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As is well known, magnetic impurities adsorbed on superconductors, e.g. of the s-wave type, can introduce a bound gap-state (Yu-Shiba-Rusinov resonance). We here investigate within a minimal model how the impurity moment arranges with respect to a weak homogeneous external magnetic field employing a fully self-consistent mean-field treatment. Our investigation reveals a critical window of impurity-to-substrate coupling constants, $J$. The width of the critical region, $\delta J$, scales like $\delta J \sim B/\Delta$, where $B$ is the magnitude of the external field and $\Delta$ is the bulk order parameter. While tuning $J$ through the window, the energy of the Yu-Shiba-Rusinov (YSR) resonance is pinned to the Fermi energy $\varepsilon_\text{F}$ and the impurity moment rotates in a continuous fashion. We emphasize the pivotal role of self-consistency: In treatments ignoring self-consistency, the critical window adopts zero width, $\delta J=0$; consequently, there is no pinning of the YSR-resonance to $\varepsilon_\text{F}$, the impurity orientation jumps and therefore this orientation cannot be controlled continuously by fine-tuning the coupling $J$. In this sense, our study highlights the significance of self-consistency for understanding intricate magnetic interactions between superconductive materials and Shiba chains.

We present the formalism and implementation of quasi-particle self-consistent GW (qsGW) and eigenvalue only quasi-particle self-consistent GW (evGW) adapted to standard quantum chemistry packages. Our implementation is benchmarked against high-level quantum chemistry computations (coupled-cluster theory) and experimental results using a representative set of molecules. Furthermore, we compare the qsGW approach for five molecules relevant for organic photovoltaics to self-consistent GW results (scGW) and analyze the effects of the self-consistency on the ground state density by comparing calculated dipole moments to their experimental values. We show that qsGW makes a significant improvement over conventional G0W0 and that partially self-consistent flavors (in particular evGW) can be excellent alternatives.

Mesoscopic fluctuations of the local density of states encode multifractal correlations in disorderedelectron systems. We study fluctuations of the local density of states in a superconducting state of weakly disordered films. We perform numerical computations in the framework of the disordered attractive Hubbard model on two-dimensional square lattices. Our numerical results are explained by an analytical theory. The numerical data and the theory together form a coherent picture of multifractal correlations of local density of states in weakly disordered superconducting films.

We study the time evolving currents flowing in an interacting, ring-shaped nanostructure after a bias voltage has been switched on. The source-to-drain current exhibits the expected relaxation towards its quasi-static equilibrium value at a rate $\Gamma_0$ reflecting the lead-induced broadening of the ring states. In contrast, the current circulating within the ring decays with a different rate $\Gamma$, which is a rapidly decaying function of the interaction strength and thus can take values orders of magnitude below $\Gamma_0$. This implies the existence of a regime in which the nanostructure is far from equilibrium even though the transmitted current is already stationary. We discuss experimental setups to observe the long-lived ring transients.

Understanding the properties of electronic transport across metal-molecule interfaces is of central importance for controlling a large variety of molecular-based devices such as organic light emitting diodes, nanoscale organic spin-valves and single-molecule switches. One of the primary experimental methods to reveal the mechanisms behind electronic transport through metal-molecule interfaces is the study of conductance as a function of molecule length in molecular junctions. Previous studies focused on transport governed either by tunneling or hopping, both at low conductance. However, the upper limit of conductance across molecular junctions has not been explored, despite the great potential for efficient information transfer, charge injection and recombination processes. Here, we study the conductance properties of highly transmitting metal-molecule-metal interfaces, using a series of single-molecule junctions based on oligoacenes with increasing length. We find that the conductance saturates at an upper limit where it is independent of molecule length. Furthermore, we show that this upper limit can be controlled by the character of the orbital hybridization at the metal-molecule interface. Using two prototype systems, in which the molecules are contacted by either Ag or Pt electrodes, we reveal two different origins for the saturation of conductance. In the case of Ag-based molecular junctions, the conductance saturation is ascribed to a competition between energy level alignment and level broadening, while in the case of Pt-based junctions, the saturation is attributed to a band-like transport. The results are explained by an intuitive model, backed by ab-initio transport calculations. Our findings shed light on the mechanisms that constrain the conductance at the high transmission limit, providing guiding principles for the design of highly conductive metal-molecule interfaces., Comment: 11 pages, 5 figures, Supplementary Information

