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Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands
Abstract
Here, we study networks of Coulombblockaded integer quantum Hall islands with even fillings $\nu =2k$ ( $k$ being an integer), including cases with $2k$ layers each of $\nu =1$ fillings. Allowing only spincurrent interactions between the islands (i.e., without any charge transfer), we obtain solvable models leading to a rich set of insulating $SU{\left(2\right)}_{k}$ topologically ordered phases. The case with $k=1$ is dual to the KalmeyerLaughlin phase, $k=2$ to Kitaev's chiral spin liquid and the MooreRead state, and $k=3$ contains a Fibonacci anyon that may be utilized for universal topological quantum computation. Additionally, we show how the $SU{\left(2\right)}_{k}$ topological phases may be obtained also in an array of islands with $\nu =2k$ integer quantum Hall states and critical spin chains in a checkerboard pattern. The array and checkerboard constructions gap out the charge mode and additional “flavor” modes by virtue of their geometry. Furthermore, we find that a fine tuning of the system parameter is not needed in the checkerboard configuration and the $\nu =2$ case. We also discuss their bulk excitations, and show that their thermal Hall conductance is universal, reflecting the central charge $c=3k/(k+2)$ of the chiral edge modes.
 Authors:

 Weizmann Inst. of Science, Rehovot (Israel)
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Publication Date:
 Research Org.:
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES); European Union (EU); German Research Foundation (DFG); Israel Science Foundation (ISF); National Science Foundation (NSF); Minerva Foundation; Federal Ministry of Education and Research (BMBF)
 OSTI Identifier:
 1661652
 Report Number(s):
 BNL2198442020JAAM
Journal ID: ISSN 24699950
 Grant/Contract Number:
 SC0012704; LEGOTOP No. 788715; 1989/14
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review B
 Additional Journal Information:
 Journal Volume: 102; Journal Issue: 16; Journal ID: ISSN 24699950
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Ebisu, Hiromi, Kalloor, Rohit R., Tsvelik, Alexei M., and Oreg, Yuval. Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands. United States: N. p., 2020.
Web. https://doi.org/10.1103/physrevb.102.165112.
Ebisu, Hiromi, Kalloor, Rohit R., Tsvelik, Alexei M., & Oreg, Yuval. Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands. United States. https://doi.org/10.1103/physrevb.102.165112
Ebisu, Hiromi, Kalloor, Rohit R., Tsvelik, Alexei M., and Oreg, Yuval. Thu .
"Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands". United States. https://doi.org/10.1103/physrevb.102.165112.
@article{osti_1661652,
title = {Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands},
author = {Ebisu, Hiromi and Kalloor, Rohit R. and Tsvelik, Alexei M. and Oreg, Yuval},
abstractNote = {Here, we study networks of Coulombblockaded integer quantum Hall islands with even fillings ν=2k (k being an integer), including cases with 2k layers each of ν=1 fillings. Allowing only spincurrent interactions between the islands (i.e., without any charge transfer), we obtain solvable models leading to a rich set of insulating SU(2)k topologically ordered phases. The case with k=1 is dual to the KalmeyerLaughlin phase, k=2 to Kitaev's chiral spin liquid and the MooreRead state, and k=3 contains a Fibonacci anyon that may be utilized for universal topological quantum computation. Additionally, we show how the SU(2)k topological phases may be obtained also in an array of islands with ν=2k integer quantum Hall states and critical spin chains in a checkerboard pattern. The array and checkerboard constructions gap out the charge mode and additional “flavor” modes by virtue of their geometry. Furthermore, we find that a fine tuning of the system parameter is not needed in the checkerboard configuration and the ν=2 case. We also discuss their bulk excitations, and show that their thermal Hall conductance is universal, reflecting the central charge c=3k/(k+2) of the chiral edge modes.},
doi = {10.1103/physrevb.102.165112},
journal = {Physical Review B},
number = 16,
volume = 102,
place = {United States},
year = {2020},
month = {10}
}
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