arXiv subjects

Akira Furusaki

Publications and source records attributed to Akira Furusaki.

78 records · Page 5Linked to original sources

arXiv2001

Spontaneous Hall effect in chiral p-wave superconductor

In a chiral superconductor with broken time-reversal symmetry a ``spontaneous Hall effect'' may be observed. We analyze this phenomenon by taking into account the surface properties of a chiral superconductor. We identify two main contributions to the spontaneous Hall effect. One contribution originates from the Bernoulli (or Lorentz) force from spontaneous currents running along the surfaces of the superconductor. The other contribution has a topological origin and is related to the intrinsic angular momentum of Cooper pairs. The latter can be described in terms of a Chern-Simons-like term in the low-energy field theory of the superconductor and has some similarities with the quantum Hall effect. The spontaneous Hall effect in a chiral superconductor is, however, non-universal. Our analysis is based on three approaches to the problem: a self-consistent solution of the Bogoliubov-de Gennes equation, a generalized Ginzburg-Landau theory, and a hydrodynamic formulation. All three methods consistently lead to the same conclusion that the spontaneous Hall resistance of a two-dimensional superconducting Hall bar is of order h/(e k_Fλ)^2, where k_F is the Fermi wave vector and λis the London penetration depth; the Hall resistance is substantially suppressed from a quantum unit of resistance. Experimental issues in measuring this effect are briefly discussed.

cond-mat.supr-con↗

arXiv2000

Crossover from the chiral to the standard universality classes in the conductance of a quantum wire with random hopping only

The conductance of a quantum wire with off-diagonal disorder that preserves a sublattice symmetry (the random hopping problem with chiral symmetry) is considered. Transport at the band center is anomalous relative to the standard problem of Anderson localization both in the diffusive and localized regimes. In the diffusive regime, there is no weak-localization correction to the conductance and universal conductance fluctuations are twice as large as in the standard cases. Exponential localization occurs only for an even number of transmission channels in which case the localization length does not depend on whether time-reversal and spin rotation symmetry are present or not. For an odd number of channels the conductance decays algebraically. Upon moving away from the band center transport characteristics undergo a crossover to those of the standard universality classes of Anderson localization. This crossover is calculated in the diffusive regime.

cond-mat.dis-nn↗

arXiv1999

The random magnetic flux problem in a quantum wire

The random magnetic flux problem on a lattice and in a quasi one-dimensional (wire) geometry is studied both analytically and numerically. The first two moments of the conductance are obtained analytically. Numerical simulations for the average and variance of the conductance agree with the theory. We find that the center of the band $ε=0$ plays a special role. Away from $ε=0$, transport properties are those of a disordered quantum wire in the standard unitary symmetry class. At the band center $ε=0$, the dependence on the wire length of the conductance departs from the standard unitary symmetry class and is governed by a new universality class, the chiral unitary symmetry class. The most remarkable property of this new universality class is the existence of an even-odd effect in the localized regime: Exponential decay of the average conductance for an even number of channels is replaced by algebraic decay for an odd number of channels.

cond-mat.dis-nn↗

arXiv1996

Tunneling through a barrier in Tomonaga-Luttinger liquid connected to reservoirs

The transport through a barrier is studied for a Tomonaga-Luttinger liquid of finite length connected to reservoirs. An effective action for the phase variable at the barrier is derived for spatially varying electric field. In the d.c. limit only the total voltage drop between the left and right reservoirs appears in the action. We discuss crossovers of the renormalization group flow and hence of the temperature and wire length dependence of the conductance, taking into account the location of the barrier.

cond-mat↗

arXiv1995

On a Network Model of Localization in a Random Magnetic Field

We consider a network model of snake states to study the localization problem of non-interacting fermions in a random magnetic field with zero average. After averaging over the randomness, the network of snake states is mapped onto $M$ coupled SU$(2N)$ spin chains in the $N \rightarrow 0$ limit. The number of snake states near the zero-field contour, $M$, is an even integer. In the large conductance limit $g = M {e^2 \over 2 π\hbar}$ ($M \gg 2$), it turns out that this system is equivalent to a particular representation of the ${\rm U}(2N) / {\rm U}(N) \times {\rm U}(N)$ sigma model ($N \rightarrow 0$) {\it without} a topological term. The beta function $β(1/M)$ of this sigma model in the $1/M$ expansion is consistent with the previously known $β(g)$ of the unitary ensemble. These results and further plausible arguments support the conclusion that all the states are localized.

cond-mat↗

arXiv1994

Gauge-invariant response functions of fermions coupled to a gauge field

We study a model of fermions interacting with a gauge field and calculate gauge-invariant two-particle Green's functions or response functions. The leading singular contributions from the self-energy correction are found to be cancelled by those from the vertex correction for small $q$ and $Ω$. As a result, the remaining contributions are not singular enough to change the leading order results of the random phase approximation. It is also shown that the gauge field propagator is not renormalized up to two-loop order. We examine the resulting gauge-invariant two-particle Green's functions for small $q$ and $Ω$, but for all ratios of $Ω/ v_F q$ and we conclude that they can be described by Fermi liquid forms without a diverging effective mass.

cond-mat↗