character. Surprisingly, the compound KHgSb with the strong SOC is topologically trivial, whereas LiAuSe is found to be a topological non-trivial insulator.

cond-mat.mtrl-sci↗

arXiv2010

Projective Ribbon Permutation Statistics: a Remnant of non-Abelian Braiding in Higher Dimensions

In a recent paper, Teo and Kane proposed a 3D model in which the defects support Majorana fermion zero modes. They argued that exchanging and twisting these defects would implement a set R of unitary transformations on the zero mode Hilbert space which is a 'ghostly' recollection of the action of the braid group on Ising anyons in 2D. In this paper, we find the group T_{2n} which governs the statistics of these defects by analyzing the topology of the space K_{2n} of configurations of 2n defects in a slowly spatially-varying gapped free fermion Hamiltonian: T_{2n}\equiv {π_1}(K_{2n})$. We find that the group T_{2n}= Z \times T^r_{2n}, where the 'ribbon permutation group' T^r_{2n} is a mild enhancement of the permutation group S_{2n}: T^r_{2n} \equiv \Z_2 \times E((Z_2)^{2n}\rtimes S_{2n}). Here, E((Z_2)^{2n}\rtimes S_{2n}) is the 'even part' of (Z_2)^{2n} \rtimes S_{2n}, namely those elements for which the total parity of the element in (Z_2)^{2n} added to the parity of the permutation is even. Surprisingly, R is only a projective representation of T_{2n}, a possibility proposed by Wilczek. Thus, Teo and Kane's defects realize `Projective Ribbon Permutation Statistics', which we show to be consistent with locality. We extend this phenomenon to other dimensions, co-dimensions, and symmetry classes. Since it is an essential input for our calculation, we review the topological classification of gapped free fermion systems and its relation to Bott periodicity.

cond-mat.mes-hall↗

arXiv2010

Magnetoconductance of the quantum spin Hall state

We study numerically the edge magnetoconductance of a quantum spin Hall insulator in the presence of quenched nonmagnetic disorder. For a finite magnetic field B and disorder strength W on the order of the bulk gap E_g, the conductance deviates from its quantized value in a manner which appears to be linear in |B| at small B. The observed behavior is in qualitative agreement with the cusp-like features observed in recent magnetotransport measurements on HgTe quantum wells. We propose a dimensional crossover scenario as a function of W, in which for weak disorder W < E_g the edge liquid is analogous to a disordered spinless 1D quantum wire, while for strong disorder W > E_g, the disorder causes frequent virtual transitions to the 2D bulk, where the originally 1D edge electrons can undergo 2D diffusive motion and 2D antilocalization.

cond-mat.mes-hall↗

arXiv2010

Entanglement entropy and entanglement spectrum of the Kitaev model

In this paper, we obtain an exact formula for the entanglement entropy of the ground state and all excited states of the Kitaev model. Remarkably, the entanglement entropy can be expressed in a simple separable form S=S_G+S_F, with S_F the entanglement entropy of a free Majorana fermion system and S_G that of a Z_2 gauge field. The Z_2 gauge field part contributes to the universal "topological entanglement entropy" of the ground state while the fermion part is responsible for the non-local entanglement carried by the Z_2 vortices (visons) in the non-Abelian phase. Our result also enables the calculation of the entire entanglement spectrum and the more general Renyi entropy of the Kitaev model. Based on our results we propose a new quantity to characterize topologically ordered states--the capacity of entanglement, which can distinguish the states with and without topologically protected gapless entanglement spectrum.

cond-mat.str-el↗

arXiv2010

Topological Magnetic Insulators with Corundum Structure

Topological insulators are new states of quantum matter in which surface states residing in the bulk insulating gap are protected by time-reversal symmetry. When a proper kind of antiferromagnetic long range order is established in a topological insulator, the system supports axionic excitations. In this paper, we study theoretically the electronic states in a transition metal oxide of corundum structure, in which both spin-orbit interaction and electron-electron interaction play crucial roles. A tight-binding model analysis predicts that materials with this structure can be strong topological insulator. Because of the electron correlation, an antiferromagnetic order may develop, giving rise to a topological magnetic insulator phase with axionic excitations.

cond-mat.mes-hall↗