Realizing topological surface states in a lower-dimensional flat band

TL;DR

This paper explores how certain anomalous topological surface states can be realized in lower dimensions through nonlocal symmetries, extending to multicomponent quantum Hall states and connecting to higher-dimensional topological insulators.

Contribution

It generalizes the realization of anomalous surface states to multicomponent quantum Hall systems and links lower-dimensional states to higher-dimensional topological insulators.

Findings

Duality mapping of bilayer systems to composite bosons with Kramers degeneracy

Realization of particle-hole symmetric integer quantum Hall states at multiples of eight components

Construction of surface topological orders related to 4D topological insulators and connections to Witten's SU(2) anomaly

Abstract

The anomalous surface states of symmetry protected topological (SPT) phases are usually thought to be only possible in conjunction with the higher dimensional topological bulk. However, it has recently been realized that a class of anomalous SPT surface states can be realized in the same dimension if symmetries are allowed to act in a nonlocal fashion. An example is the particle-hole symmetric half filled Landau level, which effectively realizes the anomalous surface state of a 3D chiral Topological Insulator (class AIII). A dual description in terms of Dirac composite fermions has also been discussed. Here we explore generalizations of these constructions to multicomponent quantum Hall states. Our results include a duality mapping of the bilayer case to composite bosons with Kramers degeneracy and the possibility of a particle hole symmetric integer quantum Hall state when the number of components is a multiple of eight. Next, we make a further extension by half filling other classes of topological bands and imposing particle hole symmetry. When applied to time-reversal invariant topological insulators we realize a different chiral class (CII) topological surface state. Notably, half-filling a 3D TI band allows for the realization of the surface of the otherwise inaccessible 4D topological insulator, which supports an anomalous 3D Dirac cone. Surface topological orders equivalent to the 3D Dirac cone (from the global anomaly standpoint) are constructed and connections to Witten's SU(2) anomaly are made. These observations may also be useful for numerical simulations of topological surface states and of Dirac fermions without fermion doubling.