Oscillatory angular dependence of the magnetoresistance in a topological insulator Bi_{1-x}Sb_{x}

The angular-dependent magnetoresistance and the Shubnikov-de Haas oscillations are studied in a topological insulator Bi_{0.91}Sb_{0.09}, where the two-dimensional (2D) surface states coexist with a three-dimensional (3D) bulk Fermi surface (FS). Two distinct types of oscillatory phenomena are discovered in the angular-dependence: The one observed at lower fields is shown to originate from the surface state, which resides on the (2\bar{1}\bar{1}) plane, giving a new way to distinguish the 2D surface state from the 3D FS. The other one, which becomes prominent at higher fields, probably comes from the (111) plane and is obviously of unknown origin, pointing to new physics in transport properties of topological insulators.Comment: 4 pages, 5 figures, revised version with improved data and analysi

Combination quantum oscillations in canonical single-band Fermi liquids

Chemical potential oscillations mix individual-band frequencies of the de Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) magneto-oscillations in canonical low-dimensional multi-band Fermi liquids. We predict a similar mixing in canonical single-band Fermi liquids, which Fermi-surfaces have two or more extremal cross-sections. Combination harmonics are analysed using a single-band almost two-dimensional energy spectrum. We outline some experimental conditions allowing for resolution of combination harmonics

Magnetic quantum oscillations in nanowires

Analytical expressions for the magnetization and the longitudinal conductivity of nanowires are derived in a magnetic field, B. We show that the interplay between size and magnetic field energy-level quantizations manifests itself through novel magnetic quantum oscillations in metallic nanowires. There are three characteristic frequencies of de Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) oscillations, F=F_0,F_1, and F_2 in contrast with a single frequency F'_0 in simple bulk metals. The amplitude of oscillations is strongly enhanced in some "magic" magnetic fields. The wire cross-section S can be measured along with the Fermi surface cross-section, S_F

Magnetic quantum oscillations in doped antiferromagnetic insulators

Energy spectrum of electrons (holes) doped into a two-dimensional antiferromagnetic insulator is quantized in an external magnetic field of arbitrary direction. A peculiar dependence of de Haas-van Alphen (dHvA) or Shubnikov-de Haas (SdH) magneto-oscillation amplitudes on the azimuthal in-plane angle from the magnetization direction and on the polar angle from the out-of-plane direction is found, which can be used as a sensitive probe of the antiferromagnetic order in doped Mott-Hubbard, spin-density wave (SDW), and conventional band-structure insulators.Comment: 4 pages 4 figure

Interplay of size and Landau quantizations in the de Haas-van Alphen oscillations of metallic nanowires

We examine the interplay between size quantization and Landau quantization in the De Haas-Van Alphen oscillations of clean, metallic nanowires in a longitudinal magnetic field for `hard' boundary conditions, i.e. those of an infinite round well, as opposed to the `soft' parabolically confined boundary conditions previously treated in Alexandrov and Kabanov (Phys. Rev. Lett. {\bf 95}, 076601 (2005) (AK)). We find that there exist {\em two} fundamental frequencies as opposed to the one found in bulk systems and the three frequencies found by AK with soft boundary counditions. In addition, we find that the additional `magic resonances' of AK may be also observed in the infinite well case, though they are now damped. We also compare the numerically generated energy spectrum of the infinite well potential with that of our analytic approximation, and compare calculations of the oscillatory portions of the thermodynamic quantities for both models.Comment: Title changed, paper streamlined on suggestion of referrees, typos corrected, numerical error in figs 2 and 3 corrected and final result simplified -- two not three frequencies (as in the previous version) are observed. Abstract altered accordingly. Submitted to Physical Review

On spherical averages of radial basis functions

A radial basis function (RBF) has the general form $$s(x)=\sum_{k=1}^{n}a_{k}\phi(x-b_{k}),\quad x\in\mathbb{R}^{d},$$ where the coefficients a 1,…,a n are real numbers, the points, or centres, b 1,…,b n lie in ℝ d , and φ:ℝ d →ℝ is a radially symmetric function. Such approximants are highly useful and enjoy rich theoretical properties; see, for instance (Buhmann, Radial Basis Functions: Theory and Implementations, [2003]; Fasshauer, Meshfree Approximation Methods with Matlab, [2007]; Light and Cheney, A Course in Approximation Theory, [2000]; or Wendland, Scattered Data Approximation, [2004]). The important special case of polyharmonic splines results when φ is the fundamental solution of the iterated Laplacian operator, and this class includes the Euclidean norm φ(x)=‖x‖ when d is an odd positive integer, the thin plate spline φ(x)=‖x‖2log  ‖x‖ when d is an even positive integer, and univariate splines. Now B-splines generate a compactly supported basis for univariate spline spaces, but an analyticity argument implies that a nontrivial polyharmonic spline generated by (1.1) cannot be compactly supported when d>1. However, a pioneering paper of Jackson (Constr. Approx. 4:243–264, [1988]) established that the spherical average of a radial basis function generated by the Euclidean norm can be compactly supported when the centres and coefficients satisfy certain moment conditions; Jackson then used this compactly supported spherical average to construct approximate identities, with which he was then able to derive some of the earliest uniform convergence results for a class of radial basis functions. Our work extends this earlier analysis, but our technique is entirely novel, and applies to all polyharmonic splines. Furthermore, we observe that the technique provides yet another way to generate compactly supported, radially symmetric, positive definite functions. Specifically, we find that the spherical averaging operator commutes with the Fourier transform operator, and we are then able to identify Fourier transforms of compactly supported functions using the Paley–Wiener theorem. Furthermore, the use of Haar measure on compact Lie groups would not have occurred without frequent exposure to Iserles’s study of geometric integration

