Bertrand I. Halperin

Anomalous low-temperature thermal properties of glasses and spin glasses

Abstract We show that a linear specific heat at low temperatures for glass follows naturally from general considerations on the glassy state. From the same considerations we obtain the experimentally observed anomalous low-temperature thermal conductivity, and we predict an ultrasonic attenuation which increases at low temperatures. Possible relationships with the linear specific heat in magnetic impurity systems are pointed out. We suggest experimental study of the relaxation of thermal and other properties.

Charge Fractionalization in Quantum Wires

One-dimensional metals, such as quantum wires or carbon nanotubes, can carry charge in arbitrary units, smaller or larger than a single electron charge. However, according to Luttinger theory, which describes the low-energy excitations of such systems, when a single electron is injected by tunneling into the middle of such a wire, it will tend to break up into separate charge pulses, moving in opposite directions, which carry definite fractions f and (1−f) of the electron charge, determined by a parameter g that measures the strength of charge interactions in the wire. (The injected electron will also produce a spin excitation, which will travel at a different velocity than the charge excitations.) Observing charge fractionalization physics in an experiment is a challenge in those (nonchiral) low-dimensional systems which are adiabatically coupled to Fermi liquid leads. We theoretically discuss a first important step towards the observation of charge fractionalization in quantum wires based on momentum-resolved tunneling and multi-terminal geometries, and explain the recent experimental results of H. Steinberg et al., Nature Physics 4, 116 (2008).

Nonlocal magnetization dynamics in ferromagnetic heterostructures

Two complementary effects modify the GHz magnetization dynamics of nanoscale heterostructures of ferromagnetic and normal materials relative to those of the isolated magnetic constituents. On the one hand, a time-dependent ferromagnetic magnetization pumps a spin angular-momentum flow into adjacent materials and, on the other hand, spin angular momentum is transferred between ferromagnets by an applied bias, causing mutual torques on the magnetizations. These phenomena are manifestly nonlocal: they are governed by the entire spin-coherent region that is limited in size by spin-flip relaxation processes. This review presents recent progress in understanding the magnetization dynamics in ferromagnetic heterostructures from first principles, focusing on the role of spin pumping in layered structures. The main body of the theory is semiclassical and based on a mean-field Stoner or spin-density-functional picture, but quantum-size effects and the role of electron-electron correlations are also discussed. A growing number of experiments support the theoretical predictions. The formalism should be useful for understanding the physics and for engineering the characteristics of small devices such as magnetic random-access memory elements.

On Anyon Superconductivity

We investigate the statistical mechanics of a gas of fractional statistics particles in 2+1 dimensions. In the case of statistics very close to Fermi statistics (statistical parameter θ=π(1−1/n), for large n), the effect of the statistics is a weak attraction. Building upon earlier RPA calculation of Fetter, Hanna, and Laughlin for the case n=2, we argue that for large n perturbation theory is reliable and exhibits superfluidity (or superconductivity after coupling to electromagnetism). We attempt to describe the order parameter for this superconducting phase in terms of “spontaneous breaking of commutativity of translations” as opposed to the usual pairing order parameters. The vortices of the superconducting anyon gas are charged, and superconducting order parameters of the usual type vanish. We investigate the characteristic P and T violating phenomenology.

Resistive transition in superconducting films

The consequences of a vortex unbinding picture of two-dimensional superconductivity are worked out. Although there is no true finite-temperature phase transition, dirty superconducting films should display anomalous behavior below the BCS transition temperature and above an effective Kosterlitz-Thouless vortex unbinding temperature. In particular, both the conductivity and fluctuation diamagnetism behave like ξ+2in this regime, where ξ+ is the correlation length calculated by Kosterlitz, ξ+-ξc exp (B/T − Tc)1/2. We estimate ξc, B, and the vortex unbinding temperature, and determine the nonlinear resistivity below Tc. A recent theory of vortex dynamics, together with a time-dependent Ginzburg-Landau theory, lead to a determination of the frequency-dependent conductivity.

The Excitonic State at the Semiconductor-Semimetal Transition

Publisher Summary Some years ago, Mott considered the role of the Coulomb attraction for a semimetal with small numbers of electrons and holes and observed that under certain conditions the electrons and holes could bind to form a nonconducting phase. Knox remarked that the ordinary Bloch wave groundstate of the crystal could become unstable against the spontaneous formation of excitons if the exciton binding energy exceeded the energy grip. The exciton instability leads to a second-order transition to a new state having a “condensate” of excitons and in which the translational periodicity of the original lattice is broken by a new “long-range order” in the electronic states. This new state is variously referred to as the “excitonic state” or as the “distorted state,” whereas the normal Bloch-wave state is referred to as the “undistorted state.” This chapter gives a brief review of the previous work on the excitonic state. The bulk of the chapter is devoted to an attempt to elucidate further the physical significance of the distorted state, and to examine more carefully than previously the question of the existence of such a state, and of the location and nature of the transition points.

Spin Current and Polarization in Impure Two-Dimensional Electron Systems with Spin-Orbit Coupling

We derive the transport equations for two-dimensional electron systems with Rashba spin-orbit interaction and short-range spin-independent disorder. In the limit of slow spatial variations, we obtain coupled diffusion equations for the electron density and spin. Using these equations we calculate electric-field induced spin accumulation and spin current in a finite-size sample for an arbitrary ratio between spin-orbit energy splitting Delta and elastic scattering rate tau(-1). We demonstrate that the spin-Hall conductivity vanishes in an infinite system independent of this ratio.

Proposed experiments to probe the non-Abelian nu = 5/2 quantum hall state.

We propose several experiments to test the non-Abelian nature of quasiparticles in the fractional quantum Hall state at nu = 5/2. In a simplified version of the experiment suggested by [S. Das Sarma, M. Freedman, and C. Nayak, Phys. Rev. Lett. 94, 166802 (2005).], interference is turned on and off when the number of localized quasiparticles between the interfering paths varies between even and odd. We find analogous effects in the thermodynamic properties of closed systems.

Theory of Spin Hall Conductivity in n-Doped GaAs

We develop a theory of extrinsic spin currents in semiconductors, resulting from spin-orbit coupling at charged scatterers, which leads to skew-scattering and side-jump contributions to the spin-Hall conductivity. Applying the theory to bulk n-GaAs, without any free parameters, we find spin currents that are in reasonable agreement with experiments by Kato et al. [Science 306, 1910 (2004)].

On the analogy between smectic a liquid crystals and superconductors

Abstract The analogy between a smectic A liquid crystal and a superconductor is made closer by a gauge transformation on the smectic system. Within the context of the Wilson-Fisher recursion relations, it is shown that the critical properties of the two systems are the same, and that therefore the phase transition from smectic A to nematic will always be at least weakly first order.