Heat transport in an ordered harmonic chain in presence of a uniform magnetic field

TL;DR

This paper analyzes heat transport in a harmonic chain of charged particles under a uniform magnetic field, deriving exact Green's function expressions and revealing how the magnetic field alters phonon transmission properties.

Contribution

It provides the first exact expressions for heat current in a charged harmonic chain with magnetic field, highlighting the impact on phonon band structure and low-frequency transmission behavior.

Findings

Transmission depends on magnetic field, splitting into two phonon bands.

Low-frequency transmission scales as ω^{3/2} and ω^{1/2} for fixed and free boundaries.

Contrast with zero magnetic field case where transmission scales as ω^2 and ω^0.

Abstract

We consider heat transport across a harmonic chain of charged particles, with transverse degrees of freedom, in the presence of a uniform magnetic field. For an open chain connected to heat baths at the two ends we obtain the nonequilibrium Green's function expression for the heat current. This expression involves two different Green's functions which can be identified as corresponding respectively to scattering processes within or between the two transverse waves. The presence of the magnetic field leads to two phonon bands of the isolated system and we show that the net transmission can be written as a sum of two distinct terms attributable to the two bands. Exact expressions are obtained for the current in the thermodynamic limit, for the the cases of free and fixed boundary conditions. In this limit, we find that at small frequency $\omega$, the effective transmission has the frequency-dependence $\omega^{3/2}$ and $\omega^{1/2}$ for fixed and free boundary conditions respectively. This is in contrast to the zero magnetic field case where the transmission has the dependence $\omega^2$ and $\omega^0$ for the two boundary conditions respectively, and can be understood as arising from the quadratic low frequency phonon dispersion.