Phase diagram of superconductivity in the integer quantum Hall regime

Schirmer, Jonathan; Liu, C. -X.; Jain, J. K.

doi:10.1073/pnas.2202948119

Phase diagram of superconductivity in the integer quantum Hall regime

Journal Article · Tue Jul 05 00:00:00 EDT 2022 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.2202948119· OSTI ID:2279783

Schirmer, Jonathan ^[1]; Liu, C. -X. ^[2]; ^[1]

Department of Physics, The Pennsylvania State University, University Park, PA 16802
Department of Physics, The Pennsylvania State University, University Park, PA 16802, Department of Physics, Princeton University, Princeton, NJ 08544

An interplay between pairing and topological orders has been predicted to give rise to superconducting states supporting exotic emergent particles, such as Majorana particles obeying non-Abelian braid statistics. We consider a system of spin polarized electrons on a Hofstadter lattice with nearest-neighbor attractive interaction and solve the mean-field Bogoliubov–de Gennes equations in a self-consistent fashion, leading to gauge-invariant observables and a rich phase diagram as a function of the chemical potential, the magnetic field, and the interaction. As the strength of the attractive interaction is increased, the system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully gapped in the bulk but has topological chiral edge current, characterizing a topologically nontrivial state. This is followed by a vortex phase in which the vortices carrying Majorana modes form a lattice; the spectrum contains a low-energy Majorana band arising from the coupling between neighboring vortex-core Majorana modes but does not have chiral edge currents. For some parameters, a dimer vortex lattice occurs with no Majorana band. The experimental feasibility and the observable consequences of skyrmions as well as Majorana modes are indicated.

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Research Organization:: Pennsylvania State Univ., University Park, PA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0005042

OSTI ID:: 2279783

Alternate ID(s):: OSTI ID: 2472123

Journal Information:: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 28 Vol. 119; ISSN 0027-8424

Publisher:: Proceedings of the National Academy of SciencesCopyright Statement

Country of Publication:: United States

Language:: English

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Phase diagram of superconductivity in the integer quantum Hall regime

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