arXiv subjects

Po-Yao Chang

Publications and source records attributed to Po-Yao Chang.

48 records · Page 3Linked to original sources

arXiv2017

Möbius Kondo Insulators

Heavy fermion materials have recently attracted attention for their potential to combine topological protection with strongly correlated electron physics. To date, the ideas of topological protection have been restricted to the heavy fermion or "Kondo" insulators with the simplest point-group symmetries. Here we argue that the presence of nonsymmorphic crystal symmetries in many heavy fermion materials opens up a new family of topologically protected heavy electron systems. Re-examination of archival resistivity measurements in nonsymmorphic heavy fermion insulators Ce$_3$Bi$_4$Pt$_3$ and CeNiSn reveals the presence of low temperature conductivity plateau, making them candidate members of the new class of material. We illustrate our ideas with a specific model for CeNiSn, showing how glide symmetries generate surface states with a novel Mobius braiding that can be detected by ARPES or non-local conductivity measurements. One of the interesting effects of strong correlation, is the development of partially localization or "Kondo breakdown" on the surfaces, which transforms Mobius surface states into quasi-one dimensional conductors, with the potential for novel electronic phase transitions.

cond-mat.str-el↗

arXiv2017

A Class of topological nodal rings and its realization in carbon networks

Topological nodal rings can be classified into three types according to the slopes in their energy dispersion. The first two are made of type-I and II nodal points, respectively, while the third is made of both. In carbon networks, all three types can exist. Under strain, phase transitions from a topological metal to a semiconductor, take place, and at the transition points, these nodal rings shrink into type-I, II, and III semi-Dirac points. These topological features exhibit diverse electron-hole pocket patterns and Landau levels, which give rise to exotic transport properties.

cond-mat.mtrl-sci↗

arXiv2017

Bell's Inequality and Entanglement in Qubits

We propose an alternative evaluation of quantum entanglement by measuring the maximum violation of the Bell's inequality without performing a partial trace operation. This proposal is demonstrated by bridging the maximum violation of the Bell's inequality and the concurrence of a pure state in an $n$-qubit system, in which one subsystem only contains one qubit and the state is a linear combination of two product states. We apply this relation to the ground states of four qubits in the Wen-Plaquette model and show that they are maximally entangled. A topological entanglement entropy of the Wen-Plaquette model could be obtained by relating the upper bound of the maximum violation of the Bell's inequality to the concurrences of a pure state with respect to different bipartitions.

quant-ph↗

arXiv2017

Skyrme insulators: insulators at the brink of superconductivity

Current theories of superfluidity are based on the idea of a coherent quantum state with topologically protected, quantized circulation. When this topological protection is absent, as in the case of $^3$He-A, the coherent quantum state no longer supports persistent superflow. Here we argue that the loss of topological protection in a superconductor gives rise to an insulating ground state. We specifically introduce the concept of a Skyrme insulator to describe the coherent dielectric state that results from the topological failure of superflow carried by a complex vector order parameter. We apply this idea to the case of SmB$_6$, arguing that the observation of a diamagnetic Fermi surface within an insulating bulk can be understood in terms of a Skyrme insulator. Our theory enables us to understand the linear specific heat of SmB$_6$ in terms of a neutral Majorana Fermi sea and leads us to predict that in low fields of order a Gauss, SmB6 will develop a Meissner effect.

cond-mat.str-el↗

arXiv2016

Topological entanglement negativity in Chern-Simons theories

We study the topological entanglement negativity between two spatial regions in (2+1)-dimensional Chern-Simons gauge theories by using the replica trick and the surgery method. For a bipartitioned or tripartitioned spatial manifold, we show how the topological entanglement negativity depends on the presence of quasiparticles and the choice of ground states. In particular, for two adjacent non-contractible regions on a tripartitioned torus, the entanglement negativity provides a simple way to distinguish Abelian and non-Abelian theories. Our method applies to a Chern-Simons gauge theory defined on an arbitrary oriented (2+1)-dimensional spacetime manifold. Our results agree with the edge theory approach in a recent work (X. Wen, S. Matsuura and S. Ryu, arXiv:1603.08534).

cond-mat.str-el↗

arXiv2016

Entanglement negativity in free-fermion systems: An overlap matrix approach

In this paper, we calculate the entanglement negativity in free-fermion systems by use of the overlap matrices. For a tripartite system, if the ground state can be factored into triples of modes, we show that the partially transposed reduced density matrix can be factorized and the entanglement negativity has a simple form. However, the factorability of the ground state in a tripartite system does not hold in general. In this situation, the partially transposed reduced density matrix can be expressed in terms of the Kronecker product of matrices. We explicitly compute the entanglement negativity for the Su-Schrieffer-Heeger model, the integer Quantum Hall state, and a homogeneous one-dimensional chain. We find that the entanglement negativity for the integer quantum Hall states shows an area law behavior. For the entanglement negativity of two adjacent intervals in a homogeneous one-dimensional gas, we find agreement with the conformal field theory. Our method provides a numerically feasible way to study the entanglement negativity in free-fermion systems.

