Thermal transport in dimerized harmonic lattices: Exact solutioncrossover behavior and extended reservoirs

摘要

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 method utilizes recent advances in analytic 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 analytic result in hand, we show that the thermal conductance is highly sensitive to the modulation of the 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., Sci. Rep. >5, 17506 (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 – orintrinsic – conductance of the lattice. Obtainingthe correct value of the intrinsic conductance through simulation of even asmall lattice where ballistic effects are important requires quite largeextended reservoir regions. Our results thus offer a route for both the designand proper simulation of thermal conductance of nanoscale devices.