Quantum--classical correspondence and dissipative to dissipationless crossover in magnetotransport phenomena

TL;DR

This paper derives a gauge-invariant quantum formula for magneto-conductivity, demonstrating quantum-classical correspondence, and explores the transition from dissipative to dissipationless transport in magnetotransport phenomena, with implications for semimetals.

Contribution

It establishes a quantum--classical correspondence in magnetotransport and reveals a dissipative-to-dissipationless crossover in Hall conductivity.

Findings

Quantum oscillation factor added to classical formula reproduces quantum results.

Identified phase shift in quantum oscillations due to dissipationless transport.

Discovered crossover from dissipative to dissipationless Hall conductivity at high magnetic fields.

Abstract

The three-dimensional magneto-conductivity tensor was derived in a gauge invariant form based on the Kubo formula considering the quantum effect under a magnetic field, such as the Landau quantization and the quantum oscillations. We analytically demonstrated that the quantum formula of the magneto-conductivity can be obtained by adding a quantum oscillation factor to the classical formula. This result establishes the quantum--classical correspondence, which has long been missing in magnetotransport phenomena. Moreover, we found dissipative-to-dissipationless crossover in the Hall conductivity by paying special attention to the analytic properties of thermal Green's function. Finally, by calculating the magnetoresistance of semimetals, we identified a phase shift in quantum oscillation originating from the dissipationless transport predominant at high fields.