Mesoscopic fluctuations of nonlinear conductance of chaotic quantum dots

The nonlinear dc conductance of a two-terminal chaotic cavity is investigated. The fluctuations of the conductance (anti)symmetric with respect to magnetic flux inversion through multichannel cavities are found analytically for arbitrary temperature, magnetic field, and interaction strength. For few-channel dots the effect of dephasing is investigated numerically. A comparison with recent experimental data is provided.Comment: 4 pages, 2 figures, v.2-notations correcte

Toward a theory of the integer quantum Hall transition: continuum limit of the Chalker-Coddington model

An N-channel generalization of the network model of Chalker and Coddington is considered. The model for N = 1 is known to describe the critical behavior at the plateau transition in systems exhibiting the integer quantum Hall effect. Using a recently discovered equality of integrals, the network model is transformed into a lattice field theory defined over Efetov's sigma model space with unitary symmetry. The transformation is exact for all N, no saddle-point approximation is made, and no massive modes have to be eliminated. The naive continuum limit of the lattice theory is shown to be a supersymmetric version of Pruisken's nonlinear sigma model with couplings sigma_xx = sigma_xy = N/2 at the symmetric point. It follows that the model for N = 2, which describes a spin degenerate Landau level and the random flux problem, is noncritical. On the basis of symmetry considerations and inspection of the Hamiltonian limit, a modified network model is formulated, which still lies in the quantum Hall universality class. The prospects for deformation to a Yang-Baxter integrable vertex model are briefly discussed.Comment: 25 pages, REVTEX, calculation of sigma_xx correcte

Duality, the Semi-Circle Law and Quantum Hall Bilayers

There is considerable experimental evidence for the existence in Quantum Hall systems of an approximate emergent discrete symmetry, $\Gamma_0(2) \subset SL(2,Z)$. The evidence consists of the robustness of the tests of a suite a predictions concerning the transitions between the phases of the system as magnetic fields and temperatures are varied, which follow from the existence of the symmetry alone. These include the universality of and quantum numbers of the fixed points which occur in these transitions; selection rules governing which phases may be related by transitions; and the semi-circular trajectories in the Ohmic-Hall conductivity plane which are followed during the transitions. We explore the implications of this symmetry for Quantum Hall systems involving {\it two} charge-carrying fluids, and so obtain predictions both for bilayer systems and for single-layer systems for which the Landau levels have a spin degeneracy. We obtain similarly striking predictions which include the novel new phases which are seen in these systems, as well as a prediction for semicircle trajectories which are traversed by specific combinations of the bilayer conductivities as magnetic fields are varied at low temperatures.Comment: 12 pages, 8 figures; discussion of magnetic field dependence modified and figures and references updated in v

Spin-splitting in the quantum Hall effect of disordered GaAs layers with strong overlap of the spin subbands

With minima in the diagonal conductance G_{xx} and in the absolute value of the derivative |dG_{xy}/dB| at the Hall conductance value G_{xy}=e^{2}/h, spin-splitting is observed in the quantum Hall effect of heavily Si-doped GaAs layers with low electron mobility 2000 cm^2/Vs in spite of the fact that the spin-splitting is much smaller than the level broadening. Experimental results can be explained in the frame of the scaling theory of the quantum Hall effect, applied independently to each of the two spin subbands.Comment: 4 pages, 4 figure

The quantum paraelectric behavior of SrTiO_{3} revisited: relevance of the structural phase transition temperature

It has been known for a long time that the low temperature behavior shown by the dielectric constant of quantum paraelectric $SrTiO_{3}$ can not be fitted properly by Barrett's formula using a single zero point energy or saturation temperature ($T_{1}$). As it was originally shown [K. A. M\"{u}ller and H. Burkard, Phys. Rev. B {\bf 19}, 3593 (1979)] a crossover between two different saturation temperatures ($T_{1l}$=77.8K and $T_{1h}$=80K) at $T\sim10K$ is needed to explain the low and high temperature behavior of the dielectric constant. However, the physical reason for the crossover between these two particular values of the saturation temperature at $T\sim10K$ is unknown. In this work we show that the crossover between these two values of the saturation temperature at $T\sim10K$ can be taken as a direct consequence of (i) the quantum distribution of frequencies $g(\Omega)\propto\Omega^{2}$ associated with the complete set of low-lying modes and (ii) the existence of a definite maximum phonon frequency given by the structural transition critical temperature $T_{tr}$.Comment: 8 pages, 3 figure

