arXiv subjects

Avraham Schiller

Publications and source records attributed to Avraham Schiller.

29 records · Page 2Linked to original sources

arXiv2003

Current Characteristics of the Single-Electron Transistor at the Degeneracy Point

The linear and nonlinear transport properties of the single-electron transistor at the degeneracy point are investigated for the case of weak single-mode tunnel junctions. Two opposing scenarios are considered, distinguished by whether or not electrons can propagate coherently between the two tunnel junctions. Each of these two scenarios corresponds to the realization of a different multichannel Kondo effect - the two-channel Kondo effect in the case where coherent propagation is allowed, and the four-channel Kondo effect in the absence of coherent propagation. A detailed analysis of the linear and nonlinear conductance is presented for each of these scenarios, within a generalized noncrossing approximation for the nonequilibrium multichannel Kondo Hamiltonian. A zero-bias anomaly is shown to develop with decreasing temperature, characterized by the anomalous power laws of the multichannel Kondo effect. A scaling function of the differential conductance with V/T (V being the applied voltage bias, T the temperature) is proposed as a distinctive experimental signature for each of these two scenarios. In the absence of coherent propagation between the leads, and for asymmetric couplings to the two leads, a crossover from four-channel to two-channel behavior is manifested in a vanishing zero-temperature conductance, and in a nonmonotonic voltage dependence of the differential conductance for small asymmetries.

cond-mat.str-el↗

arXiv2001

Noncrossing Approximation for the Anisotropic Kondo Model: Charge Fluctuations in a Quantum Box

The noncrossing approximation (NCA) is generalized to the multi-channel Kondo-spin Hamiltonian with arbitrary anisotropic exchange couplings and an external magnetic field, and applied -- in the framework of Matveev's mapping -- to the charge fluctuations in a single-electron box at the Coulomb blockade. The temperature dependences of the charge step and the capacitance are calculated for a narrow point contact. At low temperatures and close to the degeneracy point, the capacitance line shape exhibits an approximate scaling with U/\sqrt{T}, where U is the deviation in gate voltage from the degeneracy point. This scaling relation is proposed as a sharp experimental diagnostic for the non-Fermi-liquid physics of the system at low temperatures. Both the reliability and shortcomings of the Kondo NCA are discussed in detail. Through comparison with poor-man's scaling, we are able to pinpoint the omission of particle-particle processes as the origin of the NCA flaws. An extended diagrammatic scheme is devised to amend the NCA flaws.

cond-mat.str-el↗

arXiv2001

Measuring the Out-of-Equilibrium Splitting of the Kondo Resonance

An experiment is proposed to measure the out-of-equilibrium splitting of the Kondo resonance in an ultrasmall quantum dot, by adding a third, weakly coupled lead to the standard two-lead quantum-dot system, and sweeping the chemical potential of that lead. Fixing the voltage bias between the source and drain leads, we show that the differential conductance for the current through the third lead traces the out-of-equilibrium dot density of states (DOS) for the two-lead system. This enables one to measure the dot DOS in the presence of an applied voltage bias. We show that this method is robust, and extends also to the case where the coupling to the third lead is no longer weak.

cond-mat.str-el↗

arXiv2001

Projecting the Kondo Effect: Theory of the Quantum Mirage

A microscopic theory is developed for the projection (quantum mirage) of the Kondo resonance from one focus of an elliptic quantum corral to the other focus. The quantum mirage is shown to be independent of the size and the shape of the ellipse, and experiences λ_F/4 oscillations (λ_F is the surface-band Fermi wavelength) with an increasing semimajor axis length. We predict an oscillatory behavior of the mirage as a function of a weak magnetic field applied perpendicular to the sample.

cond-mat↗

arXiv2000

Out-of-Equilibrium Kondo Effect: Response to Pulsed Fields

The current in response to a rectangular pulsed bias potential is calculated exactly for a special point in the parameter space of the nonequilibrium Kondo model. Our simple analytical solution shows the all essential features predicted by the noncrossing approximation, including a hierarchy of time scales for the rise, saturation, and fall-off of the current; current oscillations with a frequency of eV/hbar; and the instantaneous reversal of the fall-off current for certain pulse lengths. Rich interference patterns are found for a nonzero magnetic field (either dc or pulsed), with several underlying time scales. These features should be observable in ultra small quantum dots.

