arXiv subjects

L. I. Glazman

Publications and source records attributed to L. I. Glazman.

At least 91 records · Page 5Linked to original sources

arXiv2003

Coulomb blockade and Kondo effect in quantum dots

We review the mechanisms of low-temperature electron transport across a quantum dot weakly coupled to two conducting leads. Conduction in this case is controlled by the interaction between electrons. At temperatures moderately lower than the single-electron 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. This increase occurs only if the dot has a non-zero spin S. We concentrate on the simplest case of S=1/2, and discuss the conductance across the dot in a broad temperature range, which includes the Kondo temperature. Temperature dependence of the linear conductance in the Kondo regime is discussed in detail. We also consider a simple (but realistic) limit in which the differential conductance at a finite bias can be fully investigated.

cond-mat.mes-hall↗

arXiv2003

Resonant tunneling of interacting electrons in a one-dimensional wire

We consider the conductance of a one-dimensional wire interrupted by a double-barrier structure allowing for a resonant level. Using the electron-electron interaction strength as a small parameter, we are able to build a non-perturbative analytical theory of the conductance valid in a broad region of temperatures and for a variety of the barrier parameters. We find that the conductance may have a non-monotonic crossover dependence on temperature, specific for a resonant tunneling in an interacting electron system.

cond-mat.mes-hall↗

arXiv2002

Linear conductance in Coulomb-blockade quantum dots in the presence of interactions and spin

We discuss the calculation of the linear conductance through a Coulomb-blockade quantum dot in the presence of interactions beyond the charging energy. In the limit where the temperature is large compared with a typical tunneling width, we use a rate-equations approach to describe the transitions between the corresponding many-body states. We discuss both the elastic and rapid-thermalization limits, where the rate of inelastic scattering in the dot is either small or large compared with the elastic transition rate, respectively. In the elastic limit, we find several cases where a closed solution for the conductance is possible, including the case of a constant exchange interaction. In the rapid-thermalization limit, a closed solution is possible in the general case. We show that the corresponding expressions for the linear conductance simplify for a Hamiltonian that is invariant under spin rotations.

cond-mat.mes-hall↗

arXiv2002

Electron energy and phase relaxation on magnetic impurities

We discuss the effect of magnetic impurities on the inelastic scattering and dephasing of electrons. Magnetic impurities mediate the energy exchange between electrons. This mechanism is especially effective at small energy transfers $E$ in the absence of Zeeman splitting, when the two-particle collision integral in the electron kinetic equation has a kernel $K\propto 1/E^2$ in a broad energy range. In a magnetic field, this mechanism is suppressed at $E$ below the Zeeman energy. Simultaneously, the Zeeman splitting of the impurity spin states reduces the electron dephasing rate, thus enhancing the effect of electron interference on conduction. We find the weak localization correction to the conductivity and the magnitude of the conductance fluctuations in the presence of magnetic field of arbitrary strength. Our results can be compared quantitatively with the experiments on energy relaxation in short metallic wires and on Aharonov-Bohm conductance oscillations in wire rings.

cond-mat.mes-hall↗

arXiv2002

Zeeman splitting of zero-bias anomaly in Luttinger liquids

Tunnelling density of states (DoS) in Luttinger liquid has a dip at zero energy, commonly known as the zero-bias anomaly (ZBA). In the presence of a magnetic field, in addition to the zero-bias anomaly, the DoS develops two peaks separated from the origin by the Zeeman energy. We find the shape of these peaks at arbitrary strength of the electron-electron interaction. The developed theory is applicable to various kinds of quantum wires, including carbon nanotubes.

cond-mat.mes-hall↗

arXiv2002

Conductance of Mesoscopic Systems with Magnetic Impurities

We investigate the combined effects of magnetic impurities and applied magnetic field on the interference contribution to the conductance of disordered metals. We show that in a metal with weak spin-orbit interaction, the polarization of impurity spins reduces the rate of electron phase relaxation, thus enhancing the weak localization correction to conductivity. Magnetic field also suppresses thermal fluctuations of magnetic impurities, leading to a recovery of the conductance fluctuations. This recovery occurs regardless the strength of the spin-orbit interaction. We calculate the magnitudes of the weak localization correction and of the mesoscopic conductance fluctuations at an arbitrary level of the spin polarization induced by a magnetic field. Our analytical results for the ``$h/e$'' Aharonov-Bohm conductance oscillations in metal rings can be used to extract spin and gyromagnetic factor of magnetic impurities from existing experimental data.

