Fractional charge and interLandau–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 systemspecific details. Aspects of the response of quantum Hall states to smooth spatial curvature are wellstudied, 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 interLandau–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 tightbinding 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 interLandau–level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.
 Authors:

^{[1]};
^{[2]}
 Purdue Univ., West Lafayette, IN (United States). Dept. of Physics and Astronomy
 Univ. of Chicago, IL (United States). Kadanoff Center for Theoretical Physics
 Publication Date:
 Grant/Contract Number:
 AC0206CH11357; FG0213ER41958; 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 00278424
 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) (SC22); USDOE Office of Science (SC), High Energy Physics (HEP) (SC25); 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 interLandau–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 interLandau–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 interLandau–level states at points of singular curvature". United States.
doi:10.1073/pnas.1609470113.
@article{osti_1266398,
title = {Fractional charge and interLandau–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 systemspecific details. Aspects of the response of quantum Hall states to smooth spatial curvature are wellstudied, 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 interLandau–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 tightbinding 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 interLandau–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}
}