arXiv subjects

F. Evers

Publications and source records attributed to F. Evers.

At least 37 records · Page 2Linked to original sources

arXiv2007

Magnetotransport of electrons in quantum Hall systems

Recent theoretical results on magnetotransport of electrons in a 2D system in the range of moderately strong transverse magnetic fields are reviewed. The phenomena discussed include: quasiclassical memory effects in systems with various types of disorder, transport in lateral superlattices, interaction-induced quantum magnetoresistance, quantum magnetooscillations in dc and ac transport, and oscillatory microwave photoconductivity.

cond-mat.dis-nn↗

arXiv2007

Anderson Transitions

The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term ``Anderson transition'' is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states. The emphasis is put on recent developments, which include: multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic systems, mechanisms of criticality in quasi-one-dimensional and two-dimensional systems and survey of corresponding critical theories, network models, and random Dirac Hamiltonians. Analytical approaches are complemented by advanced numerical simulations.

cond-mat.mes-hall↗

arXiv2007

Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class D thermal quantum Hall effect

We investigate numerically the quasiparticle density of states $\varrho(E)$ for a two-dimensional, disordered superconductor in which both time-reversal and spin-rotation symmetry are broken. As a generic single-particle description of this class of systems (symmetry class D), we use the Cho-Fisher version of the network model. This has three phases: a thermal insulator, a thermal metal, and a quantized thermal Hall conductor. In the thermal metal we find a logarithmic divergence in $\varrho(E)$ as $E\to 0$, as predicted from sigma model calculations. Finite size effects lead to superimposed oscillations, as expected from random matrix theory. In the thermal insulator and quantized thermal Hall conductor, we find that $\varrho(E)$ is finite at E=0. At the plateau transition between these phases, $\varrho(E)$ decreases towards zero as $|E|$ is reduced, in line with the result $\varrho(E) \sim |E|\ln(1/|E|)$ derived from calculations for Dirac fermions with random mass.

cond-mat.mes-hall↗

arXiv2007

Boundary multifractality in critical 1D systems with long-range hopping

Boundary multifractality of electronic wave functions is studied analytically and numerically for the power-law random banded matrix (PRBM) model, describing a critical one-dimensional system with long-range hopping. The peculiarity of the Anderson localization transition in this model is the existence of a line of fixed points describing the critical system in the bulk. We demonstrate that the boundary critical theory of the PRBM model is not uniquely determined by the bulk properties. Instead, the boundary criticality is controlled by an additional parameter characterizing the hopping amplitudes of particles reflected by the boundary.

cond-mat.mes-hall↗

arXiv2007

Ab initio study of surface stress response to charging

We explore an efficient way to numerically evaluate the response of the surface stress of a metal to changes in its superficial charge density by analysis of the strain-dependence of the work function of the uncharged surface. As an application we consider Au(111), (110) and (100) surfaces, employing density functional calculations. The sign of the calculated response parameter can be rationalized with the dependence of the surface dipole and the Fermi energy on strain. The numerical value falls within the range indicated by experiment. The magnitude can explain the experimentally observed volume changes of nanoporous materials upon charging.

cond-mat.mtrl-sci↗

arXiv2007

Wave function statistics at the symplectic 2D Anderson transition: bulk properties

The wavefunction statistics at the Anderson transition in a 2d disordered electron gas with spin-orbit coupling is studied numerically. In addition to highly accurate exponents ($α_0{=}2.172\pm 0.002, τ_2{=}1.642\pm 0.004$), we report three qualitative results: (i) the anomalous dimensions are invariant under $q\to (1-q)$ which is in agreement with a recent analytical prediction and supports the universality hypothesis. (ii) The multifractal spectrum is not parabolic and therefore differs from behavior suspected, e.g., for (integer) quantum Hall transitions in a fundamental way. (iii) The critical fixed point satisfies conformal invariance.

cond-mat.mes-hall↗

arXiv2006

Molecular Conductance from Ab Initio Calculations: Self Energies and Absorbing Boundary Conditions