Ginzburg-Landau-Gor'kov Theory of Magnetic oscillations in a type-II 2-dimensional Superconductor

We investigate de Haas-van Alphen (dHvA) oscillations in the mixed state of a type-II two-dimensional superconductor within a self-consistent Gor'kov perturbation scheme. Assuming that the order parameter forms a vortex lattice we can calculate the expansion coefficients exactly to any order. We have tested the results of the perturbation theory to fourth and eight order against an exact numerical solution of the corresponding Bogoliubov-de Gennes equations. The perturbation theory is found to describe the onset of superconductivity well close to the transition point $H_{c2}$. Contrary to earlier calculations by other authors we do not find that the perturbative scheme predicts any maximum of the dHvA-oscillations below $H_{c2}$. Instead we obtain a substantial damping of the magnetic oscillations in the mixed state as compared to the normal state. We have examined the effect of an oscillatory chemical potential due to particle conservation and the effect of a finite Zeeman splitting. Furthermore we have investigated the recently debated issue of a possibility of a sign change of the fundamental harmonic of the magnetic oscillations. Our theory is compared with experiment and we have found good agreement.Comment: 39 pages, 8 figures. This is a replacement of supr-con/9608004. Several sections changed or added, including a section on the effect of spin and the effect of a conserved number of particles. To be published in Phys. Rev.

Anomalous resistivity and the electron-polaron effect in the two-band Hubbard model with one narrow band

We search for anomalous normal and superconductive behavior in the two-band Hubbard model with one narrow band. We analyze the influence of electron-polaron effect and Altshuler-Aronov effect on effective mass enhancement and scattering times of heavy and light components in the clean case. We find anomalous behavior of resistivity at high temperatures $T>W_{h}^{*}$ both in 3D and 2D situation. The SC instability in the model is governed by enhanced Kohn-Luttinger effect for p-wave pairing of heavy electrons via polarization of light electrons.Comment: 8 pages, 4 figures, accepted for publication in Journal of Superconductivity and Novel Magnetism, based on the invited talk on Stripes XI Conference in Rome, July 201

Theory of quantum magneto-oscillations in underdoped cuprate superconductors

Magneto-oscillations in kinetic and magnetic response functions of a few underdoped cuprates are perhaps one of the most striking observations since many probes of underdoped cuprates clearly point to a non Fermi-liquid normal state. Their observation in the vortex state well below the upper critical field raises a doubt concerning their normal state origin. Here I propose an explanation of the magneto-oscillations as emerging from the quantum interference of the vortex lattice and checkerboard modulations of the electron density of states revealed by STM with atomic resolution in some cuprate superconductors. The checkerboard effectively pins the vortex lattice, when the period of the latter is commensurate with the period of the checkerboard. This condition yields 1/\sqrt{B} periodicity of the response functions versus magnetic field B, rather than 1/B periodicity of conventional normal state oscillations. Our solution of the Gross-Pitaevskii-type equation for composed charged bosons accounting for the d-wave symmetry of the order-parameter and its checkerboard modulations describes well changes in resonant frequency of the tunnel-diode oscillator circuit with YBa2Cu4O8 and the oscillatory part of the Hall resistance and magnetic susceptibility in the mixed state of YBa2Cu3O6.5.Comment: 4 pages, 3 figures, experimental conditions allowing for a resolution of conventional normal-state and unconventional vortex-state magneto-oscillations are outline

Re-ranking Permutation-Based Candidate Sets with the n-Simplex Projection

In the realm of metric search, the permutation-based approaches have shown very good performance in indexing and supporting approximate search on large databases. These methods embed the metric objects into a permutation space where candidate results to a given query can be efficiently identified. Typically, to achieve high effectiveness, the permutation-based result set is refined by directly comparing each candidate object to the query one. Therefore, one drawback of these approaches is that the original dataset needs to be stored and then accessed during the refining step. We propose a refining approach based on a metric embedding, called n-Simplex projection, that can be used on metric spaces meeting the n-point property. The n-Simplex projection provides upper- and lower-bounds of the actual distance, derived using the distances between the data objects and a finite set of pivots. We propose to reuse the distances computed for building the data permutations to derive these bounds and we show how to use them to improve the permutation-based results. Our approach is particularly advantageous for all the cases in which the traditional refining step is too costly, e.g. very large dataset or very expensive metric function