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Register a new userFractional statistics of topological defects in graphene and related structures
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We show that fractional charges bound to topological defects in the recently proposed time-reversal-invariant models on honeycomb and square lattices obey fractional statistics. The effective low-energy description is given in terms of a `doubled level-2 Chern-Simons field theory, which is parity and time-reversal invariant and implies two species of semions (particles with statistical angle pi/2) labeled by a new emergent quantum number that we identify as the fermion axial charge.
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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.
We study charge transport through a floating mesoscopic superconductor coupled to counterpropagating fractional quantum Hall edges at filling fraction $ u=2/3$. We consider a superconducting island with finite charging energy and investigate its effect on transport through the device. We calculate conductance through such a system as a function of temperature and gate voltage applied to the superconducting island. We show that transport is strongly affected by the presence of parafermionic zero modes, leading at zero temperature to a zero-bias conductance quantized in units of $ u e^2/h$ independent of the applied gate voltage.
We study the role of long-range electron-electron interactions in a system of two-dimensional anisotropic Dirac fermions, which naturally appear in uniaxially strained graphene, graphene in external potentials, some strongly anisotropic topological insulators, and engineered anisotropic graphene structures. We find that while for small interactions and anisotropy the system restores the conventional isotropic Dirac liquid behavior, strong enough anisotropy can lead to the formation of a quasi-one dimensional electronic phase with dominant charge order (anisotropic excitonic insulator).
We report on the possibility of valley number fractionalization in graphene with a topological defect that is accounted for in Dirac equation by a pseudomagnetic field. The valley number fractionalization is attributable to an imbalance on the number of one particle states in one of the two Dirac points with respect to the other and it is related to the flux of the pseudomagnetic field. We also discuss the analog effect the topological defect might lead in the induced spin polarization of the charge carriers in graphene.
We construct the symmetric-gapped surface states of a fractional topological insulator with electromagnetic $theta$-angle $theta_{em} = frac{pi}{3}$ and a discrete $mathbb{Z}_3$ gauge field. They are the proper generalizations of the T-pfaffian state and pfaffian/anti-semion state and feature an extended periodicity compared with their of integer topological band insulators counterparts. We demonstrate that the surface states have the correct anomalies associated with time-reversal symmetry and charge conservation.
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