cond-mat.mes-hall↗

arXiv2002

Persistent current in superconducting nanorings

The superconductivity in very thin rings is suppressed by quantum phase slips. As a result the amplitude of the persistent current oscillations with flux becomes exponentially small, and their shape changes from sawtooth to a sinusoidal one. We reduce the problem of low-energy properties of a superconducting nanoring to that of a quantum particle in a sinusoidal potential and show that the dependence of the current on the flux belongs to a one-parameter family of functions obtained by solving the respective Schrodinger equation with twisted boundary conditions.

cond-mat.mes-hall↗

arXiv2002

Tunneling of correlated electrons in ultra high magnetic field

Effects of the electron-electron interaction on tunneling into a metal in ultra-high magnetic field (ultra-quantum limit) are studied. The range of the interaction is found to have a decisive effect both on the nature of the field-induced instability of the ground state and on the properties of the system at energies above the corresponding gap. For a short-range repulsive interaction, tunneling is dominated by the renormalization of the coupling constant, which leads eventually to the charge-density wave instability. For a long-range interaction, there exists an intermediate energy range in which the conductance obeys a power-law scaling form, similar to that of a 1D Luttinger liquid. The exponent is magnetic-field dependent, and more surprisingly, may be positive or negative, i. e., interactions may either suppress or enhance the tunneling conductance compared to its non-interacting value. At energies near the gap, scaling breaks down and tunneling is again dominated by the instability, which in this case is an (anisotropic) Wigner crystal instability.

cond-mat.str-el↗

arXiv2001

Zero-bias anomaly in disordered wires

We calculate the low-energy tunneling density of states $ν(ε, T)$ of an $N$-channel disordered wire, taking into account the electron-electron interaction non-perturbatively. The finite scattering rate $1/τ$ results in a crossover from the Luttinger liquid behavior at higher energies, $ν\proptoε^α$, to the exponential dependence $ν(ε, T=0)\propto \exp{(-ε^*/ε)}$ at low energies, where $ε^*\propto 1/(N τ)$. At finite temperature $T$, the tunneling density of states depends on the energy through the dimensionless variable $ε/\sqrt{ε^* T}$. At the Fermi level $ν(ε=0,T) \propto \exp (-\sqrt{ε^*/T})$.

cond-mat.mes-hall↗

arXiv2001

Quantum Effects in Coulomb Blockade

We review the quantum interference effects in a system of interacting electrons confined to a quantum dot. The review starts with a description of an isolated quantum dot. We discuss the status of the Random Matrix theory (RMT) of the one-electron states in the dot, present the universal form of the interaction Hamiltonian compatible with the RMT, and derive the leading corrections to the universal interaction Hamiltonian. Next, we discuss a theoretical description of a dot connected to leads via point contacts. Having established the theoretical framework to describe such an open system, we discuss its transport and thermodynamic properties. We review the evolution of the transport properties with the increase of the contact conductances from small values to values $\sim e^2/π\hbar$. In the discussion of transport, the emphasis is put on mesoscopic fluctuations and the Kondo effect in the conductance.

cond-mat.mes-hall↗

arXiv2001

Kondo effect in real quantum dots

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.

cond-mat.mes-hall↗

arXiv2001

Kondo effect induced by a magnetic field

We study peculiarities of transport through a Coulomb blockade system tuned to the vicinity of the spin transition in its ground state. Such transitions can be induced in practice by application of a magnetic field. Tunneling of electrons between the dot and leads mixes the states belonging to the ground state manifold of the dot. Remarkably, both the orbital and spin degrees of freedom of the electrons are engaged in the mixing at the singlet-triplet transition point. We present a model which provides an adequate theoretical description of recent experiments with semiconductor quantum dots and carbon nanotubes.

