Effective edge state dynamics in the fractional quantum Hall effect
Physical Review B: Condensed Matter and Materials Physics American Physical Society 98:15 (2018)
Abstract:
We consider the behavior of quantum Hall edges away from the Luttinger liquid fixed point that occurs in the low-energy, large-system limit. Using the close links between quantum Hall wave functions and conformal field theories, we construct effective Hamiltonians from general principles and then constrain their forms by considering the effect of bulk symmetries on the properties of the edge. In examining the effect of bulk interactions on this edge, we find remarkable simplifications to these effective theories which allow for a very accurate description of the low-energy physics of quantum Hall edges relatively far away from the Luttinger liquid fixed point, and which apply to small systems and higher energies.Reply to “Comment on ‘Interpretation of thermal conductance of the ν=5/2 edge' ”
Physical Review B American Physical Society 98 (2018)
Abstract:
Feldman argues that simply having a large velocity mismatch and long wavelength disorder is not likely to result in sufficient non-equilibration of Majorana edge modes at ν=5/2 to explain recent thermal transport experiments. I agree that this picture alone is probably too simple, although small modifications of the mechanism could still be viable.Theory of the Josephson Junction Laser
Physical Review Letters American Physical Society 121 (2018)
Abstract:
We develop an analytic theory for the recently demonstrated Josephson Junction laser (Science 355, 939, 2017). By working in the time-domain representation (rather than the frequency-domain) a single non-linear equation is obtained for the dynamics of the device, which is fully solvable in some regimes of operation. The nonlinear drive is seen to lead to mode-locked output, with a period set by the round-trip time of the resonant cavity.Structure of edge-state inner products in the fractional quantum Hall effect
Physical Review B American Physical Society 97:15 (2018) 155108
Abstract:
We analyze the inner products of edge state wave functions in the fractional quantum Hall effect, specifically for the Laughlin and Moore-Read states. We use an effective description for these inner products given by a large-N expansion ansatz proposed in a recent work by J. Dubail, N. Read, and E. Rezayi [Phys. Rev. B 86, 245310 (2012)]. As noted by these authors, the terms in this ansatz can be constrained using symmetry, a procedure we perform to high orders. We then check this conjecture by calculating the overlaps exactly for small system sizes and compare the numerics with our high-order expansion. We find the effective description to be very accurate.Size constraints on a Majorana beam-splitter interferometer: Majorana coupling and surface-bulk scattering
Physical Review B American Physical Society 97:11 (2018) 115424