Fractional charge and inter-Landau–level states at points of singular curvature
Abstract
The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. In this paper, we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau–level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. Finally, an important technological implication of these results is that these inter-Landau–level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.
- Authors:
-
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907,
- Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637
- Publication Date:
- Research Org.:
- Univ. of Chicago, IL (United States); Purdue Univ., West Lafayette, IN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), High Energy Physics (HEP); Simons Foundation (United States)
- OSTI Identifier:
- 1266398
- Alternate Identifier(s):
- OSTI ID: 1470104
- Grant/Contract Number:
- AC02-06CH11357; FG02-13ER41958; SC0009924
- Resource Type:
- Published Article
- Journal Name:
- Proceedings of the National Academy of Sciences of the United States of America
- Additional Journal Information:
- Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 113 Journal Issue: 31; Journal ID: ISSN 0027-8424
- Publisher:
- Proceedings of the National Academy of Sciences
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum Hall; geometry; gravitational response; singularity; quantum computation
Citation Formats
Biswas, Rudro R., and Son, Dam Thanh. Fractional charge and inter-Landau–level states at points of singular curvature. United States: N. p., 2016.
Web. doi:10.1073/pnas.1609470113.
Biswas, Rudro R., & Son, Dam Thanh. Fractional charge and inter-Landau–level states at points of singular curvature. United States. https://doi.org/10.1073/pnas.1609470113
Biswas, Rudro R., and Son, Dam Thanh. Tue .
"Fractional charge and inter-Landau–level states at points of singular curvature". United States. https://doi.org/10.1073/pnas.1609470113.
@article{osti_1266398,
title = {Fractional charge and inter-Landau–level states at points of singular curvature},
author = {Biswas, Rudro R. and Son, Dam Thanh},
abstractNote = {The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. In this paper, we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau–level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. Finally, an important technological implication of these results is that these inter-Landau–level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.},
doi = {10.1073/pnas.1609470113},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 31,
volume = 113,
place = {United States},
year = {Tue Jul 19 00:00:00 EDT 2016},
month = {Tue Jul 19 00:00:00 EDT 2016}
}
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https://doi.org/10.1073/pnas.1609470113
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Cited by: 22 works
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