TY - JOUR
T1 - Thermal transport in dimerized harmonic lattices
T2 - Exact solution, crossover behavior, and extended reservoirs
AU - Chien, Chih Chun
AU - Kouachi, Said
AU - Velizhanin, Kirill A.
AU - Dubi, Yonatan
AU - Zwolak, Michael
N1 - Funding Information: K.A.V. was supported by the U.S. Department of Energy through the LANL/LDRD Program. Y.D. acknowledges support from the Israel Science Fund (Grant No. 1256/14). Publisher Copyright: © 2017 American Physical Society.
PY - 2017/1/23
Y1 - 2017/1/23
N2 - 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, 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.
AB - 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, 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.
UR - http://www.scopus.com/inward/record.url?scp=85010310977&partnerID=8YFLogxK
U2 - https://doi.org/10.1103/PhysRevE.95.012137
DO - https://doi.org/10.1103/PhysRevE.95.012137
M3 - Article
C2 - 28208409
SN - 2470-0045
VL - 95
JO - Physical Review E
JF - Physical Review E
IS - 1
M1 - 012137
ER -