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

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 evenmore » 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.« less
Authors:
 [1] ;  [2] ; ORCiD logo [3] ;  [4] ;  [5]
  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)
Publication Date:
Report Number(s):
LA-UR-18-28757
Journal ID: ISSN 2470-0045; PLEEE8
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 95; Journal Issue: 1; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE Laboratory Directed Research and Development (LDRD) Program
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
OSTI Identifier:
1471316
Alternate Identifier(s):
OSTI ID: 1341311