cond-mat.stat-mech↗

arXiv2015

Self-shrinkers to the mean curvature flow asymptotic to isoparametric cones

In this paper we construct an end of a self-similar shrinking solution of the mean curvature flow asymptotic to an isoparametric cone C and lying outside of C. We call a cone C in $R^{n+1}$ an isoparametric cone if C is the cone over a compact embedded isoparametric hypersurface $Γ\subset S^n$. The theory of isoparametic hypersurfaces is extremely rich and there are infinitely many distinct classes of examples, each with infinitely many members.

math.DG↗

arXiv2015

Entanglement negativity after a local quantum quench in conformal field theories

We study the time evolution of the entanglement negativity after a local quantum quench in (1+1)-dimensional conformal field theories (CFTs), which we introduce by suddenly joining two initially decoupled CFTs at their endpoints. We calculate the negativity evolution for both adjacent intervals and disjoint intervals explicitly. For two adjacent intervals, the entanglement negativity grows logarithmically in time right after the quench. After developing a plateau-like feature, the entanglement negativity drops to the ground-state value. For the case of two spatially separated intervals, a light-cone behavior is observed in the negativity evolution; in addition, a long-range entanglement, which is independent of the distance between two intervals, can be created. Our results agree with the heuristic picture that quasiparticles, which carry entanglement, are emitted from the joining point and propagate freely through the system. Our analytical results are confirmed by numerical calculations based on a critical harmonic chain.

cond-mat.stat-mech↗

arXiv2014

Majorana vortex-bound states in three-dimensional nodal noncentrosymmetric superconductors

Noncentrosymmetric superconductors (NCSs), characterized by antisymmetric spin-orbit coupling and a mixture of spin-singlet and spin-triplet pairing components, are promising candidate materials for topological superconductivity. An important hallmark of topological superconductors is the existence of protected zero-energy states at surfaces or in vortex cores. Here we investigate Majorana vortex-bound states in three-dimensional nodal and fully gapped NCSs by combining analytical solutions of Bogoliubov-de Gennes (BdG) equations in the continuum with exact diagonalization of BdG Hamiltonians. We show that depending on the crystal point-group symmetries and the topological properties of the bulk Bogoliubov-quasiparticle wave functions, different types of zero-energy Majorana modes can appear inside the vortex core. We find that for nodal NCSs with tetragonal point group $C_{4v}$ the vortex states are dispersionless along the vortex line, forming one-dimensional Majorana flat bands, while for NCSs with $D_{4}$ point-group symmetry the vortex modes are helical Majorana states with a linear dispersion along the vortex line. NCSs with monoclinic point group $C_2$, on the other hand, do not exhibit any zero-energy vortex-bound states. We show that in the case of the $C_{4v}$ ($D_4$) point group the stability of these Majorana zero modes is guaranteed by a combination of reflection ($π$ rotation), time-reversal, and particle-hole symmetry. Considering continuous deformations of the quasiparticle spectrum in the presence of vortices, we show that the flat-band vortex-bound states of $C_{4v}$ point-group NCSs can be adiabatically connected to the dispersionless vortex-bound states of time-reversal symmetric Weyl superconductors. Experimental implications of our results for thermal transport and tunneling measurements are discussed.

cond-mat.supr-con↗

arXiv2014

Symmetry-protected entangling boundary zero modes in crystalline topological insulators

Crystalline topological insulators owe their topological character to the protection that certain boundary states acquire because of certain point-group symmetries. We first show that a Hermitian operator obeying supersymmetric quantum mechanisms (SUSY QM) delivers the entanglement spectrum. We then show that such an entanglement spectrum that is compatible with a certain point-group symmetry obeys a certain local spectral symmetry. The latter result is applied to the stability analysis of four fermionic non-interacting Hamiltonians, the last of which describes graphene with a Kekule distortion. All examples have the remarkable property that their entanglement spectra inherit a local spectral symmetry from either an inversion or reflection symmetry that guarantees the stability of gapless boundary entangling states, even though all examples fail to support protected gapless boundary states at their physical boundaries.

cond-mat.str-el↗

arXiv2013

Protected boundary states in gapless topological phases

We systematically study gapless topological phases of (semi-)metals and nodal superconductors described by Bloch and Bogoliubov-de Gennes Hamiltonians. Using K-theory, a classification of topologically stable Fermi surfaces in (semi-)metals and nodal lines in superconductors is derived. We discuss a generalized bulk-boundary correspondence that relates the topological features of the Fermi surfaces and superconducting nodal lines to the presence of protected zero-energy states at the boundary of the system. Depending on the case, the boundary states are either linearly dispersing (i.e., Dirac or Majorana states) or are dispersionless, forming two-dimensional surface flat bands or one-dimensional arc surface states. We study examples of gapless topological phases in symmetry class AIII and DIII, focusing in particular on nodal superconductors, such as nodal non-centrosymmetric superconductors. For some cases we explicitly compute the surface spectrum and examine the signatures of the topological boundary states in the surface density of states.

cond-mat.supr-con↗

arXiv2009

Conductance through a single impurity in the metallic zigzag carbon nanotube

We investigate transport through a single impurity in metallic zigzag carbon nanotube and find the conductance sensitively depends on the impurity strength and the bias voltage. It is rather interesting that interplay between the current-carrying scattering state and evanescent modes leads to rich phenomena including resonant backward scattering, perfect tunneling and charge accumulations. In addition, we also find a dual relation between the backscattered conductance and the charge accumulation. At the end, relevance to the experiments is discussed.

cond-mat.mes-hall↗