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Quantum phases of disordered three-dimensional Majorana-Weyl fermions

Wilson, Justin H. and Pixley, J. H. and Goswami, Pallab and Das Sarma, S. (2017) Quantum phases of disordered three-dimensional Majorana-Weyl fermions. Physical Review B, 95 (15). Art. No. 155122. ISSN 2469-9950. doi:10.1103/PhysRevB.95.155122.

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The gapless Bogoliubov-de Gennes (BdG) quasiparticles of a clean three dimensional spinless p_x + ip_y superconductor provide an intriguing example of a thermal Hall semimetal (ThSM) phase of Majorana-Weyl fermions; such a phase can support a large anomalous thermal Hall conductivity and protected surface Majorana-Fermi arcs at zero energy. We study the effects of quenched disorder on such a gapless topological phase by carrying out extensive numerical and analytical calculations on a lattice model for a disordered, spinless p_x + ip_y superconductor. Using the kernel polynomial method, we compute both average and typical density of states for the BdG quasiparticles, from which we construct the phase diagram of three dimensional dirty p_x + ip_y superconductors as a function of disorder strength and chemical potential of the underlying normal state. We establish that the power law quasi-localized states induced by rare statistical fluctuations of the disorder potential give rise to an exponentially small density of states at zero energy, and even infnitesimally weak disorder converts the ThSM into a thermal diffusive Hall metal (ThDM). Consequently, the phase diagram of the disordered model only consists of ThDM and thermal insulating phases. We show the existence of two types of thermal insulators: (i) a trivial thermal band insulator (ThBI) [or BEC phase] with a smeared gap that can occur for suitable band parameters and all strengths of disorder, supporting only exponentially localized Lifshitz states (at low energy), and (ii) a thermal Anderson insulator that only exists for large disorder strengths compared to all band parameters. We determine the nature of the two distinct localization-delocalization transitions between these two types of insulators and ThDM. Additionally, we establish the scaling properties of an avoided (or hidden) quantum critical point for moderate disorder strengths, which govern the crossover between ThSM and ThDM phases over a wide range of energy scales. We also discuss the experimental relevance of our findings for three dimensional, time reversal symmetry breaking, triplet superconducting states.

Item Type:Article
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Wilson, Justin H.0000-0001-6903-0417
Additional Information:© 2017 American Physical Society. Received 28 December 2016; published 14 April 2017. We thank Olexei Motrunich, Gil Refael, Matthew Foster, Sarang Gopalakrishnan, and Rahul Nandkishore for useful discussions. We also thank David A. Huse for various discussions and collaborations on earlier work. This work is partially supported by JQI-NSF-PFC and LPS-MPO-CMTC (JHP, PG, and SDS), and the Airforce Office for Scientific Research (JHW). The authors acknowledge the University of Maryland supercomputing resources ( made available for conducting the research reported in this paper. Part of this work was performed at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1066293.
Group:Institute for Quantum Information and Matter
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Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Issue or Number:15
Record Number:CaltechAUTHORS:20170320-084528822
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Official Citation:Quantum phases of disordered three-dimensional Majorana-Weyl fermions Justin H. Wilson, J. H. Pixley, Pallab Goswami, and S. Das Sarma Phys. Rev. B 95, 155122 (2017) – Published 14 April 2017
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:75227
Deposited By: Ruth Sustaita
Deposited On:20 Mar 2017 16:13
Last Modified:15 Nov 2021 16:31

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