We report a combined experimental and theoretical study of the Kondo effect in a series of binuclear metal-organic complexes of the form [(Me(hfacac)_2)_2(bpym)]^0, with Me = Nickel (II), Manganese(II), Zinc (II); hfacac = hexafluoroacetylacetonate, and bpym = bipyrimidine, adsorbed on Cu(100) surface. While Kondo-features did not appear in the scanning tunneling spectroscopy spectra of non-magnetic Zn_2, a zero bias resonance was resolved in magnetic Mn_2 and Ni_2 complexes. The case of Ni_2 is particularly interesting as the experiments indicate two adsorption geometries with very different properties. For Ni_2-complexes we have employed density functional theory to further elucidate the situation. Our simulations show that one geometry with relatively large Kondo temperatures T_K ~ 10K can be attributed to distorted Ni_2 complexes, which are chemically bound to the surface via the bipyrimidine unit. The second geometry, we assign to molecular fragmentation: we suggest that the original binuclear molecule decomposes into two pieces, including Ni(hexafluoroacetylacetonate)_2, when brought into contact with the Cu-substrate. For both geometries our calculations support a picture of the (S=1)-type Kondo effect emerging due to open 3d shells of the individual Ni^{2+} ions., Comment: 11 pages, 10 figures, Supplementary Information is attached as a separate PDF file, submitted to Phys. Rev. B

The density of states (DoS), $\varrho(E)$, of graphene is investigated numerically and within the self-consistent T-matrix approximation (SCTMA) in the presence of vacancies within the tight binding model. The focus is on compensated disorder, where the concentration of vacancies, $n_\text{A}$ and $n_\text{B}$, in both sub-lattices is the same. Formally, this model belongs to the chiral symmetry class BDI. The prediction of the non-linear sigma-model for this class is a Gade-type singularity $\varrho(E) \sim |E|^{-1}\exp(-|\log(E)|^{-1/x})$. Our numerical data is compatible with this result in a preasymptotic regime that gives way, however, at even lower energies to $\varrho(E)\sim E^{-1}|\log(E)|^{-\mathfrak{x}}$, $1\leq \mathfrak{x} < 2$. We take this finding as an evidence that similar to the case of dirty d-wave superconductors, also generic bipartite random hopping models may exhibit unconventional (strong-coupling) fixed points for certain kinds of randomly placed scatterers if these are strong enough. Our research suggests that graphene with (effective) vacancy disorder is a physical representative of such systems., Comment: References updated only

The dynamics of colloidal particles in potential energy landscapes have mainly been investigated theoretically. In contrast, here we discuss the experimental realization of potential energy landscapes with the help of light fields and the observation of the particle dynamics by video microscopy. The experimentally observed dynamics in periodic and random potentials are compared to simulation and theoretical results in terms of, e.g. the mean-squared displacement, the time-dependent diffusion coefficient or the non-Gaussian parameter. The dynamics are initially diffusive followed by intermediate subdiffusive behaviour which again becomes diffusive at long times. How pronounced and extended the different regimes are, depends on the specific conditions, in particular the shape of the potential as well as its roughness or amplitude but also the particle concentration. Here we focus on dilute systems, but the dynamics of interacting systems in external potentials, and thus the interplay between particle-particle and particle-potential interactions, is also mentioned briefly. Furthermore, the observed dynamics of dilute systems resemble the dynamics of concentrated systems close to their glass transition, with which it is compared. The effect of certain potential energy landscapes on the dynamics of individual particles appears similar to the effect of interparticle interactions in the absence of an external potential.

