Phonon-mediated thermal conductance of mesoscopic wires with rough edges

Physical Review B - Condensed Matter and Materials Physics

Volumn 60, Issue 23, 1999, Pages 15593-15596

  Kambili, A ^a   Fagas, G ^a   Fal'ko V ^a   Lambert, C J ^a  

^a LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000505232     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.60.15593     Document Type: Article

References (20)

1. T. S. Tighe, Appl. Phys. Lett.70, 2687 (1997);
2. M. L. Roukes, Physica B263-264, 1 (1999) and references therein.
3. M. P. Blencowe, Phys. Rev. B59, 4992 (1999).
4. L.G.C. Rego and G. Kirczenow, Phys. Rev. Lett.81, 232 (1998).
5. For a multichannel waveguide, (formula presented)
6. L. I. Glazman, Pis’ma Zh. Éksp. Teor. Fiz. 48, 218 (1988) [JETP Lett.48, 238 (1988)];
7. G. Kirczenow, Solid State Commun.68, 715 (1988).
8. M. Büttiker, Phys. Rev. B31, 6207 (1985);
9. C.W.J. Beenakker, Rev. Mod. Phys.69, 731 (1997).
10. For a fractally rough edge, (formula presented) (formula presented)
11. B. Elattari, V. Kagalovsky, and H A. Weidenmuller, Phys. Rev. E57, 2733 (1998).
12. A. B. Pippard, Magnetoresistance in Metals (Cambridge University Press, Cambridge, 1989).
13. Z. Tesanovich, M C. Jaric, and S. Maekawa, Phys. Rev. Lett.57, 2760 (1986).
14. M. Leadbeater, V I. Falko, and C J. Lambert, Phys. Rev. Lett.81, 1274 (1998).
15. M. P. Blencowe, J. Phys.: Condens. Matter7, 5177 (1995).
16. After discretization, the equation of motion takes the form of (formula presented) where (formula presented) and (formula presented) and (formula presented) is the number of nearest neighbors of site j from cross section i. By representing (formula presented) with (formula presented) we prepare the equation of motion for the treatment by the discrete transfer-matrix method, (formula presented) The overlap integrals, (formula presented) (formula presented) carry information about surface roughness through the factors (formula presented) which indicate the existence (formula presented) or absence (formula presented) of neighboring sites. The width of each wire cross section, (formula presented) is randomly generated by introducing a random function (formula presented) where (formula presented) and (formula presented) are chosen to yield the desired harmonic content, (formula presented) are randomly taken from the interval (formula presented) and i is the coordinate along the wire axis. Finally, we normalize the fluctuation of the width to a desired rms value, so that (formula presented)
17. S.J. Robinson, Ph.D. thesis, Lancaster University, 1992;
18. W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes (FORTRAN) (Cambridge University Press, Cambridge, 1989).
19. B. Altshuler and V. Prigodin, Pis’ma Zh. Éksp. Teor. Fiz. 36 (1988) [JETP Lett.47, 43 (1988)].
20. One can also speak of a cooling time of an overheated specimen due to the phonon-mediated cooling through the wire into a bath, with (formula presented) Then, the temporal evolution of the temperature can be described by equation (formula presented) where (formula presented) is the Debye heat capacity of a specimen, and V is its volume. The cooling time can be found by integrating this equation with respect to the temperature, which yields (formula presented) We estimate (formula presented) analytically in two limits: (i) (formula presented) (with (formula presented) (formula presented) and (ii) (formula presented) of a weakly disordered wire and a strongly disordered wire with the length (formula presented) respectively. In case (i), we find approximately equal to (formula presented)In case (ii) of a long wire, we interpolate (formula presented) using (formula presented) and arrive at (formula presented)