TY - JOUR

T1 - Statistical analysis of the figure of merit of a two-level thermoelectric system

T2 - A random matrix approach

AU - Abbout, Adel

AU - Ouerdane, Henni

AU - Goupil, Christophe

PY - 2016/9/15

Y1 - 2016/9/15

N2 - Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and connected through a low-density-of-states two-level quantum dot that acts as a conducting chaotic cavity. Our exact treatment of the chaotic behavior in such devices lies on the scattering matrix formalism and yields analytical expressions for the joint probability distribution functions of the Seebeck coefficient and the transmission profile, as well as the marginal distributions, at arbitrary Fermi energy. The scattering matrices belong to circular ensembles which we sample to numerically compute the transmission function, the Seebeck coefficient, and their relationship. The exact transport coefficients probability distributions are found to be highly non-Gaussian for small numbers of conduction modes, and the analytical and numerical results are in excellent agreement. The system performance is also studied, and we find that the optimum performance is obtained for half-transparent quantum dots; further, this optimum may be enhanced for systems with few conduction modes.

AB - Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and connected through a low-density-of-states two-level quantum dot that acts as a conducting chaotic cavity. Our exact treatment of the chaotic behavior in such devices lies on the scattering matrix formalism and yields analytical expressions for the joint probability distribution functions of the Seebeck coefficient and the transmission profile, as well as the marginal distributions, at arbitrary Fermi energy. The scattering matrices belong to circular ensembles which we sample to numerically compute the transmission function, the Seebeck coefficient, and their relationship. The exact transport coefficients probability distributions are found to be highly non-Gaussian for small numbers of conduction modes, and the analytical and numerical results are in excellent agreement. The system performance is also studied, and we find that the optimum performance is obtained for half-transparent quantum dots; further, this optimum may be enhanced for systems with few conduction modes.

UR - http://www.scopus.com/inward/record.url?scp=84986913695&partnerID=8YFLogxK

U2 - 10.7566/JPSJ.85.094704

DO - 10.7566/JPSJ.85.094704

M3 - Article

AN - SCOPUS:84986913695

VL - 85

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 9

M1 - 094704

ER -