Abstract

Abstract: We calculate theelectronic viscosity (η) for a multiple quantum well structure in the presenceof disorder potential(V ~ 4 meV), the electron-electron repulsion(U₀~5-17 meV) and magnetic field in the direction in which the electrons aretrapped. The quantity η is different from the dissipation-less Hall viscosity(ηH) which cannot take non-zero value in a time reversal invariant system. TheFermi energy density of states for the system has been calculated in thet-matrix approximation assuming low concentration of impurities. Our approachinvolves calculation of the density of viscosity η(k), for temperature close to0 K, on the Brillouin zone(BZ) followed by the numerical evaluation of theintegral of η(k) over the BZ. We show that (i) η is nearly proportional to Bfor given (V,U₀) We also see the results comply with the KSS boundη/S ≥ ħ/4πkB reported by Kovtun et al. [P.K. Kovtun, D.T. Son, andA.O.Starinets, Phys. Rev. Lett. 94, 111601 (2005); Taro Kimura, arXiv:1004.2688(Unpublished)], where S is the entropy per particle.

PACS 73.43.-f, 73.63.Hs,73.21.-b , 73.21 Fg

Keywords: Multiple quantum well;Electronic viscosity; t-matrix approximation; Fermi energy density of states.