Large $N$ theory of critical Fermi surfaces II: conductivity
Abstract
A Fermi surface coupled to a scalar field can be described in a expansion by choosing the fermion-scalar Yukawa coupling to be random in the -dimensional flavor space, but invariant under translations. We compute the conductivity of such a theory in two spatial dimensions for a critical scalar. We find a Drude contribution, and verify that the proposed contribution to the optical conductivity at frequency has vanishing co-efficient for a convex Fermi surface. We also describe the influence of impurity scattering of the fermions, and find that while the self energy resembles a marginal Fermi liquid, the resistivity and optical conductivity behave like a Fermi liquid.
Keywords
Cite
@article{arxiv.2207.08841,
title = {Large $N$ theory of critical Fermi surfaces II: conductivity},
author = {Haoyu Guo and Aavishkar A. Patel and Ilya Esterlis and Subir Sachdev},
journal= {arXiv preprint arXiv:2207.08841},
year = {2023}
}
Comments
50 pages, 1 figure. This analysis appeared originally in the supplement of arXiv:2203.04990, and has now been extracted into this paper. Part I is arXiv:2103.08615. (v4) Added references. (v5) Added appendix showing cancellation of diagrams. Added reference to arXiv:2208.04328. (v8) Fixed typo