arXiv subjects

B. Kramer

Publications and source records attributed to B. Kramer.

At least 37 records · Page 2Linked to original sources

arXiv2002

Control of Dephasing and Phonon Emission in Coupled Quantum Dots

We predict that phonon subband quantization can be detected in the non-linear electron current through double quantum dot qubits embedded into nano-size semiconductor slabs, acting as phonon cavities. For particular values of the dot level splitting $Δ$, piezo-electric or deformation potential scattering is either drastically reduced as compared to the bulk case, or strongly enhanced due to phonon van Hove singularities. By tuning $Δ$ via gate voltages, one can either control dephasing, or strongly increase emission into phonon modes with characteristic angular distributions.

cond-mat.mes-hall↗

arXiv2001

Scaling of level statistics at the metal-insulator transition

Using the Anderson model for disordered systems the fluctuations in electron spectra near the metal--insulator transition were numerically calculated for lattices of sizes up to 28 x 28 x 28 sites. The results show a finite--size scaling of both the level spacing distribution and the variance of number of states in a given energy interval, that allows to locate the critical point and to determine the critical exponent of the localization length.

cond-mat.dis-nn↗

arXiv2001

Transport through a one-dimensional quantum dot

We examine the effects of long-range interactions in a quantum wire with two impurities. We employ the bosonization technique and derive an effective action for the system. The effect of the long-range interaction on the charging energy and spectral properties of the island formed by the impurities and the linear transport is discussed.

cond-mat.mes-hall↗

arXiv2001

Transport in quantum wires with impurities at finite temperatures

The temperature dependence of Coulomb blockade peaks of a one dimensional quantum dot is calculated. The Coulomb interaction is treated microscopically using the Luttinger liquid model. The electron interaction is assumed to be non-homogeneous with a maximum strength near the quantum dot. The conductance peaks show non-analytic power law behaviour induced by the interaction. It is shown that there is a crossover in the power law which is related to the inhomogeneity of the interaction.

cond-mat.mes-hall↗

arXiv2001

Dynamics of a large-spin-boson system in the strong coupling regime

We investigate collective effects of an ensemble of biased two level systems interacting with a bosonic bath in the strong coupling regime. The two level systems are described by a large pseudo-spin J. An equation for the expectation value M(t) of the z-component of the pseudo spin is derived and solved numerically for an ohmic bath at T=0. In case of a large cut-off frequency of the spectral function, a Markov approximation is justified and an analytical solution is presented. We find that M(t) relaxes towards a highly correlated state with maximum value $\pm J$ for large times. However, this relaxation is extremely slow for most parameter values so as if the system was "frozen in" by interaction with the bosonic bath.

cond-mat.mes-hall↗

arXiv2001

Decay rate and renormalized frequency shift of a quantum wire Wannier exciton in a planar microcavity

The superradiant decay rate and frequency shift of a Wannier exciton in a one-dimensional quantum wire are studied. It is shown that the dark mode exciton can be examined experimentally when the quantum wire is embedded in a planar microcavity. It is also found that the decay rate is greatly enhanced as the cavity length $L_{c}$ is equal to the multiple wavelength of the emitted photon. Similar to its decay rate counterpart, the frequency shift also shows discontinuities at resonant modes.

cond-mat.mes-hall↗

arXiv2001

New selection rules for resonant Raman scattering on quantum wires

The bosonisation technique is used to calculate the resonant Raman spectrum of a quantum wire with two electronic sub-bands occupied. Close to resonance, the cross section at frequencies in the region of the inter sub-band transitions shows distinct peaks in parallel polarisation of the incident and scattered light that are signature of collective higher order spin density excitations. This is in striking contrast to the conventional selection rule for non-resonant Raman scattering according to which spin modes can appear only in perpendicular polarisation. We predict a new selection rule for the excitations observed near resonance, namely that, apart from charge density excitations, only spin modes with positive group velocities can appear as peaks in the spectra in parallel configuration close to resonance. The results are consistent with all of the presently available experimental data.

cond-mat.str-el↗

arXiv2000

Phonons and Phonon Confinement in Transport through Double Quantum Dots

We calculate the electron-phonon interaction coefficients for surface acoustic waves and for phonons in free standing quantum wells. These are used to derive the inelastic current through a double quantum dot caused by spontaneous emission of phonons. For the case of the free standing structure (phonon cavity), we predict a staircase-like inelastic current superimposed by van Hove singularities. Therefore, the phonon confinement can be detected by electron transport measurements.

cond-mat.mes-hall↗

arXiv2000

Charge and spin addition energies of one dimensional quantumn dot

We derive the effective action for a one dimensional electron island formed between a double barrier in a single channel quantum wire including the electron spin. Current and energy addition terms corresponding to charge and spin are identified. The influence of the range and the strength of the electron interaction and other system parameters on the charge and spin addition energies, and on the excitation spectra of the modes confined within the island is studied. We find by comparison with experiment that spin excitations in addition to non-zero range of the interaction and inhomogeneity effects are important for understanding the electron transport through one dimensional quantum islands in cleaved-edge-overgrowth systems.

