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

Journal Article · Mon Jan 23 00:00:00 EST 2017 · Physical Review E

DOI:https://doi.org/10.1103/PhysRevE.95.012137· OSTI ID:1471316

Chien, Chih-Chun ^[1]; Kouachi, Said ^[2]; Velizhanin, Kirill A. ^[3]; Dubi, Yonatan ^[4]; Zwolak, Michael ^[5]

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1. University of California, Merced, CA (United States)
2. Qassim University, Al-Gassim, Buraydah (Saudi Arabia)
3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
4. Ben-Gurion University of the Negev, Beer-Sheva (Israel)
5. National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States)

In this paper, 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)]. 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. Finally, our results thus offer a route for both the design and proper simulation of thermal conductance of nanoscale devices.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: Laboratory Directed Research and Development (LDRD); USDOE
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1471316
• Alternate ID(s): OSTI ID: 1341311
• Report Number(s): LA-UR--18-28757
• Journal Information: Physical Review E, Journal Name: Physical Review E Journal Issue: 1 Vol. 95; ISSN PLEEE8; ISSN 2470-0045
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS