Gauge field theory approach to spin transport in a 2D electron gas

We discuss the Pauli Hamiltonian including the spin-orbit interaction within an U(1) x SU(2) gauge theory interpretation, where the gauge symmetry appears to be broken. This interpretation offers new insight into the problem of spin currents in the condensed matter environment, and can be extended to Rashba and Dresselhaus spin-orbit interactions. We present a few outcomes of the present formulation: i) it automatically leads to zero spin conductivity, in contrast to predictions of Gauge symmetric treatments, ii) a topological quantization condition leading to voltage quantization follows, and iii) spin interferometers can be conceived in which, starting from a arbitrary incoming unpolarized spinor, it is always possible to construct a perfect spin filtering condition.Comment: Invited contribution to Statphys conference, June 2009, Lviv (Ukraine

Equilibrium currents in a Corbino graphene ring

We address the description of a graphene Corbino disk in the context of a tight binding approach that includes both kinetic and Rashba spin-orbit coupling due to an external out-of-plane electric field. Persistent equilibrium currents are induced by an external magnetic field breaking time reversal symmetry. By direct diagonalization, we compute the spectrum and focus on the dispersion near the $K$ points at the Fermi level. The dispersion keenly reproduces that of a continuum model in spite of the complexity of the boundary conditions. We validate the assumptions of the continuum model in terms of predominant zig-zag boundaries conditions and weak sub-band coupling. The wave functions displaying the lowest transverse modes are obtained, showing the predominance of edge states with charge density at the zig-zag edges. The persistent charge currents, nevertheless, do not follow the traditional argument of current cancellation from levels below the Fermi level, and thus they depart in the tight-binding from those found in the continuum model.Comment: 8 pages, 6 figure

Influence of quenched dilution on the quasi-long-range ordered phase of the 2d XY model

The influence of non magnetic impurities in the 2d XY model is investigated through Monte Carlo (MC) simulations. The general picture of the transition is fully understood from the Harris criterion which predicts that the universality class is unchanged, and the Berezinskii-Kosterlitz-Thouless description of the topological transition remains valid. We nevertheless address here the question about the influence of dilution on the quasi-long-range order at low temperatures. In particular, we study the asymptotic of the pair correlation function and report the MC estimates for the critical exponent $\eta$ at different dilutions. In the weak dilution region, our MC calculations are further supported by simple spin-wave-like calculations.Comment: 8 pages, 7 eps figure

Finite temperature behavior of strongly disordered quantum magnets coupled to a dissipative bath

We study the effect of dissipation on the infinite randomness fixed point and the Griffiths-McCoy singularities of random transverse Ising systems in chains, ladders and in two-dimensions. A strong disorder renormalization group scheme is presented that allows the computation of the finite temperature behavior of the magnetic susceptibility and the spin specific heat. In the case of Ohmic dissipation the susceptibility displays a crossover from Griffiths-McCoy behavior (with a continuously varying dynamical exponent) to classical Curie behavior at some temperature $T^*$. The specific heat displays Griffiths-McCoy singularities over the whole temperature range. For super-Ohmic dissipation we find an infinite randomness fixed point within the same universality class as the transverse Ising system without dissipation. In this case the phase diagram and the parameter dependence of the dynamical exponent in the Griffiths-McCoy phase can be determined analytically.Comment: 23 pages, 12 figure

Using torsion to manipulate spin currents

We address the problem of quantum particles moving on a manifold characterised by the presence of torsion along a preferential axis. In fact, such a torsion may be taylored by the presence of a single screw dislocation, whose Burgers vector measures the torsion amplitude. The problem, first treated in the relativistic limit describing fermions that couple minimally to torsion, is then analysed in the Pauli limit We show that torsion induces a geometric potential and also that it couples generically to the phase of the wave function, giving rise to the possibility of using torsion to manipulate spin currents in the case of spinor wave functions. These results emerge as an alternative strategy for using screw dislocations in the design of spintronic-based devices

Continuum model for chiral induced spin selectivity in helical molecules

A minimal model is exactly solved for electron spin transport on a helix. Electron transport is assumed to be supported by well oriented $p_z$ type orbitals on base molecules forming a staircase of definite chirality. In a tight binding interpretation, the SOC opens up an effective $\pi_z-\pi_z$ coupling via interbase $p_{x,y}-p_z$ hopping, introducing spin coupled transport. The resulting continuum model spectrum shows two Kramers doublet transport channels with a gap proportional to the SOC. Each doubly degenerate channel satisfies time reversal symmetry, nevertheless, a bias chooses a transport direction and thus selects for spin orientation. The model predicts which spin orientation is selected depending on chirality and bias, changes in spin preference as a function of input Fermi level and scattering suppression protected by the SO gap. We compute the spin current with a definite helicity and find it to be proportional to the torsion of the chiral structure and the non-adiabatic Aharonov- Anandan phase. To describe room temperature transport we assume that the total transmission is the result of a product of coherent steps limited by the coherence length

Quasi-long-range ordering in a finite-size 2D Heisenberg model

We analyse the low-temperature behaviour of the Heisenberg model on a two-dimensional lattice of finite size. Presence of a residual magnetisation in a finite-size system enables us to use the spin wave approximation, which is known to give reliable results for the XY model at low temperatures T. For the system considered, we find that the spin-spin correlation function decays as 1/r^eta(T) for large separations r bringing about presence of a quasi-long-range ordering. We give analytic estimates for the exponent eta(T) in different regimes and support our findings by Monte Carlo simulations of the model on lattices of different sizes at different temperatures.Comment: 9 pages, 3 postscript figs, style files include

Topological transition in a two-dimensional model of liquid crystal

Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P\_4$. The system is studied through standard Finite-Size Scaling and conformal rescaling of density profiles of correlation functions. A topological transition between a paramagnetic phase at high temperature and a critical phase at low temperature is observed. The low temperature limit is discussed in the spin wave approximation and confirms the numerical results

Aperiodic Ising Quantum Chains

Some years ago, Luck proposed a relevance criterion for the effect of aperiodic disorder on the critical behaviour of ferromagnetic Ising systems. In this article, we show how Luck's criterion can be derived within an exact renormalisation scheme for Ising quantum chains with coupling constants modulated according to substitution rules. Luck's conjectures for this case are confirmed and refined. Among other outcomes, we give an exact formula for the correlation length critical exponent for arbitrary two-letter substitution sequences with marginal fluctuations of the coupling constants.Comment: 27 pages, LaTeX, 1 Postscript figure included, using epsf.sty and amssymb.sty (one error corrected, some minor changes