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854:{\displaystyle {\mathcal {F}}_{n}^{ab}(\mathbf {k} )={\frac {1}{2i}}\int d^{d}\mathbf {r} {\Big (}{\frac {\partial u_{n}^{*}}{\partial k_{a}}}{\frac {\partial u_{n}}{\partial k_{b}}}-{\frac {\partial u_{n}^{*}}{\partial k_{b}}}{\frac {\partial u_{n}}{\partial k_{a}}}{\Big )}}
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1325:{\displaystyle \sigma _{H}={\frac {ie^{2}}{4\pi \hbar }}\sum _{n}\oint _{BZB}dk_{j}\int d^{2}r{\Big (}u_{n}^{*}{\frac {\partial u_{n}}{\partial k_{j}}}-{\frac {\partial u_{n}^{*}}{\partial k_{j}}}u_{n}^{*}{\Big )}}
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tags using the button below. This will let reviewers know a new draft has been submitted in their area of interest. For instance, if you wrote about a female astronomer, you would want to add the
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is a formula for topological band theory due to D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs. It was invented to explain various theoretical results such as the
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527:{\displaystyle \sigma _{H}^{ab}={\frac {e^{2}}{\hbar }}\sum _{n}\int _{BZ}{\frac {d^{2}\mathbf {k} }{(2\pi )^{2}}}{\mathcal {F}}_{n}^{ab}(\mathbf {k} )}
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The electrons are modeled as a fluid of independent particles with an infinite set of phases, one per .. band or ...
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from experienced editors. These venues are only for help with editing and the submission process, not to get reviews.
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is considered an open research problem where the interaction between electrons becomes a major relevant factor.
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https://www.researchgate.net/publication/370658307_Integer_Quantum_Hall_Effect_and_Chern_Simons_Theories
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Physical Review
Letters 49, 405 (1982) D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs
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968:{\displaystyle \int _{BZ}d^{2}\mathbf {k} {\mathcal {F}}_{n}^{ab}(\mathbf {k} )=2\pi \ C_{n}}
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to find examples of
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In this case the sum is over the full set of bands below the Fermi energy
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is the graphical solution to Harper's equation, where the energy ratio
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Where the sum is made over fully occupied bands below the fermi Energy
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To improve your odds of a faster review, tag your draft with relevant
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https://www.nobelprize.org/uploads/2018/06/haldane-lecture-slides.pdf
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Quantized
Conductance in a Two-Dimensional Periodic Potential
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1618:Integer quantum hall and Chern Simons Theories
1450:The TKNN formula can explain the levels of the
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178:– a basic overview on how to edit Knowledge.
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1390:{\displaystyle 2\pi \alpha }
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141:at the AfC Help Desk or get
1452:Integer quantum Hall Effect
356:Integer Quantum Hall Effect
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190:– how to include references
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1514:{\displaystyle \rho _{xy}}
1484:{\displaystyle \rho _{xx}}
68:independent of the subject
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111:your business or employer
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225:Knowledge:Good articles
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366:The formula
304:Last edited
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1670:Categories
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568:and where
276:Easy tools
93:plagiarize
1564:ν
1500:ρ
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712:∗
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671:∫
476:π
438:∫
428:∑
422:ℏ
390:σ
291:Advanced:
247:Astronomy
243:Biography
156:talk page
144:live help
133:, please
89:copyright
64:secondary
1588:See also
317:contribs
308:UtherSRG
210:reliable
107:yourself
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60:reliable
282: (
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253:tags.
249:, and
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158:of a
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