Fermi-liquid theory for the Anderson model out of equilibrium

Resonant tunneling through quantum dot under a finite bias voltage at zero temperature is investigated by using the adaptive time-dependent density matrix renormalization group (TdDMRG) method. Quantum dot is modeled by the Anderson Hamiltonian with the one-dimensional nearest-neighbor tightbinding leads. Initially the ground state wave function is calculated with the usual DMRG method. Then the time evolution of the wave function due to the slowly changing bias voltage between the two leads is calculated by using the TdDMRG technique. Even though the system size is finite, the expectation values of current operator show steady-like behavior for a finite time interval, in which the system is expected to resemble the real nonequilibrium steady state of the infinitely long system. We show that from the time intervals one can obtain quantitatively correct results for differential conductance in a wide range of bias voltage. Finally we observe an anomalous behavior in the expectation value of the double occupation operator at the dot hn " n # i as a function of bias voltage.

show abstract

“…For this purpose we use an asymptotic expression for in the low energy, low bias voltage and low temperature, 24) …”

Section: Zero Magnetic Field 511 Currentmentioning

confidence: 99%

Time-Dependent DMRG Study on Quantum Dot under a Finite Bias Voltage

et al. 2008

View full text Add to dashboard Cite

show abstract

“…[27][28][29][30][31][32][33][34][35] We have shown that the Keldysh Green's function 36,37 is solvable in the opposite limit eV → ∞, where the excitations of whole energy scales equally contribute to the dynamics. In this limit, the model can be mapped onto a nonHermitian Hamiltonian of two effective sites in a doubled Hilbert space that is defined in the thermal field theory.…”

Section: -12mentioning

confidence: 99%

Exact Green's function for a multiorbital Anderson impurity at high bias voltages

Oguri

Sakano

2015

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

We study the nonequilibrium Keldysh Green's function for an N -orbital Anderson model at high bias voltages, extending a previous work which for the case only with the spin degrees of freedom N = 2, to arbitrary N . Our approach uses an effective non-Hermitian Hamiltonian that is defined with respect to a Liouville-Fock space in the context of a thermal field theory. The result correctly captures the relaxation processes at high energies, and is asymptotically exact not only in the highbias limit but also in the high-temperature limit at thermal equilibrium. We also present an explicit continued-fraction representation of the Green's function. It clearly shows that the imaginary part is recursively determined by the decay rate of intermediate states with at most N − 1 particle-holepair excitations. These high-bias properties follow from the conservations of a generalized charge and current in the Liouville-Fock space. We also examine temperature dependence of the spectral function in equilibrium, comparing the exact results with the numerical finite-T and analytical T → ∞ results of the non-crossing approximation (NCA).

show abstract

“…The application along this line seems to be interesting in relation to the metal-insulator transition observed in two-dimensional systems. 28) Furthermore, extensions to the finite temperatures 29) and nonequilibrium situations 30) are left for future studies.…”

Section: Remarksmentioning

confidence: 99%

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

2002

Self Cite

View full text Add to dashboard Cite

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...

show abstract

Fermi-liquid theory for the Anderson model out of equilibrium

Cited by 114 publications

References 19 publications

Time-Dependent DMRG Study on Quantum Dot under a Finite Bias Voltage

Time-Dependent DMRG Study on Quantum Dot under a Finite Bias Voltage

Exact Green's function for a multiorbital Anderson impurity at high bias voltages

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

Contact Info

Product

Resources

About