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Title: Fractional charge and inter-Landau–level states at points of singular curvature

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:
 [1] ;  [2]
  1. Purdue Univ., West Lafayette, IN (United States). Dept. of Physics and Astronomy
  2. Univ. of Chicago, IL (United States). Kadanoff Center for Theoretical Physics
Publication Date:
Grant/Contract Number:
AC02-06CH11357; FG02-13ER41958; SC0009924
Type:
Published Article
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Volume: 113; Journal Issue: 31; Journal ID: ISSN 0027-8424
Publisher:
National Academy of Sciences, Washington, DC (United States)
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) (SC-22); USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Simons Foundation (United States)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum Hall; geometry; gravitational response; singularity; quantum computation
OSTI Identifier:
1266398
Alternate Identifier(s):
OSTI ID: 1470104

Biswas, Rudro R., and Son, Dam Thanh. Fractional charge and inter-Landau–level states at points of singular curvature. United States: N. p., 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. doi:10.1073/pnas.1609470113.
Biswas, Rudro R., and Son, Dam Thanh. 2016. "Fractional charge and inter-Landau–level states at points of singular curvature". United States. doi: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 = {2016},
month = {7}
}