Griffiths phase in the thermal quantum Hall effect

Abstract

Two dimensional disordered superconductors with broken spin-rotation and time-reversal invariance, e.g. with p_x+ip_y pairing, can exhibit plateaus in the thermal Hall coefficient (the thermal quantum Hall effect). Our numerical simulations show that the Hall insulating regions of the phase diagram can support a sub-phase where the quasiparticle density of states is divergent at zero energy, \rho(E)\sim |E|^{1/z-1}, with a non-universal exponent $z>1$, due to the effects of rare configurations of disorder (``Griffiths phase'').Comment: 4+ pages, 5 figure

Multicriticality of Two-dimensional Class D Disordered Topological Superconductors

“…The results suggest that the low-energy DOS shows a power-law divergence ρ(ε) ∼ |ε| −α , with a non-universal exponent α. The power-law divergence is consistent with the Griffiths effects previously proposed in a study of a 2D network model in class D [25].…”

“…The logarithmic scaling of the low-energy DOS at the MIT point means that the dynamical critical exponent is the same as the space dimension: z = d = 2. In that regard, the type of MIT of the DTM-TQH boundary in the class D model is not different from the Anderson transitions in the standard Wigner-Dyson symmetry classes, where z = d. The power-law scaling of the low-energy DOS in the localized phases could be related to Griffiths singularities, as suggested by a similar power-law divergence found in a 2D class-D network model [25].…”

“…In addition to metal-insulator transitions (MIT) and thermal quantum Hall transitions, class D systems may have tricritical points where all the three phases meet. Another 2D disordered system in class D with Majorana particles results from fermionization of the randombond Ising model (RBIM) in 2D [19][20][21][22][23][24][25]. The phase diagram of the RBIM does not contain a metallic phase [21], but has an intriguing multicritical Nishimori point.…”

“…Both disordered superconductors in class D and the RBIM can be reformulated as network models [20,25], which are convenient for numerical simulations and have been extensively studied [14,20,[25][26][27][28][29][30][31][32]. However, many properties of the phases and phase transitions in class D disordered superconductors remain elusive.…”

Quantum Hall effects in normal and superconducting systems: localization and multifractality

“…A brief comment on the regions of localized phases where the interplaquette coupling is very weak ( 2 sin θ close to zero or to unity), is in order here. As shown recently [116], in this situation the DOS of the RBIM acquires a non-universal power-law singularity, 1 1 | | z E /with 1 z > associated with Griffiths strings [117,118]. The same mechanism of the formation of divergent DOS in these parts of the localized phases is expected to be operative in the CF model as well.…”