Electrical and thermal transport properties of C60 molecules are investigated with density-functional-theory based calculations. These calculations suggest that the optimum contact geometry for an electrode terminated with a single-Au atom is through binding to one or two C-atoms of C60 with a tendency to promote the sp2-hybridization into an sp3-type one. Transport in these junctions is primarily through an unoccupied molecular orbital that is partly hybridized with the Au, which results in splitting the degeneracy of the lowest unoccupied molecular orbital triplet. The transmission through these junctions, however, cannot be modeled by a single Lorentzian resonance, as our results show evidence of quantum interference between an occupied and an unoccupied orbital. The interference results in a suppression of conductance around the Fermi energy. Our numerical findings are readily analyzed analytically within a simple two-level model., Comment: 13 pages, 9 figures

Quantum size effects in armchair graphene nano-ribbons (AGNR) with hydrogen termination are investigated via density functional theory (DFT) in Kohn-Sham formulation. "Selection rules" will be formulated, that allow to extract (approximately) the electronic structure of the AGNR bands starting from the four graphene dispersion sheets. In analogy with the case of carbon nanotubes, a threefold periodicity of the excitation gap with the ribbon width (N, number of carbon atoms per carbon slice) is predicted that is confirmed by ab initio results. While traditionally such a periodicity would be observed in electronic response experiments, the DFT analysis presented here shows that it can also be seen in the ribbon geometry: the length of a ribbon with L slices approaches the limiting value for a very large width 1 << N (keeping the aspect ratio small N << L) with 1/N-oscillations that display the electronic selection rules. The oscillation amplitude is so strong, that the asymptotic behavior is non-monotonous, i.e., wider ribbons exhibit a stronger elongation than more narrow ones., Comment: 5 pages, 6 figures

Friedel's sum rule provides an explicit expression for a conductance functional, $\mathcal{G}[n]$, valid for the single impurity Anderson model at zero temperature. The functional is special because it does not depend on the interaction strength $U$. As a consequence, the Landauer conductance for the Kohn-Sham (KS) particles of density functional theory (DFT) coincides with the true conductance of the interacting system. The argument breaks down at temperatures above the Kondo scale, near integer filling, $n_{\text{d}\sigma}\approx 1/2$ for spins $\sigma{=}\uparrow\downarrow$. Here, the true conductance is strongly suppressed by the Coulomb blockade, while the KS-conductance still indicates resonant transport. Conclusions of our analysis are corroborated by DFT studies with numerically exact exchange-correlation functionals reconstructed from calculations employing the density matrix renormalization group., Comment: 4 pages, 4 figures

We clarify an important aspect of density functional theories, the broadening of the derivative discontinuity (DD) in a quantum system, with fluctuating particle number. Our focus is on a correlated model system, the single level quantum dot in the regime of the Coulomb blockade. We find that the DD-broadening is controlled by the small parameter $\Gamma/U$, where $\Gamma$ is the level broadening due to contacting and $U$ is a measure of the charging energy. Our analysis suggests, that Kondoesque fluctuations have a tendency to increase the DD-broadening, in our model by a factor of two., Comment: 4 pages, 2 figures

We analyze the critical behavior of the dephasing rate induced by short-range electron-electron interaction near an Anderson transition of metal-insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the transition width with temperature. Assuming no spin degeneracy, the critical behavior can be studied by performing the scaling analysis in the vicinity of the non-interacting fixed point, since the latter is stable with respect to the interaction. We combine an analytical treatment (that includes the identification of operators responsible for dephasing in the formalism of the non-linear sigma-model and the corresponding renormalization-group analysis in $2+\epsilon$ dimensions) with numerical simulations on the Chalker-Coddington network model of the quantum Hall transition. Finally, we discuss the current understanding of the Coulomb interaction case and the available experimental data., Comment: 33 pages, 7 figures, elsart style

The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. We focus on the character of criticality as well as on underlying symmetries and topologies that are crucial for understanding phase diagrams and the critical behavior., Comment: 36 pages. Published in "50 Years of Anderson Localization", ed. by E. Abrahams (World Scientific, 2010); reprinted in IJMPB

We report on the observation of Kondo and split Kondo peaks in single-molecule transistors containing a single spin transition molecule with a Fe2+ ion. Coulomb blockade characteristics reveal a double quantum dot behavior in a parallel configuration, making our system a molecular equivalent to a semiconducting double-quantum-dot system. As the gate voltage is increased the charging of the second dot by an additional electron induces a splitting of the Kondo peak. We discuss possible origins of this effect including a spin transition into a high-spin state.

