Spin quantum Hall effect in a layered disordered

Victor Kagalovsky

Sami Shamoon College of Engineering


Class C of disordered superconductors has spin rotational symmetry, but no time reversal symmetry. It can be realized in a singlet superconductor with an order parameter that breaks time reversal symmetry, such as d+id'. The experimental availability of layered superconductors motivates us to study the 3D generalization of the SU(2) network model. We present phase diagrams in three parameter space, Delta y which respectively control strengths of spin-rotation symmetry breaking, inter-layer coupling and transition driving parameter. When Delta, a finite value of gives rise to a formation of metallic domain (whereas in a 2D there is only one critical energy. The energy width of this metallic region satisfies W(t) t^{2d}, where 2d is a critical exponent for the divergence of the localization length in an isolated single layer. For a nonzero Delta we predict the existence of four different phases: spin quantum Hall phases with sigma_xy = 0, 1, 2 respectively and metallic phase. The corresponding critical lines scale as W(t) t^1{QHE}, where QHE is a critical exponent for the divergence of the localization length in an ordinary quantum Hall effect. On the metallic side of the transition we find scaling of the conductivity sigma (\epsilon - \epsilon_{cr})^{3d}$ . We find the same value 3d 0.96 for the divergence of the localization length and for the conductivity scaling for various Delta and t. Along the line epsilon = Delta = 0 we predict and confirm numerically that sigma t.