Quantum oscillations in a topological insulator Bi_{1-x}Sb_{x}

We have studied transport and magnetic properties of Bi_{1-x}Sb_x, which is believed to be a topological insulator - a new state of matter where an insulating bulk supports an intrinsically metallic surface. In nominally insulating Bi_{0.91}Sb_{0.09} crystals, we observed strong quantum oscillations of the magnetization and the resistivity originating from a Fermi surface which has a clear two-dimensional character. In addition, a three-dimensional Fermi surface is found to coexist, which is possibly due to an unusual coupling of the bulk to the surface. This finding demonstrates that quantum oscillations can be a powerful tool to directly probe the novel electronic states in topological insulators.Comment: 4 pages, 4 figure

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

Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability distributions. The JSD has several interesting properties. It arises in information theory and, unlike the Kullback-Leibler divergence, it is symmetric, always well defined and bounded. We show that the quantum JSD (QJSD) shares with the relative entropy most of the physically relevant properties, in particular those required for a "good" quantum distinguishability measure. We relate it to other known quantum distances and we suggest possible applications in the field of the quantum information theory.Comment: 14 pages, corrected equation 1

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

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

Topological change of the Fermi surface in ternary iron-pnictides with reduced c/a ratio: A dHvA study of CaFe2P2

We report a de Haas-van Alphen effect study of the Fermi surface of CaFe2P2 using low temperature torque magnetometry up to 45 T. This system is a close structural analogue of the collapsed tetragonal non-magnetic phase of CaFe2As2. We find the Fermi surface of CaFe2P2 to differ from other related ternary phosphides in that its topology is highly dispersive in the c-axis, being three-dimensional in character and with identical mass enhancement on both electron and hole pockets (~1.5). The dramatic change in topology of the Fermi surface suggests that in a state with reduced (c/a) ratio, when bonding between pnictogen layers becomes important, the Fermi surface sheets are unlikely to be nested

Full oxide heterostructure combining a high-Tc diluted ferromagnet with a high-mobility conductor

We report on the growth of heterostructures composed of layers of the high-Curie temperature ferromagnet Co-doped (La,Sr)TiO3 (Co-LSTO) with high-mobility SrTiO3 (STO) substrates processed at low oxygen pressure. While perpendicular spin-dependent transport measurements in STO//Co-LSTO/LAO/Co tunnel junctions demonstrate the existence of a large spin polarization in Co-LSTO, planar magnetotransport experiments on STO//Co-LSTO samples evidence electronic mobilities as high as 10000 cm2/Vs at T = 10 K. At high enough applied fields and low enough temperatures (H < 60 kOe, T < 4 K) Shubnikov-de Haas oscillations are also observed. We present an extensive analysis of these quantum oscillations and relate them with the electronic properties of STO, for which we find large scattering rates up to ~ 10 ps. Thus, this work opens up the possibility to inject a spin-polarized current from a high-Curie temperature diluted oxide into an isostructural system with high-mobility and a large spin diffusion length.Comment: to appear in Phys. Rev.

A Generalization of the Convex Kakeya Problem

Given a set of line segments in the plane, not necessarily finite, what is a convex region of smallest area that contains a translate of each input segment? This question can be seen as a generalization of Kakeya's problem of finding a convex region of smallest area such that a needle can be rotated through 360 degrees within this region. We show that there is always an optimal region that is a triangle, and we give an optimal \Theta(n log n)-time algorithm to compute such a triangle for a given set of n segments. We also show that, if the goal is to minimize the perimeter of the region instead of its area, then placing the segments with their midpoint at the origin and taking their convex hull results in an optimal solution. Finally, we show that for any compact convex figure G, the smallest enclosing disk of G is a smallest-perimeter region containing a translate of every rotated copy of G.Comment: 14 pages, 9 figure

Heavy quasiparticles in the ferromagnetic superconductor ZrZn2

We report a study of the de Haas-van Alphen effect in the normal state of the ferromagnetic superconductor ZrZn2. Our results are generally consistent with an LMTO band structure calculation which predicts four exchange-split Fermi surface sheets. Quasiparticle effective masses are enhanced by a factor of about 4.9 implying a strong coupling to magnetic excitations or phonons. Our measurements provide insight in to the mechanism for superconductivity and unusual thermodynamic properties of ZrZn2.Comment: 5 pages, 2 figures (one color