We present a calculation of the free energy, the surface free energy and the elastic constants ("Lam'e parameters" i.e, Poisson ratio, Young's modulus) of graphene flakes on the level of the density functional theory employing different standard functionals. We observe that the Lam'e parameters in small flakes can differ from the bulk values by 30% for hydrogenated zig-zag edges. The change results from the edge of the flake that compresses the interior. When including the vibrational zero point motion, we detect a decrease in the bending rigidity by ~26%. This correction is depending on the flake size, N, because the vibrational frequencies flow with growing N due to the release of the edge induced compression. We calculate Grueneisen parameters and find good agreement with previous authors., Comment: 11 pages, 12 figures

We investigate the interplay of particle number, N, and structural properties of selected clusters with N=12 up to N=562 by employing Gupta potentials parameterized for Aluminum and extensive Monte-Carlo simulations. Our analysis focuses on closed shell structures with extra atoms. The latter can put the cluster under a significant stress and we argue that typically such a strained system exhibits a reduced energy barrier for (surface) diffusion of cluster atoms. Consequently, also its surface melting temperature, T_S, is reduced, so that T_S separates from and actually falls well below the bulk value. The proposed mechanism may be responsible for the suppression of the surface melting temperature observed in a recent experiments., Comment: 9 pages, 7 figures, 1 table, REVTeX 4; submitted to Phys.Rev.B

We present an ultra-high-precision numerical study of the spectrum of multifractal exponents $\Delta_q$ characterizing anomalous scaling of wave function moments $<|\psi|^{2q}>$ at the quantum Hall transition. The result reads $\Delta_q = 2q(1-q)[b_0 + b_1(q-1/2)^2 + ...]$, with $b_0 = 0.1291\pm 0.0002$ and $b_1 = 0.0029\pm 0.0003$. The central finding is that the spectrum is not exactly parabolic, $b_1\ne 0$. This rules out a class of theories of Wess-Zumino-Witten type proposed recently as possible conformal field theories of the quantum Hall critical point., Comment: 4 pages, 4 figures

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., Comment: Mini-review for Proceedings of the DFG Priority Progamme "Quantum Hall Systems"; to be published in a special issue of Physica Status Solidi (b); 27 pages, 22 figures

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., Comment: 63 pages, 39 figures, submitted to Rev. Mod. Phys

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., Comment: epl-style, 7 pages, 1 figure, to appear in Europhysics Letters

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., Comment: 7 pages, 4 figures, some typos corrected

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., Comment: Lecture notes summerschool ``Nano-Electronics'', Bad Herrenalb September 1-4 2005; to appear in CFN Lectures on Functional Nanostructures, Vol. II, ``Nano-Electronics'', Springer Lecture Notes in Physics (2006)

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., Comment: 8 pages, 8 figures, published version

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., Comment: Chapter contributed to the CRC Handbook on Molecular and Nanoelectronics, ed. S. Lyshevski

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 ($\alpha_0{=}2.172\pm 0.002, \tau_2{=}1.642\pm 0.004$), 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., Comment: 4 pages, 3 figures

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., Comment: 4 pages, 3 figures

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., Comment: Published version

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, \rho(E)\sim |E|^{1/z-1}, with a non-universal exponent $z>1$, due to the effects of rare configurations of disorder (``Griffiths phase'')., Comment: 4+ pages, 5 figures

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 $\nu = 1/3$ 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., Comment: 5 pages, 3 figures

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., Comment: 9 pages, 7 postscript figures

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 $\Delta_q$ governing the scaling of moments $<|\psi|^{2q}>\sim L^{-qd-\Delta_q}$ 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 $\Delta_2=-1/4$ and $\Delta_3=-3/4$. The multifractality spectrum obtained from numerical simulations is given with a good accuracy by the parabolic approximation $\Delta_q\simeq q(1-q)/8$ 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 ($\Delta_q$), conductances ($X_q$), and Green functions at the localization transition with a critical density of states are discussed., Comment: 16 pages, submitted to J. Phys. A, Special Issue on Random Matrix Theory

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., Comment: 4 pages, submitted to Physical Review B

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 $\eta$ 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, $\Delta_q\simeq q(1-q)/8$ and $X_q\simeq q(3-q)/4$., Comment: 4 pages, 3 figures

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., Comment: 4 pages, 4 figures

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, $S_c(\omega)$, is broadened on a scale of the cyclotron frequency $\omega_c$ and has a sharp dip $\propto |\omega-\omega_c|$. For small antidots, $S_c(\omega)$ is strongly modulated with a period equal to $\omega_c$ and has sharp square-root singularities for a series of resonant frequencies. For large antidots, $S_c(\omega)$ has a hard gap at $\omega<\omega_c$ between two sharp peaks, associated respectively with edge states and free cyclotron orbits., Comment: 9 pages, 4 figures