Calculating an exact self energy for ab initio transport calculations relevant to ``Molecular Electronics'' can be troublesome. Errors or insufficient approximations made at this step are often the reason why many molecular transport studies become inconclusive. We propose a simple and efficient approximation scheme, that follows from interpreting the self energy as an absorbing boundary condition of an effective Schroedinger equation. In order to explain the basic idea, a broad introduction into the physics incorporated in these self energies is given. The method is further illustrated using a tight binding wire as a toy model. Finally, also more realistic applications for transport calculations based on the density functional theory are included.

cond-mat.mes-hall↗

arXiv2006

Pride, Prejudice, and Penury of {\it ab initio} transport calculations for single molecules

Recent progress in measuring the transport properties of individual molecules has triggered a substantial demand for {\it ab initio} transport calculations. Even though program packages are commercially available and placed on custom tailored to address this task, reliable information often is difficult and very time consuming to attain in the vast majority of cases, namely when the molecular conductance is much smaller than $e^2/h$. The article recapitulates procedures for molecular transport calculations from the point of view of time-dependent density functional theory. Emphasis is describing the foundations of the ``standard method''. Pitfalls will be uncovered and the domain of applicability discussed.

cond-mat.mes-hall↗

arXiv2006

Surface criticality and multifractality at localization transitions

We develop the concept of surface multifractality for localization-delocalization (LD) transitions in disordered electronic systems. We point out that the critical behavior of various observables related to wave functions near a boundary at a LD transition is different from that in the bulk. We illustrate this point with a calculation of boundary critical and multifractal behavior at the 2D spin quantum Hall transition and in a 2D metal at scales below the localization length.

cond-mat.mes-hall↗

arXiv2006

Exact relations between multifractal exponents at the Anderson transition

Two exact relations between mutlifractal exponents are shown to hold at the critical point of the Anderson localization transition. The first relation implies a symmetry of the multifractal spectrum linking the multifractal exponents with indices $q<1/2$ to those with $q>1/2$. The second relation connects the wave function multifractality to that of Wigner delay times in a system with a lead attached.

cond-mat.mes-hall↗

arXiv2005

Griffiths phase in the thermal quantum Hall effect

Two dimensional disordered superconductors with broken spin-rotation and time-reversal invariance, e.g. with p_x+ip_y pairing, can exhibit plateaus in the thermal Hall coefficient (the thermal quantum Hall effect). Our numerical simulations show that the Hall insulating regions of the phase diagram can support a sub-phase where the quasiparticle density of states is divergent at zero energy, ρ(E)\sim |E|^{1/z-1}, with a non-universal exponent $z>1$, due to the effects of rare configurations of disorder (``Griffiths phase'').

cond-mat.mes-hall↗

arXiv2004

Universality of the edge tunneling exponent of fractional quantum Hall liquids

Recent calculations of the edge tunneling exponents in quantum Hall states appear to contradict their topological nature. We revisit this issue and find no fundamental discrepancies. In a microscopic model of fractional quantum Hall liquids with electron-electron interaction and confinement, we calculate the edge Green's function via exact diagonalization. Our results for $ν= 1/3$ and 2/3 suggest that in the presence of Coulomb interaction, the sharpness of the edge and the strength of the edge confining potential, which can lead to edge reconstruction, are the parameters that are relevant to the universality of the electron tunneling I-V exponent.

cond-mat.mes-hall↗

arXiv2003

The conductance of molecular wires and DFT based transport calculations

The experimental value for the zero bias conductance of organic molecules coupled by thiol-groups to gold electrodes tends to be much smaller than the theoretical result based on density functional theory (DFT) calculations, often by orders of magnitude. To address this puzzle we have analyzed the regime within which the approximations made in these calculations are valid. Our results suggest that a standard step in DFT based transport calculations, namely approximating the exchange-correlation potential in quasistatic nonequilibrium by its standard equilibrium expression, is not justified at weak coupling. We propose, that the breakdown of this approximation is the most important source for overestimating the width of the experimentally observed conductance peak and therefore also of the zero bias conductance. We present a numerical study on the conductance of the organic molecule that has recently been studied experimentally by Reichert et. al. (PRL 88, 176804 (2002)) that fully agrees with this conclusion.

