arXiv subjects

G. Zarand

Publications and source records attributed to G. Zarand.

At least 37 records · Page 2Linked to original sources

arXiv2008

Dynamical correlations in the spin-half two-channel Kondo model

Dynamical correlations of various local operators are studied in the spin-half two-channel Kondo (2CK) model in the presence of channel anisotropy or external magnetic field. A conformal field theory-based scaling approach is used to predict the analytic properties of various spectral functions in the vicinity of the two-channel Kondo fixed point. These analytical results compare well with highly accurate density matrix numerical renormalization group results. The universal cross-over functions interpolating between channel-anisotropy or magnetic field-induced Fermi liquid regimes and the two-channel Kondo, non-Fermi liquid regimes are determined numerically. The boundaries of the real 2CK scaling regime are found to be rather restricted, and to depend both on the type of the perturbation and on the specific operator whose correlation function is studied. In a small magnetic field, a universal resonance is observed in the local fermion's spectral function. The dominant superconducting instability appears in the composite superconducting channel.

cond-mat.str-el↗

arXiv2007

Theory of inelastic scattering from quantum impurities

We use the framework set up recently to compute non-perturbatively inelastic scattering from quantum impurities [G. Zaránd {\it et al.}, Phys. Rev. Lett. {\bf 93}, 107204 (2004)] to study the the energy dependence of the single particle $S$-matrix and the inelastic scattering cross section for a number of quantum impurity models. We study the case of the spin $S=1/2$ two-channel Kondo model, the Anderson model, and the usual $S=1/2$ single-channel Kondo model. We discuss the difference between non-Fermi liquid and Fermi liquid models and study how a cross-over between the non-Fermi liquid and Fermi liquid regimes appears in case of channel anisotropy for the $S=1/2$ two-channel Kondo model. We show that for the most elementary non-Fermi liquid system, the two-channel Kondo model, half of the scattering remains inelastic even at the Fermi energy. Details of the derivation of the reduction formulas and a simple path integral approach to connect the $T$-matrix to local correlation functions are also presented.

cond-mat.str-el↗

arXiv2007

Dynamical conductance in the two-channel Kondo regime of a double dot system

We study finite-frequency transport properties of the double-dot system recently constructed to observe the two-channel Kondo effect [R. M. Potok et al., Nature 446, 167 (2007)]. We derive an analytical expression for the frequency-dependent linear conductance of this device in the Kondo regime. We show how the features characteristic of the 2-channel Kondo quantum critical point emerge in this quantity, which we compute using the results of conformal field theory as well as numerical renormalization group methods. We determine the universal cross-over functions describing non-Fermi liquid vs. Fermi liquid cross-overs and also investigate the effects of a finite magnetic field.

cond-mat.mes-hall↗

arXiv2007

Inelastic scattering from quantum impurities

We review the non-perturbative theoretical framework set up recently to compute the inelastic scattering cross section from quantum impurities [G. Zaránd {\it et al.}, Phys. Rev. Lett. {\bf 93}, 107204 (2004)] and show how it can be applied to a number of quantum impurity models. We first use this method for the $S=1/2$ single-channel Kondo model and the Anderson model. In both cases, a large plateau is found in the inelastic scattering rate for incoming energies above $T_K$, and a quasi-linear regime appears in the energy range $0.05 T_K < ω< 0.5 T_K$, in agreement with the experimental observations. We also present results for the 2-channel Kondo model, the prototype of all non-Fermi liquid models, and show that there half of the scattering remains inelastic even at the Fermi energy.

cond-mat.str-el↗

arXiv2006

Dissipative quantum phase transition in a quantum dot

We study the transport properties of a quantum dot (QD) with highly resistive gate electrodes, and show that the QD displays a quantum phase transition analogous to the famous dissipative phase transition first identified by S. Chakravarty [Phys. Rev. Lett. {\bf 49}, 681 (1982)]; for a review see [A. J. Leggett {\em et al.}, Rev. Mod. Phys. {\bf 59}, 1 (1987)]. At temperature T=0, the charge on the central island of a conventional QD changes smoothly as a function of gate voltage, due to quantum fluctuations. However, for sufficiently large gate resistance charge fluctuations on the island can freeze out even at the degeneracy point, causing the charge on the island to change in sharp steps as a function of gate voltage. For $R_g<R_C$ the steps remain smeared out by quantum fluctuations. The Coulomb blockade peaks in conductance display anomalous scaling at intermediate temperatures, and at very low temperatures a sharp step develops in the QD conductance.