We investigate the quantum effects, in particular the Landau-level quantization, in the scattering of a particle the nonadiabatic classical dynamics of which is governed by an adiabatic invariant. As a relevant example, we study the scattering of a drifting particle on a magnetic barrier in the quantum limit where the cyclotron energy is much larger than a broadening of the Landau levels induced by the nonadiabatic transitions. We find that, despite the level quantization, the exponential suppression $\exp(-2\pi d/\delta)$ (barrier width $d$, orbital shift per cyclotron revolution $\delta$) of the root-mean-square transverse displacement experienced by the particle after the scattering is the same in the quantum and the classical regime., Comment: 4 pages

We investigate numerically the statistics of wavefunction amplitudes $\psi({\bf r})$ at the integer quantum Hall transition. It is demonstrated that in the limit of a large system size the distribution function of $|\psi|^2$ is log-normal, so that the multifractal spectrum $f(\alpha)$ is exactly parabolic. Our findings lend strong support to a recent conjecture for a critical theory of the quantum Hall transition., Comment: 4 pages Latex

We study theoretically the magnetoresistance $\rho_{xx}(B)$ of a two-dimensional electron gas scattered by a random ensemble of impenetrable discs in the presence of a long-range correlated random potential. We believe that this model describes a high-mobility semiconductor heterostructure with a random array of antidots. We show that the interplay of scattering by the two types of disorder generates new behavior of $\rho_{xx}(B)$ which is absent for only one kind of disorder. We demonstrate that even a weak long-range disorder becomes important with increasing $B$. In particular, although $\rho_{xx}(B)$ vanishes in the limit of large $B$ when only one type of disorder is present, we show that it keeps growing with increasing $B$ in the antidot array in the presence of smooth disorder. The reversal of the behavior of $\rho_{xx}(B)$ is due to a mutual destruction of the quasiclassical localization induced by a strong magnetic field: specifically, the adiabatic localization in the long-range Gaussian disorder is washed out by the scattering on hard discs, whereas the adiabatic drift and related percolation of cyclotron orbits destroys the localization in the dilute system of hard discs. For intermediate magnetic fields in a dilute antidot array, we show the existence of a strong negative magnetoresistance, which leads to a nonmonotonic dependence of $\rho_{xx}(B)$., Comment: 21 pages, 13 figures

We study the quasiclassical magnetotransport of non-interacting fermions in two dimensions moving in a random array of strong scatterers (antidots, impurities or defects) on the background of a smooth random potential. We demonstrate that the combination of the two types of disorder induces a novel mechanism leading to a strong negative magnetoresistance, followed by the saturation of the magnetoresistivity $\rho_{xx}(B)$ at a value determined solely by the smooth disorder. Experimental relevance to the transport in semiconductor heterostructures is discussed., Comment: 4 pages, 2 figures

In Phys. Rev. Lett. 84, 1760 (2000) A.O.Gogolin has challenged the established point of view that Mott's law for the dynamical conductivity of a 1 dimensional insulator is correct. We present the result of a numerical solution of Berezinskii's recursion relations that demonstrate unambigously that the earlier solutions are indeed valid in contrast to Gogolin's claim., Comment: Comment on Phys. Rev. Lett. 84, 1760 (2000), by A.O.Gogolin; 1 page, 1 figure

Critical fluctuations of wave functions and energy levels at the Anderson transition are studied for the family of the critical power-law random banded matrix ensembles. It is shown that the distribution functions of the inverse participation ratios (IPR) $P_q$ are scale-invariant at the critical point, with a power-law asymptotic tail. The IPR distribution, the multifractal spectrum and the level statistics are calculated analytically in the limits of weak and strong couplings, as well as numerically in the full range of couplings., Comment: 14 pages, 13 eps figures

Statistics of the inverse participation ratio (IPR) at the critical point of the localization transition is studied numerically for the power-law random banded matrix model. It is shown that the IPR distribution function is scale-invariant, with a power-law asymptotic ``tail''. This scale invariance implies that the fractal dimensions $D_q$ are non-fluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between $D_2$ and the spectral compressibility $\chi$ is violated in the regime of strong multifractality, with $\chi\to 1$ in the limit $D_2\to 0$., Comment: 4 pages, 3 eps figures

