We review mechanisms of low-temperature electronic transport through a quantum dot weakly coupled to two conducting leads. Transport in this case is dominated by electron-electron interaction. At temperatures moderately lower than the charging energy of the dot, the linear conductance is suppressed by the Coulomb blockade. Upon further lowering of the temperature, however, the conductance may start to increase again due to the Kondo effect. We concentrate on lateral quantum dot systems and discuss the conductance in a broad temperature range, which includes the Kondo regime.

We evaluate the dynamic structure factor S(q, ω) of interacting one-dimensional spinless fermions with a nonlinear dispersion relation. The combined effect of the nonlinear dispersion and of the interactions leads to new universal features of S(q, ω). The sharp peak S(q, ω) ∝ qδ(ω − uq), characteristic for the Tomonaga-Luttinger model, broadens up; S(q, ω) for a fixed q becomes finite at arbitrarily large ω. The main spectral weight, however, is confined to a narrow frequency interval of the width δω ∼ q 2 /m. At the boundaries of this interval the structure factor exhibits power-law singularities with exponents depending on the interaction strength and on the wave number q.PACS numbers: 71.10.Pm, 72.15.Nj Low-energy properties of fermionic systems are sensitive to interactions between fermions. The effect of interactions is the strongest in one dimension (1D), where single-particle correlation functions exhibit power-law singularities, in a striking departure from the behavior in higher dimensions. Much of our current understanding of 1D fermions is based on the Tomonaga-Luttinger (TL) model [1]. The crucial ingredient of the model is the assumption of a strictly linear fermionic dispersion relation. The TL model, often used in conjunction with a powerful bosonization technique [2], allows one to evaluate various correlation functions, such as momentum-resolved [3,4] and local [5] single-particle densities of states.Unlike the single-particle correlation functions, the two-particle correlation functions of the TL model exhibit behavior rather compatible with that expected for a Fermi liquid with the linear spectrum of quasiparticles. For example, the dynamic structure factor (the densitydensity correlation function)at small q takes the form [3] S TL (q, ω) ∝ qδ(ω − uq). It means that the quanta of density waves propagating with plasma velocity u are true eigenstates of the TL model; these bosonic excitations have an infinite lifetime. Below we show that such a simple behavior is an artefact of the linear spectrum approximation. In reality, the spectrum of fermions always has some nonlinearity,where the upper/lower sign corresponds to the right/left movers (R/L), and k = p ∓ p F are momenta measured from the Fermi points ± p F . (For Galilean-invariant systems the expansion (2) terminates at k 2 .) The finite curvature (1/m = 0) affects drastically the functional form of S(q, ω). In a clear deviation from the results of TL model, power-law singularities now arise not only in the single-particle correlation functions, but in the structure factor as well. We show that the singularities in these two very different objects have a common origin, proliferation of low-energy particle-hole pairs, and evaluate the corresponding exponents.Because of the success of the bosonization technique [2], it is tempting to treat the spectrum nonlinearity as a weak interaction between the TL bosons. Indeed, the nonlinearity gives rise to a three-boson interaction with the coupling constant ∝ 1/m [6]. However, attempts to treat this ...

Exchange interaction within a quantum dot strongly affects the transport through it in the Kondo regime. In a striking difference with the results of the conventional model, where this interaction is neglected, here the temperature and magnetic field dependence of the conductance may become non-monotonic: its initial increase follows by a drop when temperature and magnetic field are lowered.PACS numbers: 72.15. Qm, 73.23.Hk, 73.63.Kv The conventional theory of the Kondo effect in tunneling [1] is based on the Anderson impurity model [2]. The use of this model for describing the electron transport through a conducting grain was first suggested in [3], and later successfully applied in the context of quantum dots in the Coulomb blockade regime (see, e.g., [4]). In these applications, the quantum dot is modeled by one singly occupied energy level. The model predicts monotonic increase of the tunneling conductance with lowering the temperature. By now, a strong experimental evidence exists for such behavior [5].To measure transport across the dot, at least two leads should be attached to it. The problem of transmission through a dot is similar to that of transition between channels in a multichannel scattering problem. If the system is described by the Anderson model, then the corresponding transition rate turns out to be proportional to the total scattering cross-section. Therefore the two problems, calculation of the tunneling conductance G, and evaluation of the magnetic impurity contribution to the resistivity of a bulk metal, are equivalent [6]. Well below the Kondo temperature, the scattering cross-section reaches the unitary limit; accordingly, G saturates at the level G ∼ e 2 /πh. In a real quantum dot, the truncation of the spectrum to a single level is not always possible. For example, dots with ground state spin S > 1/2 are not described by the Anderson impurity model [7]. In this paper we demonstrate that in general the problem of transport through a dot does not map onto the problem of resistivity in a bulk metal. In the most interesting case, the tunneling conductance first rises and than drops when temperature is lowered. The conductance dependence on the magnetic field is also non-monotonic.The confining potential forming a lateral quantum dot is smooth. The dot-lead junction is essentially an electron waveguide [8]. Making it narrower, one pinches the propagating modes off. Coulomb blockade develops when the last propagating mode is near its pinch-off. Therefore, for lateral dots in the Coulomb blockade regime the number of channels per junction is one.We start with a discussion of the dependence of the zero-temperature conductance on the magnetic field applied in the plane of the dot. The in-plane field results in the Zeeman splitting B of the spin states of the dot, but barely affects the orbital degrees of freedom. At a finite B, the ground state of the system is not degenerate; therefore, at T = 0 an electron experiences only potential scattering. The amplitudes of scattering S s;αα ′ of elec...

We evaluate the spectral function of interacting fermions in one dimension. Contrary to the Tomonaga-Luttinger model, our treatment accounts for the nonlinearity of the free fermion spectrum. In a striking departure from the Luttinger liquid theory, the spectrum nonlinearity restores the main feature of the Fermi liquid: a Lorentzian peak in the spectral function on the particle mass-shell. At the same time, the spectral function displays a power-law singularity on the hole mass-shell, similar to that in the Luttinger liquid.

We demonstrate that in a wide range of temperatures Coulomb drag between two weakly coupled quantum wires is dominated by processes with a small interwire momentum transfer. Such processes, not accounted for in the conventional Luttinger liquid theory, cause drag only because the electron dispersion relation is not linear. The corresponding contribution to the drag resistance scales with temperature as T2 if the wires are identical, and as T5 if the wires are different.