cond-mat.mes-hall↗

arXiv2005

Effect of spin-orbit interaction on a magnetic impurity in the vicinity of a surface

We propose a new mechanism for surface-induced magnetic anisotropy to explain the thickness-dependence of the Kondo resistivity of thin films of dilute magnetic alloys. The surface anisotropy energy, generated by spin-orbit coupling on the magnetic impurity itself, is an oscillating function of the distance d from the surface and decays as 1/d^2. Numerical estimates based on simple models suggest that this mechanism, unlike its alternatives, gives rise to an effect of the desired order of magnitude.

cond-mat.str-el↗

arXiv2005

Schwinger Boson approach to the fully screened Kondo model

We apply the Schwinger boson scheme to the fully screened Kondo model and generalize the method to include antiferromagnetic interactions between ions. Our approach captures the Kondo crossover from local moment behavior to a Fermi liquid with a non-trivial Wilson ratio. When applied to the two impurity model, the mean-field theory describes the "Varma Jones" quantum phase transition between a valence bond state and a heavy Fermi liquid.

cond-mat.str-el↗

arXiv2005

Orbital fluctuations and strong correlations in quantum dots

In this lecture note we focus our attention to quantum dot systems where exotic strongly correlated behavior develops due to the presence of orbital or charge degrees of freedom. After giving a concise overview of the theory of transport and Kondo effect through a single electron transistor, we discuss how SU(4) Kondo effect develops in dots having orbitally degenerate states and in double dot systems, and then study the singlet-triplet transition in lateral quantum dots. Charge fluctuations and Matveev's mapping to the two-channel Kondo model in the vicinity of charge degeneracy point are also discussed.

cond-mat.mes-hall↗

arXiv2005

Theory of Manganese-Manganese interaction in GaMnAs

We investigate the interaction of two Mn ions in the dilute magnetic semiconductor GaMnAs using the variational envelope wave function approach within the framework of six band model of the valence band. We find that the effective interaction between the Mn core spins at a typical separation d is strongly anisotropic for active Mn concentrations less than x = 1.3%, but it is almost isotropic for shorter distances (d < 13A). As a result, in unannealed and strongly compensated samples strong frustration effects must be present. We also verify that an effective Hamiltonian description can be used in the dilute limit, x < 1.3%, and extract the parameters of this effective Hamiltonian.

cond-mat.mtrl-sci↗

arXiv2005

Frustration of Decoherence in Open Quantum Systems

We study a model of frustration of decoherence in an open quantum system. Contrary to other dissipative ohmic impurity models, such as the Kondo model or the dissipative two-level system, the impurity model discussed here never presents overdamped dynamics even for strong coupling to the environment. We show that this unusual effect has its origins in the quantum mechanical nature of the coupling between the quantum impurity and the environment. We study the problem using analytic and numerical renormalization group methods and obtain expressions for the frequency and temperature dependence of the impurity susceptibility in different regimes.

cond-mat.other↗

arXiv2004

Dissipation-induced quantum phase transition in a quantum box

In a recent work, Le Hur has shown that dissipative coupling to gate electrodes may play an important role in a quantum box near its degeneracy point [K. Le Hur, Phys. Rev. Lett. {\bf 92}, 196804 (2004)]: While quantum fluctuations of the charge of the dot tend to round Coulomb blockade charging steps of the box, strong enough dissipation suppresses these fluctuations and leads to the reappearance of sharp charging steps. In the present paper we study this quantum phase transition in detail using bosonization and numerical renormalization group methods in the limit of vanishing level spacing.

cond-mat.str-el↗

arXiv2004

Theory of inelastic scattering from magnetic impurities

We use the numerical renormalization group method tocalculate the single particle matrix elements $\cal T$ of the many body $T$-matrix of the conduction electrons scattered by a magnetic impurity at T=0 temperature. Since $\cal T$ determines both the total and the elastic, spin-diagonal scattering cross sections, we are able to compute the full energy-, spin- and magnetic field dependence of the inelastic scattering cross section, $σ_{\rm inel}(ω)$. We find an almost linear frequency dependence of $σ_{\rm inel}(ω)$ below the Kondo temperature, $T_K$, which crosses over to a $\sim ω^2$ behavior only at extremely low energies. Our method can be generalized to other quantum impurity models.