cond-mat.str-el↗

arXiv2000

Tomonaga-Luttinger features in the resonant Raman spectra of quantum wires

The differential cross section for resonant Raman scattering from the collective modes in a one dimensional system of interacting electrons is calculated non-perturbatively using the bosonization method. The results indicate that resonant Raman spectroscopy is a powerful tool for studying Tomonaga-Luttinger liquid behaviour in quasi-one dimensional electron systems.

cond-mat.str-el↗

arXiv1999

Numerical study on Anderson transitions in three-dimensional disordered systems in random magnetic fields

The Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for systems both with and without an additional random scalar potential. We find the critical exponent $ν$ for the localization length to be $1.45 \pm 0.09$ with a strong random scalar potential. Without it, the exponent is smaller but increases with the system sizes and extrapolates to the above value within the error bars. These results support the conventional classification of universality classes due to symmetry. Fractal dimensionality of the wave function at the critical point is also estimated by the equation-of-motion method.

cond-mat.dis-nn↗

arXiv1998

Critical level statistics at the Anderson transition in four-dimensional disordered systems

The level spacing distribution is numerically calculated at the disorder-induced metal--insulator transition for dimensionality d=4 by applying the Lanczos diagonalisation. The critical level statistics are shown to deviate stronger from the result of the random matrix theory compared to those of d=3 and to become closer to the Poisson limit of uncorrelated spectra. Using the finite size scaling analysis for the probability distribution Q_n(E) of having n levels in a given energy interval E we find the critical disorder W_c = 34.5 \pm 0.5, the correlation length exponent ν= 1.1 \pm 0.2 and the critical spectral compressibility k_c \approx 0.5.

cond-mat.dis-nn↗

arXiv1998

Anderson transitions in three-dimensional disordered systems with randomly varying magnetic flux

The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are considered. We find a critical exponent of $ν=1.45\pm0.09$ with random scalar potential. Without it, $ν$ is smaller but increases with the system size and extrapolates within the error bars to a value close to the above. The present results support the conventional classification of universality classes due to symmetry.

cond-mat.dis-nn↗

arXiv1997

Phase diagram of localization in a magnetic field

The phase diagram of localization is numerically calculated for a three-dimensional disordered system in the presence of a magnetic field using the Peierls substitution. The mobility edge trajectory shifts in the energy-disorder space when increasing the field. In the band center, localized states near the phase boundary become delocalized. The obtained field dependence of the critical disorder is in agreement with a power law behavior expected from scaling theory. Close to the tail of the band the magnetic field causes localization of extended states.

cond-mat.dis-nn↗

arXiv1997

Energy-level statistics and localization of 2d electrons in random magnetic fields

Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this model, extended states have recently been proposed to exist in the middle of the band. In contrast, from our calculations of the large-$s$ behavior of the nearest neighbor level spacing distribution $P(s)$ and from a finite size scaling analysis we find only localized states in the suggested energy and disorder range.

cond-mat.mes-hall↗

arXiv1996

Crossover from critical orthogonal to critical unitary statistics at the Anderson transition

We report a novel scale-independent, Aharonov-Bohm flux controlled crossover from critical orthogonal to critical unitary statistics at the disorder induced metal insulator transition. Our numerical investigations show that at the critical point the level statistics are definitely distinct and determined by fundamental symmetries. The latter is similar to the behavior of the metallic phase known from random matrix theory. The Aharonov-Bohm flux dependent crossover is characteristic of the critical ensemble.

cond-mat↗

arXiv1996

Mean-field limit of the random flux model

The problem of non--interacting electrons on a square lattice subject to a random magnetic flux is mapped onto a one--dimensional model with infinitely many orbitals per site. Linking each orbital with $N(\gg1)$ other orbitals maps the problem onto Wegner's $N$-orbital model in the same limit, while the original problem corresponds to $N=1$. The exact solution for $N=\infty$, the mean--field limit, is discussed and compared with numerical results. An outline of a $1/N$-expansion is given.

cond-mat↗

arXiv1996

Crossover of Level Statistics between Strong and Weak Localization in Two Dimensions

We investigate numerically the statistical properties of spectra of two-dimensional disordered systems by using the exact diagonalization and decimation method applied to the Anderson model. Statistics of spacings calculated for system sizes up to 1024 $\times$ 1024 lattice sites exhibits a crossover between Wigner and Poisson distributions. We perform a self-contained finite-size scaling analysis to find a single-valued one-parameter function $γ(L/ξ)$ which governs the crossover. The scaling parameter $ξ(W)$ is deduced and compared with the localization length. $γ( L/ξ)$ does {\em not} show critical behavior and has two asymptotic regimes corresponding to weakly and strongly localized states.

cond-mat↗