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Why is the Hall conductance quantized?

Nature Reviews Physics volume 2, pages 392–393 (2020)Cite this article

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Why the Hall conductance is quantized was an open problem in condensed matter theory for much of the past 40 years. Spyridon Michalakis who worked on the solution — published in 2015 — gives a personal take on how the field evolved.

I reached out to Matthew B. Hastings with what I hoped was a complete proof. When I heard him say in his usual baritone voice: “Congrats, you actually did it,” I felt like the weight of the world had lifted off my shoulders. I was 29 at the time and halfway through my first postdoc. I had considered quitting academia several times, but I kept at it because of the support of friends and family, as well as something Matt had said to me early on: “This is your problem. You can do this.” When I finally posted the result on the arXiv in 2009, I thought about how my PhD advisor, Bruno Nachtergaele, would celebrate each of his student’s papers. So on the 40th anniversary of the quantum Hall effect (QHE), I wish to celebrate the work of all the brilliant minds who have worked diligently over the past four decades to elucidate this remarkable phenomenon. Having turned 40 myself this year, and seeing all the exciting research activity the QHE has inspired, I know the best is yet to come.

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Authors and Affiliations

  1. Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA

    Spyridon Michalakis

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  1. Spyridon Michalakis
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Correspondence to Spyridon Michalakis.

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The author declares no competing interests.

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Related link

Aizenman’s list of open problems in mathematical physics: http://web.math.princeton.edu/~aizenman/OpenProblems_MathPhys/

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Michalakis, S. Why is the Hall conductance quantized?. Nat Rev Phys 2, 392–393 (2020). https://doi.org/10.1038/s42254-020-0212-6

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  • DOI: https://doi.org/10.1038/s42254-020-0212-6

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