J. Bonča

Effect of inelastic processes on tunneling.

We study an electron that interacts with phonons or other linear or nonlinear excitations as it resonantly tunnels. The method we use is based on mapping a many-body problem in a large variational space exactly onto a one-body problem. The method is conceptually simpler than previous Green`s function approaches, and allows the essentially exact numerical solution of much more general problems. We solve tunneling problems with transverse channels, multiple sites coupled to phonons, and multiple phonon degrees of freedom and excitations.

The Holstein Polaron

We describe a variational method to solve the Holstein model for an electron coupled to dynamical, quantum phonons on an infinite lattice. The variational space can be systematically expanded to achieve high accuracy with modest computational resources (12-digit accuracy for the 1d polaron energy at intermediate coupling). We compute ground and low-lying excited state properties of the model at continuous values of the wavevector

INELASTIC TUNNELING THROUGH MESOSCOPIC STRUCTURES

k

Bipolarons in the extended Holstein Hubbard model

in essentially all parameter regimes. Our results for the polaron energy band, effective mass and correlation functions compare favorably with those of other numerical techniques including DMRG, Global Local and exact diagonalization. We find a phase transition for the first excited state between a bound and unbound system of a polaron and an additional phonon excitation. The phase transition is also treated in strong coupling perturbation theory.

Multiple-impurity Anderson model for quantum dots coupled in parallel

Our objective is to study resonant tunneling of an electron in the presence of inelastic scattering by optical phonons. Using a recently developed technique, based on exact mapping of a many-body problem onto a one-body problem, we compute transmission through a single site at finite temperatures. We also compute current through a single site at finite temperatures and an arbitrary strength of the potential drop over the tunneling region. Transmission vs. incident electron energy at finite temperatures displays additional peaks due to phonon absorption processes. Current at a voltage bias smaller than the phonon frequency is dominated by elastic processes. We apply the method to an electron tunneling through the Aharonov-Bohm ring coupled to optical phonons. Elastic part of electron-phonon scattering does not affect the phase of the electron. Dephasing occurs only through inelastic processes.

Magnetic fluctuations and resonant peak in cuprates: Towards a microscopic theory

There is growing evidence that electron-phonon coupling plays an important role in determining exotic properties of novel materials such as colossal magnetoresistance 1 and high-Tc compounds. 2 Since electrons in these materials are strongly correlated, the interplay between an attractive electron-phonon interaction and Coulomb repulsion may be important in determining physics at finite doping. In particular, when the electron-phonon interaction is local, as is the case in the Holstein model, finite Coulomb repulsion leads to the formation of an intrasite bipolaron, 3‐5 with an effective mass of the order of the polaron effective mass. 5 It has been recently discovered that a longer-range electron-phonon interaction leads to a decrease in the effective mass of a polaron in the strong-coupling regime. 6,7 The lower mass can have important consequences, because lighter polarons and bipolarons are more likely to remain mobile and less likely to trap on impurities or from mutual repulsion. Motivated by this discovery, we investigate a sim

Dimensionality effects on the Holstein polaron

The system of several N quantum dots coupled in parallel to the same single-mode conduction channel can be modeled as a single-channel N-impurity Anderson model. Using the generalized Schrieffer-Wolff transformation we show that near the particle-hole symmetric point, the effective Hamiltonian in the local moment regime is the N-impurity S =1/2 Kondo model. The conduction-band-mediated RKKY exchange interaction between the dots is ferromagnetic and at intermediate temperatures locks the moments into a maximal spin S =N / 2 ground state. We provide an analytical estimate for the RKKY interaction. At low temperatures the spin is partially screened by the conduction electrons to N /2�1/2 due to the Kondo effect. By comparing accurate numerical renormalization group results for magnetic susceptibility of the N-impurity Anderson model to the exact Bethe ansatz results of a S =N /2 SU2 Kondo system we show that at low-temperature the quantum dots can be described by the effective S =N / 2 Kondo model. Moreover, the Kondo temperature is independent of the number of impurities N. We demonstrate the robustness of the spin N / 2 ground state as well as of the associated S =N / 2 Kondo effect by studying the stability of the system with respect to various experimentally relevant perturbations. We finally explore various quantum phase transitions driven by these perturbations.

Kondo effect in triple quantum dots

Magnetic fluctuations and evolution of the resonant peak with doping in superconducting cuprates are studied within the planar t-J model. The analysis is based on the equations of motion for spins and the memory-function approach to dynamics of magnetic response where the main damping of the low-energy spin collective mode comes from the decay into fermionic degrees of freedom. In general the normal-state damping is large, leading to a overdamped collective mode. At an intermediate doping in the superconducting phase, a d-wave gap leads to a sharp resonant peak with reduced intensity and downward dispersion. At low doping the damping function is closely related to the c-axis optical conductivity, and the resonant-peak behavior is determined by two energy scales: the pseudogap and the coherent superconducting gap.

Inelastic Quantum Transport

Based on a recently developed variational method, we explore the properties of the Holstein polaron on an infinite lattice in D dimensions, where 1≤D≤4. The computational method converges as a power law, so that highly accurate results can be achieved with modest resources. We present the most accurate ground state energy (with no small parameter) to date for polaron problems, 21 digits for the one-dimensional (ID) polaron at intermediate coupling. The dimensionality effects on polaron band dispersion, effective mass, and electron-phonon (el-ph) correlation functions are investigated in all coupling regimes. It is found that the crossover to large effective mass of the higher-dimensional polaron is much sharper than the 1D polaron. The correlation length between the electron and phonons decreases significantly as the dimension increases. Our results compare favorably with those of the quantum Monte Carlo, dynamical mean-field theory, density-matrix renormalization-group, and Toyozawa variational methods. We demonstrate that the Toyozawa wave function is qualitatively correct for the ground-state energy and the two-point electron-phonon correlation functions, but fails for the three-point functions. Based on this finding, we propose an improved Toyozawa variational wave function.

Enhanced conductance through side-coupled double quantum dots

Numerical analysis of the simplest odd-numbered system of coupled quantum dots reveals an interplay between magnetic ordering, charge fluctuations, and the tendency of itinerant electrons in the leads to screen magnetic moments. The transition from local-moment to molecular-orbital behavior is visible in the evolution of correlation functions as the interdot coupling is increased. Resulting Kondo phases are presented in a phase diagram which can be sampled by measuring the zero-bias conductance. We discuss the origin of the even-odd effects by comparing with the double quantum dot.