Theory of Anomalous Quantum Hall Effects in Graphene

Recent successes in manufacturing of atomically thin graphite samples (graphene) have stimulated intense experimental and theoretical activity. The key feature of graphene is the massless Dirac type of low-energy electron excitations. This gives rise to a number of unusual physical properties of this system distinguishing it from conventional two-dimensional metals. One of the most remarkable properties of graphene is the anomalous quantum Hall effect. It is extremely sensitive to the structure of the system; in particular, it clearly distinguishes single- and double-layer samples. In spite of the impressive experimental progress, the theory of quantum Hall effect in graphene has not been established. This theory is a subject of the present paper. We demonstrate that the Landau level structure by itself is not sufficient to determine the form of the quantum Hall effect. The Hall quantization is due to Anderson localization which, in graphene, is very peculiar and depends strongly on the character of disorder. It is only a special symmetry of disorder that may give rise to anomalous quantum Hall effects in graphene. We analyze the symmetries of disordered single- and double-layer graphene in magnetic field and identify the conditions for anomalous Hall quantization.Comment: 13 pages (article + supplementary material), 5 figure

Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation

The critical thermodynamics of the two-dimensional N-vector cubic and MN models is studied within the field-theoretical renormalization-group (RG) approach. The beta functions and critical exponents are calculated in the five-loop approximation and the RG series obtained are resummed using the Borel-Leroy transformation combined with the generalized Pad\'e approximant and conformal mapping techniques. For the cubic model, the RG flows for various N are investigated. For N=2 it is found that the continuous line of fixed points running from the XY fixed point to the Ising one is well reproduced by the resummed RG series and an account for the five-loop terms makes the lines of zeros of both beta functions closer to each another. For the cubic model with N\geq 3, the five-loop contributions are shown to shift the cubic fixed point, given by the four-loop approximation, towards the Ising fixed point. This confirms the idea that the existence of the cubic fixed point in two dimensions under N>2 is an artifact of the perturbative analysis. For the quenched dilute O(M) models ($MN$ models with N=0) the results are compatible with a stable pure fixed point for M\geq1. For the MN model with M,N\geq2 all the non-perturbative results are reproduced. In addition a new stable fixed point is found for moderate values of M and N.Comment: 26 pages, 3 figure

Critical dynamics and effective exponents of magnets with extended impurities

We investigate the asymptotic and effective static and dynamic critical behavior of (d=3)-dimensional magnets with quenched extended defects, correlated in $\epsilon_d$ dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining $d-\epsilon_d$ dimensions. The field-theoretical renormalization group perturbative expansions being evaluated naively do not allow for the reliable numerical data. We apply the Chisholm-Borel resummation technique to restore convergence of the two-loop expansions and report the numerical values of the asymptotic critical exponents for the model A dynamics. We discuss different scenarios for static and dynamic effective critical behavior and give values for corresponding non-universal exponents.Comment: 12 pages, 6 figure

Effect of Tilted Magnetic Field on the Anomalous H=0 Conducting Phase in High-Mobility Si MOSFETs

The suppression by a magnetic field of the anomalous H=0 conducting phase in high-mobility silicon MOSFETs is independent of the angle between the field and the plane of the 2D electron system. In the presence of a parallel field large enough to fully quench the anomalous conducting phase, the behavior is similar to that of disordered GaAs/AlGaAs heterostructures: the system is insulating in zero (perpendicular) field and exhibits reentrant insulator-quantum Hall effect-insulator transitions as a function of perpendicular field. The results demonstrate that the suppression of the low-T phase is related only to the electrons' spin.Comment: 4 pages, including 3 figures. We corrected several typos in the figures and caption

Anomalous state of a 2DEG in vicinal Si MOSFET in high magnetic fields

We report the observation of an anomalous state of a 2D electron gas near a vicinal surface of a silicon MOSFET in high magnetic fields. It is characterised by unusual behaviour of the conductivities $\sigma_{xx}$ and $\sigma_{xy}$, which can be described as a collapse of the Zeeman spin splitting accompanied by a large peak in $\sigma_{xx}$ and an anomalous peak in $\sigma_{xy}$. It occurs at densities corresponding to the position of the Fermi level above the onset of the superlattice mini-gap inherent to the vicinal system. The range of fields and densities where this effect exists has been determined, and it has been shown that it is suppressed by parallel magnetic fields