3D Quantum Phases of Majorana and Weyl Fermions Analyzed

by Tommy on 20/12/2016

I’ve been trying to come to grips with these exotic fermionic phases of matter for a while now.


Quantum phases of disordered three-dimensional Majorana-Weyl fermions, Justin H. Wilson, J. H. Pixley, Pallab Goswami and S. Das Sarma (16 December 2016)

The gapless Bogoliubov-de Gennes (BdG) quasiparticles of a clean three dimensional spinless px+ipy superconductor provide an intriguing example of a thermal Hall semimetal (ThSM) phase of Majorana-Weyl fermions in class D of the Altland-Zirnbauer symmetry classification; such a phase can support a large anomalous thermal Hall conductivity and protected surface Majorana-Fermi arcs at zero energy. We study the effect of quenched disorder on such a topological phase with both numerical and analytical methods. Using the kernel polynomial method, we compute the average and typical density of states for the BdG quasiparticles; based on this, we construct the disordered phase diagram. We show for infinitesimal disorder, the ThSM is converted into a diffusive thermal Hall metal (ThDM) due to rare statistical fluctuations. Consequently, the phase diagram of the disordered model only consists of ThDM and thermal insulating phases. Nonetheless, there is a cross-over at finite energies from a ThSM regime to a ThDM regime, and we establish the scaling properties of the avoided quantum critical point which marks this cross-over. Additionally, we show the existence of two types of thermal insulators: (i) a trivial thermal band insulator (ThBI) [or BEC phase] supporting only exponentially localized Lifshitz states (at low energy), and (ii) a thermal Anderson insulator (AI) at large disorder strengths. We determine the nature of the two distinct localization transitions between these two types of insulators and ThDM.We also discuss the experimental relevance of our results for three dimensional, time reversal symmetry breaking, triplet superconducting states.

Every little bit helps. I wish I had more time for this kind of thing, though.

A ‘readers’ stipend would be nice.


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