Determination of topological edge quantum numbers of fractional quantum Hall phases by thermal conductance measurements

Saurabh Kumar Srivastav; Ravi Kumar; Christian Spånslätt; K Watanabe; T Taniguchi; Alexander D Mirlin; Yuval Gefen; Anindya Das

doi:10.1038/s41467-022-32956-z

Determination of topological edge quantum numbers of fractional quantum Hall phases by thermal conductance measurements

Nat Commun. 2022 Sep 3;13(1):5185. doi: 10.1038/s41467-022-32956-z.

Authors

Saurabh Kumar Srivastav^#¹, Ravi Kumar^#¹, Christian Spånslätt², K Watanabe³, T Taniguchi³, Alexander D Mirlin^{4

5

6

7}, Yuval Gefen^{4

8}, Anindya Das⁹

Affiliations

¹ Department of Physics, Indian Institute of Science, Bangalore, 560012, India.
² Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, S-412 96, Göteborg, Sweden.
³ National Institute of Material Science, 1-1 Namiki, Tsukuba, 305-0044, Japan.
⁴ Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021, Karlsruhe, Germany.
⁵ Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76128, Karlsruhe, Germany.
⁶ Petersburg Nuclear Physics Institute, 188300, St. Petersburg, Russia.
⁷ L. D. Landau Institute for Theoretical Physics RAS, 119334, Moscow, Russia.
⁸ Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel.
⁹ Department of Physics, Indian Institute of Science, Bangalore, 560012, India. anindya@iisc.ac.in.

^# Contributed equally.

Abstract

To determine the topological quantum numbers of fractional quantum Hall (FQH) states hosting counter-propagating (CP) downstream (N_d) and upstream (N_u) edge modes, it is pivotal to study quantized transport both in the presence and absence of edge mode equilibration. While reaching the non-equilibrated regime is challenging for charge transport, we target here the thermal Hall conductance G_Q, which is purely governed by edge quantum numbers N_d and N_u. Our experimental setup is realized with a hexagonal boron nitride (hBN) encapsulated graphite gated single layer graphene device. For temperatures up to 35 mK, our measured G_Q at ν = 2/3 and 3/5 (with CP modes) match the quantized values of non-equilibrated regime (N_d + N_u)κ₀T, where κ₀T is a quanta of G_Q. With increasing temperature, G_Q decreases and eventually takes the value of the equilibrated regime ∣N_d - N_u∣κ₀T. By contrast, at ν = 1/3 and 2/5 (without CP modes), G_Q remains robustly quantized at N_dκ₀T independent of the temperature. Thus, measuring the quantized values of G_Q in two regimes, we determine the edge quantum numbers, which opens a new route for finding the topological order of exotic non-Abelian FQH states.