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Thermal transport in dimerized harmonic lattices: Exact solution, crossover behavior, and extended reservoirs



Chih-Chun Chien, Said Kouachi, Kirill Velizhanin, Yonatan Dubi, Michael P. Zwolak


We present a method for calculating analytically the thermal conductance of a classical harmonic lattice with both alternating masses and nearest-neighbor couplings when placed between individual Langevin reservoirs at different temperatures. The technique utilizes recent advances in diagonalization techniques for certain classes of tridiagonal matrices. It recovers the results from a previous method that was for alternating onsite parameters only, and extends the applicability to realistic systems in which masses and couplings alternate simultaneously. With this analytical result in hand, we show that the thermal conductance is highly sensitive to the modulation of both the masses and couplings. This is due to the existence of topologically-induced edge modes at the lattice-reservoir interface and is also a reflection of the symmetries of the lattice. We make a connection to a recent work that demonstrates thermal transport is analogous to chemical reaction rates in solution given by Kramers' theory (Velizhanin et al., 2015). In particular, we show that the turnover behavior in the presence of edge modes prevents calculations based on single-site reservoirs from coming close to the natural -- or intrinsic -- conductance of the lattice. Obtaining the correct value of the intrinsic conductance through simulation of even a small lattice where ballistic effects are important requires quite large extended reservoir regions. Our results thus offer a route for both the design and proper simulation of thermal conductance of nanoscale devices.
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)


Thermal Transport, Nanomechnical Lattices, Simulation Techniques


Chien, C. , Kouachi, S. , Velizhanin, K. , Dubi, Y. and Zwolak, M. (2017), Thermal transport in dimerized harmonic lattices: Exact solution, crossover behavior, and extended reservoirs, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), [online],, (Accessed July 19, 2024)


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Created January 22, 2017, Updated October 12, 2021