We study the low-frequency behavior of the {\it ac} conductivity $\sigma(\omega)$ of a two-dimensional fermion gas subject to a smooth random potential (RP) or random magnetic field (RMF). We find a non-analytic $\propto|\omega|$ correction to ${\rm Re} \sigma$, which corresponds to a $1/t^2$ long-time tail in the velocity correlation function. This contribution is induced by return processes neglected in Boltzmann transport theory. The prefactor of this $|\omega|$-term is positive and proportional to $(d/l)^2$ for RP, while it is of opposite sign and proportional to $d/l$ in the weak RMF case, where $l$ is the mean free path and $d$ the disorder correlation length. This non-analytic correction also exists in the strong RMF regime, when the transport is of a percolating nature. The analytical results are supported and complemented by numerical simulations., Comment: 12 pages, RevTeX, 7 figures

We calculate the semiclassical magnetoresistivity $\rho_{xx}(B)$ of non-interacting fermions in two dimensions moving in a weak and smoothly varying random potential or random magnetic field. We demonstrate that in a broad range of magnetic fields the non-Markovian character of the transport leads to a strong positive magnetoresistance. The effect is especially pronounced in the case of a random magnetic field where $\rho_{xx}(B)$ becomes parametrically much larger than its B=0 value., Comment: REVTEX, 4 pages, 2 eps figures

An effective Hamiltonian for spinless electrons in the lowest Landau level (LLL) close to half filling is derived. As opposed to the treatment in standard Chern-Simons theories (CS) we first project to the LLL and only then apply a CS-transformation on the Hamiltonian. The transformed field operators act in the lowest Landau level only {\it and} have fermionic commutation relations for small wavenumbers ignoring gauge field fluctuations. When acting on the Hamiltonian at half filling the {\it gauge transformation removes the monopole term in the interaction and does not eliminate the magnetic field., Comment: 4 pages

We study the semiclassical kinetics of 2D fermions in a smoothly varying magnetic field $B({\bf r})$. The nature of the transport depends crucially on both the strength $B_0$ of the random component of $B({\bf r})$ and its mean value $\bar{B}$. For $\bar{B}=0$, the governing parameter is $\alpha=d/R_0$, where $d$ is the correlation length of disorder and $R_0$ is the Larmor radius in the field $B_0$. While for $\alpha\ll 1$ the Drude theory applies, at $\alpha\gg 1$ most particles drift adiabatically along closed contours and are localized in the adiabatic approximation. The conductivity is then determined by a special class of trajectories, the "snake states", which percolate by scattering at the saddle points of $B({\bf r})$ where the adiabaticity of their motion breaks down. The external field also suppresses the diffusion by creating a percolation network of drifting cyclotron orbits. This kind of percolation is due only to a weak violation of the adiabaticity of the cyclotron rotation, yielding an exponential drop of the conductivity at large $\bar{B}$. In the regime $\alpha\gg 1$ the crossover between the snake-state percolation and the percolation of the drift orbits with increasing $\bar{B}$ has the character of a phase transition (localization of snake states) smeared exponentially weakly by non-adiabatic effects. The ac conductivity also reflects the dynamical properties of particles moving on the fractal percolation network. In particular, it has a sharp kink at zero frequency and falls off exponentially at higher frequencies. We also discuss the nature of the quantum magnetooscillations. Detailed numerical studies confirm the analytical findings. The shape of the magnetoresistivity at $\alpha\sim 1$ is in good agreement with experimental data in the FQHE regime near $\nu=1/2$., Comment: 22 pages REVTEX, 14 figures

We study the violation of the adiabaticity of the electron dynamics in a slowly varying magnetic field. We formulate and solve exactly a non-adiabatic scattering problem. In particular, we consider scattering on a magnetic field inhomogeneity which models scatterers in the composite-fermion theory of the half-filled Landau level. The calculated non-adiabatic shift of the guiding center is exponentially small and exhibits an oscillatory behavior related to the "self-commensurability" of the drifting cyclotron orbit. The analytical results are complemented with a numerical simulation., Comment: 4 pages REVTEX, 3 figures included