cond-mat.mes-hall↗

arXiv2002

Wave function statistics and multifractality at the spin quantum Hall transition

The statistical properties of wave functions at the critical point of the spin quantum Hall transition are studied. The main emphasis is put onto determination of the spectrum of multifractal exponents $Δ_q$ governing the scaling of moments $<|ψ|^{2q}>\sim L^{-qd-Δ_q}$ with the system size $L$ and the spatial decay of wave function correlations. Two- and three-point correlation functions are calculated analytically by means of mapping onto the classical percolation, yielding the values $Δ_2=-1/4$ and $Δ_3=-3/4$. The multifractality spectrum obtained from numerical simulations is given with a good accuracy by the parabolic approximation $Δ_q\simeq q(1-q)/8$ but shows detectable deviations. We also study statistics of the two-point conductance $g$, in particular, the spectrum of exponents $X_q$ characterizing the scaling of the moments $ $. Relations between the spectra of critical exponents of wave functions ($Δ_q$), conductances ($X_q$), and Green functions at the localization transition with a critical density of states are discussed.

cond-mat.mes-hall↗

arXiv2002

Quantum Hall ferromagnets, cooperative transport anisotropy, and the random field Ising model

We discuss the behaviour of a quantum Hall system when two Landau levels with opposite spin and combined filling factor near unity are brought into energetic coincidence using an in-plane component of magnetic field. We focus on the interpretation of recent experiments under these conditions [Zeitler et al, Phys. Rev. Lett. 86, 866 (2001); Pan et al, Phys. Rev. B 64, 121305 (2001)], in which a large resistance anisotropy develops at low temperatures. Modelling the systems involved as Ising quantum Hall ferromagnets, we suggest that this transport anisotropy reflects domain formation induced by a random field arising from isotropic sample surface roughness.

cond-mat.mes-hall↗

arXiv2002

Multifractality at the spin quantum Hall transition

Statistical properties of critical wave functions at the spin quantum Hall transition are studied both numerically and analytically (via mapping onto the classical percolation). It is shown that the index $η$ characterizing the decay of wave function correlations is equal to 1/4, at variance with the $r^{-1/2}$ decay of the diffusion propagator. The multifractality spectra of eigenfunctions and of two-point conductances are found to be close-to-parabolic, $Δ_q\simeq q(1-q)/8$ and $X_q\simeq q(3-q)/4$.

cond-mat.mes-hall↗

arXiv2001

Dimensionality dependence of the wave function statistics at the Anderson transition

The statistics of critical wave functions at the Anderson transition in three and four dimensions are studied numerically. The distribution of the inverse participation ratios (IPR) $P_q$ is shown to acquire a scale-invariant form in the limit of large system size. Multifractality spectra governing the scaling of the ensemble-averaged IPRs are determined. Conjectures concerning the IPR statistics and the multifractality at the Anderson transition in a high spatial dimensionality are formulated.

cond-mat.dis-nn↗

arXiv2001

Cyclotron resonance in antidot arrays

We study the dynamical properties of an electron gas scattered by impenetrable antidots in the presence of a strong magnetic field. We find that the lineshape of the cyclotron resonance is very different from the Lorentzian and is not characterized by the Drude scattering rate. We show that the dissipative dynamical response of skipping orbits, $S_c(ω)$, is broadened on a scale of the cyclotron frequency $ω_c$ and has a sharp dip $\propto |ω-ω_c|$. For small antidots, $S_c(ω)$ is strongly modulated with a period equal to $ω_c$ and has sharp square-root singularities for a series of resonant frequencies. For large antidots, $S_c(ω)$ has a hard gap at $ω<ω_c$ between two sharp peaks, associated respectively with edge states and free cyclotron orbits.

cond-mat.dis-nn↗