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Direct determination of the topological thermal conductance via local power measurement


Thermal conductance measurements are sensitive to both charge and chargeless energy flow and are an essential measurement technique in condensed-matter physics. For two-dimensional topological insulators, the determination of thermal Hall (transverse) conductance and thermal longitudinal conductance is crucial for the understanding of topological order in the underlying state. Such measurements have not been accomplished, even in the extensively studied quantum Hall effect regime. Here we report a local power measurement technique that we use to reveal the topological thermal Hall conductance, going beyond the ubiquitous two-terminal conductance. For example, we show that the thermal Hall conductance is approximately zero in the v = 2/3 particle–hole conjugated state. This is in contrast to the two-terminal thermal conductance that gives a non-universal value that depends on the extent of thermal equilibration between the counter-propagating edge modes. Moreover, we demonstrate the utility of this technique in studying the power carried by the current fluctuations of a partitioned edge mode with an out-of-equilibrium distribution.

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Fig. 1: Device configuration for measuring heat transfer.
Fig. 2: Power carried by downstream modes.
Fig. 3: Thermal conductance of the v = 2/3 P–H conjugated state.
Fig. 4: Measuring power carried by out-of-equilibrium edge mode distributions at v = 2.

Data availability

The raw noise measurements (and other) data generated and analysed during the current study are available from the corresponding author on reasonable request. Source data are provided with this paper.


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We acknowledge C. Spånslätt, J. Park, A. D. Mirlin and K. Snizhko for useful discussions. M.H. acknowledges the continuous support of the Sub-Micron Center staff, the support of the European Research Council under the European Community’s Seventh Framework Program (FP7/2007-2013)/ERC under grant agreement number 713351 and the partial support of the Minerva foundation under grant number 713534.

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Authors and Affiliations



R.A.M. and S.K. fabricated the devices, performed the measurements and analysed the data. M.H. supervised the experiment and the analysis. V.U. grew the GaAs heterostructures. All authors contributed to the writing of the manuscript.

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Correspondence to Moty Heiblum.

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Nature Physics thanks Francois Parmentier and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Sections 1–8, Figs. 1–5 and Table 1.

Source data

Source Data Fig. 2

Statistical source data for Fig. 2d.

Source Data Fig. 3

Statistical source data for Fig. 3c.

Source Data Fig. 4

Statistical source data for Fig. 4e,f.

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Melcer, R.A., Konyzheva, S., Heiblum, M. et al. Direct determination of the topological thermal conductance via local power measurement. Nat. Phys. 19, 327–332 (2023).

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