Torsional anomalies, Hall viscosity, and bulk-boundary correspondence in topological states

By T. Hughes, R. Leigh, Onkar Parrikar. 2012

137 citations recorded by the source corpus.

We study the transport properties of topological insulators, encoding them in a generating functional of gauge and gravitational sources. Much of our focus is on the simple example of a free massive Dirac fermion, the so-called Chern insulator, especially in 2+1 dimensions. In such cases, when parity and time-reversal symmetry are broken, it is necessary to consider the gravitational sources to include a frame and an independent spin connection with torsion. In 2+1 dimensions, the simplest parity-odd response is the Hall viscosity. We compute the Hall viscosity of the Chern insulator using a careful regularization scheme, and find that although the Hall viscosity is generally divergent, the difference in Hall viscosities of distinct topological phases is well defined and determined by the mass gap. Furthermore, on a 1+1-dimensional edge between topological phases, the jump in the Hall viscosity across the interface is encoded, through familiar anomaly inflow mechanisms, in the structure of anomalies. In particular, we find new torsional contributions to the covariant diffeomorphism anomaly in 1+1 dimensions. Including parity-even contributions, we find that the renormalized generating functionals of the two topological phases differ by a chiral gravity action with a negative cosmological constant. This (nondynamical) chiral gravity action and the corresponding physics of the interface theory is reminiscent of well-known properties of dynamical holographic gravitational systems. Finally, we consider some properties of spectral flow of the edge theory driven by torsional dislocations.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/5c315adc6f488a65bdcbcc1811e9e5919fcd946a

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Novel effects of strains in graphene and other two dimensional materials (2015, methodology): “Computation of the Hall viscosity in topological matter and its relation to the total angular momentum is one of the most active areas of research nowadays involving all the geometrical tools concerning the study of QFT in curved background fields including torsion [57, 150, 151].”