Thermal balance and quantum heat transport in nanostructures thermalized by local Langevin heat baths

Abstract

Modeling of thermal transport in practical nanostructures requires making trade-offs between the size of the system and the completeness of the model. We study quantum heat transfer in a selfconsistent thermal bath setup consisting of two lead regions connected by a center region. Atoms both in the leads and in the center region are coupled to quantum Langevin heat baths that mimic the damping and dephasing of phonon waves by anharmonic scattering. This approach treats the leads and the center region on same footing and thereby allows for a simple and physically transparent thermalization of the system, enabling also perfect acoustic matching between the leads and the center region. Increasing the strength of the coupling reduces the mean free path of phonons and gradually shifts phonon transport from ballistic regime to diffusive regime. In the center region, the bath temperatures are determined self-consistently from the requirement of zero net energy exchange between the local heat bath and each atom. By solving the stochastic equations of motion in frequency space and averaging over noise using the general fluctuation-dissipation relation derived by Dhar and Roy [J. Stat. Phys. 125, 801 (2006)], we derive the formula for thermal current, which contains the Caroli formula for phonon transmission function and reduces to the Landauer-Büttiker formula in the limit of vanishing coupling to local heat baths. We prove that the bath temperatures measure local kinetic energy and can, therefore, be interpreted as true atomic temperatures. In a setup where phonon reflections are eliminated, Boltzmann transport equation under gray approximation with full phonon dispersion is shown to be equivalent to the self-consistent heat bath model. We also study thermal transport through two-dimensional constrictions in square lattice and graphene and discuss the differences between the exact solution and linear approximations.

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Inelastic effects in molecular transport junctions: The probe technique at high bias

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Thermopower of molecular junctions: Tunneling to hopping crossover in DNA

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