Perturbation Study of the Conductance through an Interacting Region Connected to Multi-Mode Leads

Abstract

We study the effects of electron correlation on transport through an interacting region connected to multi-mode leads based on the perturbation expansion with respect to the interelectron interaction. At zero temperature the conductance defined in the Kubo formalism can be written in terms of a single-particle Green's function at the Fermi energy, and it can be mapped onto a transmission coefficient of the free quasiparticles described by an effective Hamiltonian. We apply this formulation to a two-dimensional Hubbard model of finite size connected to two noninteracting leads. We calculate the conductance in the electron-hole symmetric case using the order U 2 self-energy. The conductance shows several maximums in the U dependence in some parameter regions of t y /t x , where t x (t y ) is the hopping matrix element in the x-(y-) directions. This is caused by the resonance occurring in some of the subbands, and is related with the U dependence of the eigenvalues of the effective Hamiltonian.KEYWORDS: conductance, subband structure, electron correlation, perturbation expansion, Hubbard model, two-dimension §1. IntroductionLow-dimensional electron systems have been one of the current interests in the fields of the condensed matter physics and materials science. For instance, in some of the organic conductors, the electron correlation has been considered to be important to understand the physical properties. 1)The Kondo effect in quantum dots 2, 3, 4) has also been studied intensively from theoretical 5, 6) and experimental 7,8,9) sides. When the average number of the electrons in a quantum dot is odd, the perfect transmission due to the Kondo resonance situated at the Fermi energy occurs at low temperatures. Recently, artificial molecules which are realized by arranging two or more quantum dots have also been studied. 10,11) Theoretically, the crossover from the high-temperature Coulombblockade to low-temperature Fermi-liquid behaviors of the quantum dots has been studied using advanced numerical methods such as the numerical renormalization group 12, 13) and quantum Monte Carlo methods. 14,15,16) In a previous work, one of the authors has studied the conductance of small interacting systems 1 connected to two single-mode leads, 17,18) and has calculated the conductance of a Hubbard chain of finite size N using the order U 2 self-energy. The results obtained in the electron-hole symmetric case depend strongly on whether N is even or odd. In the even cases, the conductance decreases with increasing N showing a tendency toward a Mott-Hubbard insulator. On the other hand, in the odd cases the perfect transmission due to the Kondo resonance occurs. 18)The purpose of the present work is to generalize the formulation to the multi-mode systems where the interacting system is connceted to noninteracting leads with a number of channels. As in the single-mode case, at T = 0 the contributions of the vertex corrections on the dc conductance g vanish. Then the conductance is determined by the value of the single-particle Green...

Crossover between two different Kondo couplings in side-coupled double quantum dots

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Numerical renormalization group approach to a quartet quantum-dot array connected to reservoirs: Gate-voltage dependence of the conductance

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“…Similarly, at T = 0 the charge displacement N el caused by the hybridizations Γ L and Γ R can be expressed, using the Friedel sum rule, 20,21 as…”

“…This expression is for the current flowing from left to right (or right to left), and has been derived from the Kubo formula using a multi-channel formulation for the dc conductance. 21…”