Dissertation Defense: Barry Bradlyn, Yale University, “Linear response and Berry curvature in two-dimensional topological phases”

Event time: 
Friday, May 22, 2015 -
2:00pm to 3:00pm
Sloane Physics Laboratory (SPL), 52 See map
217 Prospect St.
New Haven, CT 06511
(Location is wheelchair accessible)
Event description: 

One hallmark of topological phases with broken time reversal symmetry is the appearance of quantized non-dissipative transport coefficients, the archetypical example being the quantized Hall conductivity in quantum Hall states. Here I will talk about two other non-dissipative transport coefficients that appear in such systems - the Hall viscosity and the thermal Hall conductivity. In the first part of the talk, I will start by reviewing previous results concerning the Hall viscosity, including its relation to a topological invariant known as the shift. Next, I will show how the Hall viscosity can be computed from a Kubo formula. For Galilean invariant systems, the Kubo formula implies a relationship between the viscosity and conductivity tensors which may have relevance for experiment. In the second part of the talk, I will discuss the thermal Hall conductivity, its relation to the topological central charge of the edge theory, and in particular the absence of a bulk contribution to the thermal Hall current. I will do this by constructing a low-energy effective theory in a curved non-relativistic background, allowing for torsion. I will show that the bulk contribution to the thermal current takes the form of an “energy magnetization” current, and hence show that it does not contribute to heat transport. To conclude, I will present a method for computing the topological central charge and orbital spin variance of a topological phase directly from bulk wavefunctions, as a Berry curvature associated to certain deformations of the spatial metric. I will show explicit results of this computation—as well as a related derivation of the Hall conductivity and Hall viscosity—for trial wavefunctions that can be represented as conformal blocks in a chiral conformal field theory (CFT). These calculations make use of the gauge and gravitational anomalies in the CFT.