Universal Scaling Theory of the Boundary Geometric Tensor in Disordered Metals

Miklós Antal Werner, Arne Brataas, Felix von Oppen, and Gergely Zaránd
Phys. Rev. Lett. 122, 106601 – Published 12 March 2019
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Abstract

We investigate the finite-size scaling of the boundary quantum geometric tensor (QGT) numerically close to the Anderson localization transition in the presence of small external magnetic fields. The QGT exhibits universal scaling and reveals the crossover between the orthogonal and unitary critical states in weak random magnetic fields. The flow of the QGT near the critical points determines the critical exponents. Critical distributions of the QGT are universal and exhibit a remarkable isotropy even in a homogeneous magnetic field. We predict universal and isotropic Hall conductance fluctuations at the metal-insulator transition in an external magnetic field.

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  • Received 25 July 2018
  • Revised 25 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.106601

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Miklós Antal Werner1, Arne Brataas2, Felix von Oppen3, and Gergely Zaránd1

  • 1Exotic Quantum Phases “Momentum” Research Group, Department of Theoretical Physics, Budapest University of Technology and Economics, 1111 Budapest, Budafoki út 8, Hungary
  • 2Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
  • 3Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany

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Issue

Vol. 122, Iss. 10 — 15 March 2019

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