arXiv subjects
Publications and source records attributed to S. Ryu.
We propose a criterion to determine the existence of zero-energy edge states for a class of particle-hole symmetric systems. A loop is assigned for each system, and its topology and a symmetry play an essential role. Applications to d-wave superconductors are demonstrated.
Concept of the topological order is useful to characterize anisotropic superconductivities. The spin Hall conductance distinguishes superconductivities with the same symmetry. The Chern number for the spin Hall conductance is given by the covering degree of a closed surface around the Dirac monopole. It gives a clear illustration for the on-critical condition for the $d_{x^2-y^2}$ supreconductivitiy with non zero chemical potential. Non trivial topological orders on the triangular lattice are also presented and demonstrated by the topological objects.
Motivated by the geometric character of spin Hall conductance, the topological invariants of generic superconductivity are discussed based on the Bogoliuvov-de Gennes equation on lattices. They are given by the Chern numbers of degenerate condensate bands for unitary order, which are realizations of Abelian chiral anomalies for non-Abelian connections. The three types of Chern numbers for the $x,y$ and $z$-directions are given by covering degrees of some doubled surfaces around the Dirac monopoles. For nonunitary states, several topological invariants are defined by analyzing the so-called $q$-helicity. Topological origins of the nodal structures of superconducting gaps are also discussed.
Gade [R. Gade, Nucl. Phys. B \textbf{398}, 499 (1993)] has shown that the local density of states for a particle hopping on a two-dimensional bipartite lattice in the presence of weak disorder and in the absence of time-reversal symmetry(chiral unitary universality class) is anomalous in the vicinity of the band center $ε=0$ whenever the disorder preserves the sublattice symmetry. More precisely, using a nonlinear-sigma-model that encodes the sublattice (chiral) symmetry and the absence of time-reversal symmetry she argues that the disorder average local density of states diverges as $|ε|^{-1}\exp(-c|\lnε|^κ)$ with $c$ some non-universal positive constant and $κ=1/2$ a universal exponent. Her analysis has been extended to the case when time-reversal symmetry is present (chiral orthogonal universality class) for which the same exponent $κ=1/2$ was predicted. Motrunich \textit{et al.} [O. Motrunich, K. Damle, and D. A. Huse, Phys. Rev. B \textbf{65}, 064206 (2001)] have argued that the exponent $κ=1/2$ does not apply to the typical density of states in the chiral orthogonal universality class. They predict that $κ=2/3$ instead. We confirm the analysis of Motrunich \textit{et al.} within a field theory for two flavors of Dirac fermions subjected to two types of weak uncorrelated random potentials: a purely imaginary vector potential and a complex valued mass potential. This model is believed to belong to the chiral orthogonal universality class. Our calculation relies in an essential way on the existence of infinitely many local composite operators with negative anomalous scaling dimensions.
To study relaxation dynamics of the two-dimensional XY gauge glass, we integrate directly the equations of motion and investigate the energy function. As usual, it decays exponentially at high temperatures; at low but non-zero temperatures, it is found to exhibit an algebraic relaxation. We compute the relaxation time $τ$ as a function of the temperature $T$ and find that the rapid increase of $τ$ at low temperatures is well described by $τ\sim (T-T_g)^{-b}$ with $T_g = 0.22 \pm 0.02$ and $b = 0.76 \pm 0.05$, which strongly suggests a finite-temperature glass transition. The decay of vorticity is also examined and explained in terms of a simple heuristic model, which attributes the fast relaxation at high temperatures to annihilation of unpinned vortices.