A Diagrammer's Note on Superconducting Fluctuation Transport for Beginners: II. Hall and Nernst Effects with Perturbational Treatment of Magnetic Field

TL;DR

This paper reviews a diagrammatic approach to superconducting fluctuation transport, specifically the Hall and Nernst effects, using perturbation theory for weak magnetic fields and discussing related linear response theories.

Contribution

It introduces a perturbational treatment of magnetic fields in superconducting fluctuation transport and reviews linear response theories for Hall conductivity in Dirac fermions.

Findings

Perturbational analysis of Hall and Nernst effects in superconductors.

Review of linear response theory for Dirac fermions in 2+1 dimensions.

Discussion of Chern-Simons effective action and exact formulas for Hall conductivity.

Abstract

A diagrammatic approach based on thermal Green function to superconducting fluctuation transport is reviewed focusing on Hall and Nernst effects. The treatment of weak magnetic field is carefully discussed within the linear order perturbation. In the Appendix the linear response theory for the DC Hall conductivity of the Dirac fermion in 2+1 space-time dimensions is reviewed. One focus is the Chern-Simons effective action for the gauge field. Another is the exact formula by Ishikawa and Matsuyama.