title: Thermal transport in dimerized harmonic lattices: Exact solution, crossover behavior, and extended reservoirs.
abstract: 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 applicable for alternating on-site 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)]2045-232210.1038/srep17506. 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.
authors.affiliation: School of Natural Sciences, University of California, Merced, California 95343, USA.
authors.forename: Chih-Chun
authors.initials: CC
authors.lastname: Chien
authors.affiliation: Department of Mathematics, Qassim University, Al-Gassim, Buraydah 51452, Saudi Arabia.
authors.forename: Said
authors.initials: S
authors.lastname: Kouachi
authors.affiliation: Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: Kirill A
authors.initials: KA
authors.lastname: Velizhanin
authors.affiliation: Department of Chemistry and the Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel.
authors.forename: Yonatan
authors.initials: Y
authors.lastname: Dubi
authors.affiliation: Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Zwolak