2012/11/30 by Taylor L. Hughes, Robert G. Leigh, Onkar Parrikar · 3 citations
Mathematics · Physics and Astronomy · #Atomic and Subatomic Physics Research #Gravitation #Mathematics #Parity (physics) #Physics #Quantum many-body systems #Quantum mechanics #Theoretical physics #Topological Materials and Phenomena #Topological insulator #Topology (electrical circuits) #cond-mat.mes-hall #hep-th
paper · pdf · doi:10.1103/physrevd.88.025040
published as Phys. Rev. D 88, 025040 (2013) · 59 pages, 6 figures; v2 updated in response to referee comments. Extra emphasis on universal viscosity term for curved spaces
arxiv created 2013/06/12 · openalex publication_date 2013/07/23 · arxiv updated 2013/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.