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Mechanical dissipation via image potential states on a topological insulator surface


Joule energy loss due to resistive heating is omnipresent in today’s electronic devices whereas quantum-mechanical dissipation is largely unexplored. Here, we experimentally observe a suppression of the Joule dissipation in Bi2Te3 due to topologically protected surface states. Instead, a different type of dissipation mechanism is observed by pendulum atomic force microscopy, which is related to single-electron tunnelling resonances into image potential states that are slightly above the Bi2Te3 surface. The application of a magnetic field leads to the breakdown of the topological protection of the surface states and restores the expected Joule dissipation process. Nanomechanical energy dissipation experienced by the cantilever of the pendulum atomic force microscope provides a rich source of information on the dissipative nature of the quantum-tunnelling phenomena on the topological insulator surface, with implications for coupling a mechanical oscillator to the generic quantum material.

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Fig. 1: STM, STS and pAFM measurements on the Bi2Te3 surface performed at T = 5 K.
Fig. 2: Series of field emission resonances measured with a static and oscillating STM tip, and simultaneous energy dissipation measurement at T = 5 K.
Fig. 3: Voltage- and distance-dependent AFM dissipation measured at T = 5 K on Bi2Te3 surface.
Fig. 4: Energy dissipation map on Bi2Te3 plotted versus distance and tip–sample voltage.
Fig. 5: Energy dissipation as a function of B changing in the range 0 T < B < 800 mT measured at T = 5 K on the Bi2Te3 surface.
Fig. 6: Single-electron tunnelling between IPSs of the Bi2Te3 sample and an oscillating AFM tip.

Data availability

The data that support the findings of this study are available from the corresponding authors on reasonable request.


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We acknowledge fruitful discussions with E. Tosatti. The Basel group acknowledges financial support from the Swiss National Science Foundation (SNSF), the COST action Project MP1303, the SINERGIA Project CRSII2 136287/1, the European Union’s Horizon 2020 research and innovation programme (ERC Advanced Grant no. 834402) and the Swiss Nanoscience Institute (project no. P1301). O.G. acknowledges financial support from TÜBİTAK project 114F036 and the COST action project MP1303 (TÜBİTAK112T818).

Author information




O.G. proposed the experiment. D.Y., M.K. and U.G. performed the experiments. E.M. coordinated the project. All authors discussed the results and contributed to the preparation of the paper.

Corresponding authors

Correspondence to D. Yildiz or M. Kisiel.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary Notes 1–4 and Figs. 1–8.

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Yildiz, D., Kisiel, M., Gysin, U. et al. Mechanical dissipation via image potential states on a topological insulator surface. Nat. Mater. 18, 1201–1206 (2019).

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