cond-mat.mes-hall↗

arXiv2001

Electron energy relaxation in the presence of magnetic impurities

We study inelastic electron-electron scattering mediated by the exchange interaction of electrons with magnetic impurities, and find the kernel of the corresponding two-particle collision integral. In a wide region of parameters, the kernel K is proportional to the inverse square of the transferred energy, $K\propto J^4/E^2$. The exchange constant J is renormalized due to the Kondo effect, yielding an additional weak dependence of K on the energies of the colliding electrons. At small energy transfers, the $1/E^2$ divergence is cut off; the cut-off energy is determined by the dynamics of the impurity spins. The obtained results may provide a quantitative explanation of the experiments of Pothier et al. [Phys. Rev. Lett. 79, 3490 (1997)] on anomalously strong energy relaxation in short metallic wires.

cond-mat.mes-hall↗

arXiv2000

Magnetic field-induced Kondo effects in Coulomb blockade systems

We review the peculiarities of transport through a quantum dot caused by the spin transition in its ground state. Such transitions can be induced by a magnetic field. Tunneling of electrons between the dot and leads mixes the states belonging to the ground state manifold of the dot. Unlike the conventional Kondo effect, this mixing, which occurs only at the singlet-triplet transition point, involves both the orbital and spin degrees of freedom of the electrons. We present theoretical and experimental results that demonstrate the enhancement of the conductance through the dot at the transition point.

cond-mat.mes-hall↗

arXiv2000

Conduction through a quantum dot near a singlet-triplet transition

Kondo effect in the vicinity of a singlet-triplet transition in a vertical quantum dot is considered. This system is shown to map onto a special version of the two-impurity Kondo model. At any value of the control parameter, the system has a Fermi-liquid ground state. Explicit expressions for the linear conductance as a function of the control parameter and temperature $T$ are obtained. At T=0, the conductance reaches the unitary limit $\sim 4e^2/h$ at the triplet side of the transition, and decreases with the increasing distance to the transition at the singlet side. At finite temperature, the conductance exhibits a peak near the transition point.

cond-mat.mes-hall↗

arXiv2000

Magnetic-field-induced Luttinger liquid

It is shown that a strong magnetic field applied to a bulk metal induces a Luttinger-liquid phase. This phase is characterized by the zero-bias anomaly in tunneling: the tunneling conductance scales as a power-law of voltage or temperature. The tunneling exponent increases with the magnetic field as BlnB. The zero-bias anomaly is most pronounced for tunneling with the field applied perpendicular to the plane of the tunneling junction.

cond-mat.mes-hall↗

arXiv2000

Oscillatory Exchange Coupling and Positive Magnetoresistance in Epitaxial Oxide Heterostructures

Oscillations in the exchange coupling between ferromagnetic $La_{2/3}Ba_{1/3}MnO_3$ layers with paramagnetic $LaNiO_3$ spacer layer thickness has been observed in epitaxial heterostructures of the two oxides. This behavior is explained within the RKKY model employing an {\it ab initio} calculated band structure of $LaNiO_3$, taking into account strong electron scattering in the spacer. Antiferromagnetically coupled superlattices exhibit a positive current-in-plane magnetoresistance.

cond-mat.mtrl-sci↗

arXiv2000

Universality of the Kondo Effect in a Quantum Dot out of Equilibrium

We study the Kondo effect in a quantum dot driven out of equilibrium by an external ac field. The Kondo effect can be probed by measuring the dc current induced by an auxiliary dc bias $V_{dc}$ applied across the dot. In the absence of ac perturbation, the corresponding differential conductance $G(V_{dc})$ is known to exhibit a sharp peak at $V_{dc}=0$, which is the manifestation of the Kondo effect. In the equilibrium, there exists only one energy scale, the Kondo temperature $T_K$, which controls all the low-energy physics of the system; $G$ is some universal function of $eV_{dc}/T_K$. We demonstrate that the dot out of equilibrium is also characterized by a universal behavior: conductance $G$ depends on the ac field only through two dimensionless parameters, which are the frequency $ω$ and the amplitude of the ac perturbation, both divided by $T_K$. We find analytically the large- and small-frequency asymptotes of the universal dependence of $G$ on these parameters. The obtained results allow us to predict the behavior of the conductance in the crossover regime $\hbarω\sim T_K$.

cond-mat.mes-hall↗