cond-mat.str-el↗

arXiv2000

Toward a systematic 1/d expansion: Two particle properties

We present a procedure to calculate 1/d corrections to the two-particle properties around the infinite dimensional dynamical mean field limit. Our method is based on a modified version of the scheme of Ref. onlinecite{SchillerIngersent}}. To test our method we study the Hubbard model at half filling within the fluctuation exchange approximation (FLEX), a selfconsistent generalization of iterative perturbation theory. Apart from the inherent unstabilities of FLEX, our method is stable and results in causal solutions. We find that 1/d corrections to the local approximation are relatively small in the Hubbard model.

cond-mat.str-el↗

arXiv1999

Theory of Scanning Tunneling Spectroscopy of a Magnetic Adatom on a Metallic Surface

A comprehensive theory is presented for the voltage, temperature, and spatial dependence of the tunneling current between a scanning tunneling microscope (STM) tip and a metallic surface with an individual magnetic adatom. Modeling the adatom by a nondegenerate Anderson impurity, a general expression is derived for a weak tunneling current in terms of the dressed impurity Green function, the impurity-free surface Green function, and the tunneling matrix elements. This generalizes Fano's analysis to the interacting case. The differential-conductance lineshapes seen in recent STM experiments with the tip directly over the magnetic adatom are reproduced within our model, as is the rapid decay, \sim 10Å, of the low-bias structure as one moves the tip away from the adatom. With our simple model for the electronic structure of the surface, there is no dip in the differential conductance at approximately one lattice spacing from the magnetic adatom, but rather we see a resonant enhancement. The formalism for tunneling into small clusters of magnetic adatoms is developed.

cond-mat.str-el↗

arXiv1999

Correlated hopping in the Falicov-Kimball model: A large-dimensions study

The Falicov-Kimball model with a correlated-hopping interaction is solved using an extended dynamical mean-field theory that becomes exact in the limit of large dimensions. The effect of correlated hopping is to introduce nonlocal self-energy components that retain full dynamics as D goes to infinity, thus introducing an explicit k-dependence to the single-particle self-energy. An explicit solution for the homogeneous phase at D = 2 reveals significant nonlocal dynamical contributions in the physically relevant regime of a moderately large correlated-hopping amplitude, indicating that important nonlocal correlations are omitted in Hubbard-like models upon neglecting the correlated-hopping interaction.

cond-mat.str-el↗

arXiv1998

Mixed-valent regime of the two-channel Anderson impurity as a model for UBe_13

We investigate the mixed-valent regime of a two-configuration Anderson impurity model for uranium ions, with separate quadrupolar and magnetic doublets. With a new Monte Carlo approach and the non-crossing approximation we find: (i) A non-Fermi-liquid fixed point with two-channel Kondo model critical behavior; (ii) Distinct energy scales for screening the low-lying and excited doublets; (iii) A semi-quantitative explanation of magnetic-susceptibility data for U$_{1-x}$Th$_x$Be$_{13}$ assuming 60-70% quadrupolar doublet ground-state weight, supporting the quadrupolar-Kondo interpretation.

cond-mat.str-el↗

arXiv1996

Renormalization-group study of a magnetic impurity in a Luttinger liquid

A generalized Anderson model for a magnetic impurity in an interacting one-dimensional electron gas is studied via a mapping onto a classical Coulomb gas. For weak potential scattering, the local-moment parameter regime expands as repulsive bulk interactions become stronger, but the Kondo scale for the quenching of the impurity moment varies nonmonotonically. There also exist two regimes dominated by backward potential scattering: one in which the impurity is nonmagnetic, and another in which an unquenched local moment survives down to very low temperatures.

cond-mat↗

arXiv1994

Effects of Next-Nearest-Neighbor Hopping on the Hole Motion in an Antiferromagnetic Background

In this paper we study the effect of next-nearest-neighbor hopping on the dynamics of a single hole in an antiferromagnetic (Néel) background. In the framework of large dimensions the Green function of a hole can be obtained exactly. The exact density of states of a hole is thus calculated in large dimensions and on a Bethe lattice with large coordination number. We suggest a physically motivated generalization to finite dimensions (e.g., 2 and 3). In $d=2$ we present also the momentum dependent spectral function. With varying degree, depending on the underlying lattice involved, the discrete spectrum for holes is replaced by a continuum background and a few resonances at the low energy end. The latter are the remanents of the bound states of the $t-J$ model. Their behavior is still largely governed by the parameters $t$ and $J$. The continuum excitations are more sensitive to the energy scales $t$ and $t_1$.

cond-mat↗