Dynamics of a Magnetic Needle Magnetometer: Sensitivity to Landau-Lifshitz-Gilbert Damping.

An analysis of a single-domain magnetic needle (MN) in the presence of an external magnetic field B is carried out with the aim of achieving a high-precision magnetometer. We determine the uncertainty ΔB of such a device due to Gilbert dissipation and the associated internal magnetic field fluctuations that give rise to diffusion of the MN axis direction n and the needle orbital angular momentum. The levitation of the MN in a magnetic trap and its stability are also analyzed.

Band of critical States in anderson localization in a strong magnetic field with random spin-orbit scattering.

The Anderson localization problem for a noninteracting two-dimensional electron gas subject to a strong magnetic field, disordered potential, and spin-orbit coupling is studied numerically on a square lattice. The nature of the corresponding localization-delocalization transition and the properties of the pertinent extended states depend on whether the spin-orbit coupling is uniform or fully random. For uniform spin-orbit coupling (such as Rashba coupling due to a uniform electric field), there is a band of metallic extended states in the center of a Landau band as in a "standard" Anderson metal-insulator transition. However, for fully random spin-orbit coupling, the familiar pattern of Landau bands disappears. Instead, there is a central band of critical states with definite fractal structure separated at two critical energies from two side bands of localized states. Moreover, finite size scaling analysis suggests that for this novel transition, on the localized side of a critical energy E_{c}, the localization length diverges as ξ(E)∝exp(α/sqrt[|E-E_{c}|]), a behavior which, together with the emergence of a band of critical states, is reminiscent of a Berezinskii-Kosterlitz-Thouless transition.

Feshbach resonance without a closed-channel bound state.

The physics of Feshbach resonance is analyzed using an analytic expression for the s-wave scattering phase shift and the scattering length a which we derive within a two-channel tight-binding model. Employing a unified treatment of bound states and resonances in terms of the Jost function, it is shown that, for strong interchannel coupling, Feshbach resonance can occur even when the closed channel does not have a bound state. This may extend the range of ultracold atomic systems that can be manipulated by Feshbach resonance. The dependence of the sign of a on the coupling strength in the unitary limit is elucidated. As a by-product, analytic expressions are derived for the background scattering length, the external magnetic field at which resonance occurs, and the energy shift ε-ε(B), where ε is the scattering energy and ε(B) is the bound-state energy in the closed channel (when there is one).

Kondo correlations and Majorana bound states in a metal to quantum-dot to topological-superconductor junction.

Electron transport through a normal-metal-quantum-dot-topological-superconductor junction is studied and reveals interlacing physics of Kondo correlations with two Majorana fermions bound states residing on the opposite ends of the topological superconductor. When the strength of the Majorana fermion coupling exceeds the temperature T, this combination of Kondo-Majorana fermion physics might be amenable for an experimental test: The usual peak of the temperature dependent zero bias conductance σ(V=0,T) splits and the conductance has a dip at T=0. The heights of the conductance side peaks decrease with magnetic field.

Absence of localization in disordered two-dimensional electron gas at weak magnetic field and strong spin-orbit coupling.

The one-parameter scaling theory of localization predicts that all states in a disordered two-dimensional system with broken time reversal symmetry are localized even in the presence of strong spin-orbit coupling. While at constant strong magnetic fields this paradigm fails (recall the quantum Hall effect), it is believed to hold at weak magnetic fields. Here we explore the nature of quantum states at weak magnetic field and strongly fluctuating spin-orbit coupling, employing highly accurate numerical procedure based on level spacing distribution and transfer matrix technique combined with one parameter finite-size scaling hypothesis. Remarkably, the metallic phase, (known to exist at zero magnetic field), persists also at finite (albeit weak) magnetic fields, and eventually crosses over into a critical phase, which has already been confirmed at high magnetic fields. A schematic phase diagram drawn in the energy-magnetic field plane elucidates the occurrence of localized, metallic and critical phases. In addition, it is shown that nearest-level statistics is determined solely by the symmetry parameter ß and follows the Wigner surmise irrespective of whether states are metallic or critical.

Unusual electronic properties of clean and disordered zigzag graphene nanoribbons.

We revisit the problem of electron transport in clean and disordered zigzag graphene nanoribbons, and expose numerous hitherto unknown peculiar properties of these systems at zero energy, where both sublattices decouple because of chiral symmetry. For clean ribbons, we give a quantitative description of the unusual power-law dispersion of the central energy bands and of its main consequences, including the strong divergence of the density of states near zero energy, and the vanishing of the transverse localization length of the corresponding edge states. In the presence of off-diagonal disorder, which respects the lattice chiral symmetry, all zero-energy localization properties are found to be anomalous. Recasting the problem in terms of coupled Brownian motions enables us to derive numerous asymptotic results by analytical means. In particular the typical conductance gN of a disordered sample of width N and length L is shown to decay as exp(-CNw√L), for arbitrary values of the disorder strength w, while the relative variance of ln gN approaches a non-trivial constant KN. The dependence of the constants CN and KN on the ribbon width N is predicted. From the mere viewpoint of the transfer-matrix formalism, zigzag ribbons provide a case study with many unusual features. The transfer matrix describing propagation through one unit cell of a clean ribbon is not diagonalizable at zero energy. In the disordered case, we encounter non-trivial random matrix products such that all Lyapunov exponents vanish identically.

Quantum dots with even number of electrons: kondo effect in a finite magnetic field

We show that the Kondo effect can be induced by an external magnetic field in quantum dots with an even number of electrons. If the Zeeman energy B is close to the single-particle level spacing Delta in the dot, the scattering of the conduction electrons from the dot is dominated by an anisotropic exchange interaction. A Kondo resonance then occurs despite the fact that B exceeds by far the Kondo temperature T(K). As a result, at low temperatures T<