cond-mat.mes-hall↗

arXiv2003

Anomalous behavior of spin wave resonances in Ga_{1-x}Mn_{x}As thin films

We report ferromagnetic and spin wave resonance absorption measurements on high quality epitaxially grown Ga_{1-x}Mn_{x}As thin films. We find that these films exhibit robust ferromagnetic long-range order, based on the fact that up to seven resonances are detected at low temperatures, and the resonance structure survives to temperatures close to the ferromagnetic transition. On the other hand, we observe a spin wave dispersion which is linear in mode number, in qualitative contrast with the quadratic dispersion expected for homogeneous samples. We perform a detailed numerical analysis of the experimental data and provide analytical calculations to demonstrate that such a linear dispersion is incompatible with uniform magnetic parameters. Our theoretical analysis of the ferromagnetic resonance data, combined with the knowledge that strain-induced anisotropy is definitely present in these films, suggests that a spatially dependent magnetic anisotropy is the most likely reason behind the anomalous behavior observed.

cond-mat↗

arXiv2003

Singlet-Triplet Transition in lateral Quantum Dots: A Numerical Renormalization Group Study

We discuss transport through a lateral quantum dot in the vicinity of a singlet-triplet spin transition in its ground state. Extracting the scattering phase shifts from the numerical renormalization group spectra, we determine the linear conductance at zero temperature as a function of a Zeeman field and the splitting of the singlet and triplet states. We find reduced low-energy transport, and a non-monotonic magnetic field dependence both in the singlet and the triplet regime. For a generic set of dot parameters and no Zeeman splitting, the singlet-triplet transition may be identified with the conductance maximum. The conductance is least sensitive to the magnetic field in the region of the transition, where it decreases upon application of a magnetic field. Our results are in good agreement with recent experimental data.

cond-mat.mes-hall↗

arXiv2003

Orbital Kondo behavior from dynamical structural defects

The interaction between an atom moving in a model double-well potential and the conduction electrons is treated using renormalization group methods in next-to-leading logarithmic order. A large number of excited states is taken into account and the Kondo temperature $T_K$ is computed as a function of barrier parameters. We find that for special parameters $T_K$ can be close to $1 {\rm K}$ and it can be of the same order of magnitude as the renormalized splitting $Δ$. However, in the perturbative regime we always find that $T_K \alt Δ$ with a $T_K \alt 1 {\rm K}$ [Aleiner {\em et al.}, Phys. Rev. Lett. {\bf 86}, 2629 (2001)]. We also find that $Δ$ remains unrenormalized at energies above the Debye frequency, $ω_{\rm Debye}$.

cond-mat.str-el↗

arXiv2003

SU(4) Fermi Liquid State and Spin Filtering in a Double Quantum Dot System

We study a symmetrical double quantum dot (DD) system with strong capacitive inter-dot coupling using renormalization group methods. The dots are attached to separate leads, and there can be a weak tunneling between them. In the regime where there is a single electron on the DD the low-energy behavior is characterized by an SU(4)-symmetric Fermi liquid theory with entangled spin and charge Kondo correlations and a phase shift $π/4$. Application of an external magnetic field gives rise to a large magneto-conductance and a crossover to a purely charge Kondo state in the charge sector with SU(2) symmetry. In a four lead setup we find perfectly spin polarized transmission.

cond-mat.str-el↗

arXiv2001

The Role of Electron-Hole Symmetry Breaking in the Kondo Problems

In studying the different Kondo problems it is generally assumed that breaking the electron-hole symmetry does not affect the perturbative infrared divergencies. It is shown here that, in contrast, breaking that symmetry may in some cases lead to observable modifications while in other cases it does not.

cond-mat.str-el↗

arXiv2001

Thermodynamics of the anisotropic two-channel Kondo problem

We construct and solve numerically the thermodynamic Bethe Ansatz equations for the spin-anisotropic two-channel Kondo model in arbitrary external field $h$. At high temperatures the specific heat and the susceptibility show power law dependence. For $h \to 0$ and at temperatures below the Kondo temperature $T_K$ a two-channel Kondo effect develops characterized by a Wilson ratio 8/3, and a logarithmic divergence of the susceptibility and the linear specific heat coefficient. Finite magnetic field, $h>0$ drives the system to a Fermi liquid fixed point with an unusual Wilson ratio which depends sensitively on $h$.

cond-mat.str-el↗