Mechanical dissipation via image potential states on a topological insulator surface

ABSTRACT 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. Access through your institution Buy or subscribe This is a preview of subscription content, access via your institution

ACCESS OPTIONS Access through your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $29.99 / 30 days cancel any time

Learn more Subscribe to this journal Receive 12 print issues and online access $259.00 per year only $21.58 per issue Learn more Buy this article * Purchase on SpringerLink * Instant access

to full article PDF Buy now Prices may be subject to local taxes which are calculated during checkout ADDITIONAL ACCESS OPTIONS: * Log in * Learn about institutional subscriptions * Read our

FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS EFFECTIVE LIFTING OF THE TOPOLOGICAL PROTECTION OF QUANTUM SPIN HALL EDGE STATES BY EDGE COUPLING Article Open access

16 June 2022 ULTRAFAST ENHANCEMENT OF ELECTRON-PHONON COUPLING VIA DYNAMIC QUANTUM WELL STATES Article Open access 26 June 2023 LAYER-BY-LAYER DISENTANGLEMENT OF BLOCH STATES Article 23

March 2023 DATA AVAILABILITY The data that support the findings of this study are available from the corresponding authors on reasonable request. REFERENCES * Chen, Y. L. et al. Experimental

realization of a three-dimensional topological insulator, Bi2Te3. _Science_ 325, 178–181 (2009). Article  CAS  Google Scholar  * Hasan, M. Z. & Kane, C. L. Colloquium: Topological

insulators. _Rev. Mod. Phys._ 82, 3045–3067 (2010). Article  CAS  Google Scholar  * Seo, J. et al. Transmission of topological surface states through surface barriers. _Nature_ 466, 343–346

(2010). Article  CAS  Google Scholar  * Zhang, T. et al. Experimental demonstration of topological surface states protected by time-reversal symmetry. _Phys. Rev. Lett._ 103, 266803 (2009).

Article  Google Scholar  * He, H.-T. et al. Impurity effect on weak antilocalization in the topological insulator Bi2Te3. _Phys. Rev. Lett._ 106, 166805 (2011). Article  Google Scholar  *

Straub, D. & Himpsel, F. J. Spectroscopy of image-potential states with inverse photoemission. _Phys. Rev. B_ 33, 2256–2262 (1986). Article  CAS  Google Scholar  * Dose, V. Image

potential surface states. _Phys. Scr._ 36, 669–672 (1987). Article  CAS  Google Scholar  * Echenique, P. & Uranga, M. Image potential states at surfaces. _Surf. Sci._ 247, 125–132

(1991). Article  CAS  Google Scholar  * Berthold, W. et al. Momentum-resolved lifetimes of image-potential states on Cu(100). et al. _Phys. Rev. Lett._ 88, 056805 (2002). Article  CAS 

Google Scholar  * Wahl, P., Schneider, M. A., Diekhöner, L., Vogelgesang, R. & Kern, K. Quantum coherence of image-potential states. _Phys. Rev. Lett._ 91, 106802 (2003). Article  CAS 

Google Scholar  * Schouteden, K. & Van Haesendonck, C. Quantum confinement of hot image-potential state electrons. _Phys. Rev. Lett._ 103, 266805 (2009). Article  CAS  Google Scholar  *

Niesner, D. & Fauster, T. Image-potential states and work function of graphene. _J. Phys. Condens. Matter_ 26, 393001 (2014). Article  Google Scholar  * Sobota, J. A. et al. Ultrafast

optical excitation of a persistent surface-state population in the topological insulator Bi2Se3. _Phys. Rev. Lett._ 108, 117403 (2012). Article  CAS  Google Scholar  * Sobota, J. A. et al.

Direct optical coupling to an unoccupied Dirac surface state in the topological insulator Bi2Se3. _Phys. Rev. Lett._ 111, 136802 (2013). Article  CAS  Google Scholar  * Niesner, D. et al.

Unoccupied topological states on bismuth chalcogenides. _Phys. Rev. B_ 86, 205403 (2012). Article  Google Scholar  * Niesner, D. et al. Bulk and surface electron dynamics in a p-type

topological insulator SnSb2Te4. _Phys. Rev. B_ 89, 081404 (2014). Article  Google Scholar  * Niesner, D. et al. Electron dynamics of unoccupied states in topological insulators. _J. Electron

Spectrosc. Relat. Phenom._ 195, 258–262 (2014). Article  CAS  Google Scholar  * Gundlach, K. H. Zur berechnung des tunnelstroms durch eine trapezförmige potentialstufe. _Solid State

Electron._ 9, 949–957 (1966). Article  Google Scholar  * Höfer, U. et al. Time-resolved coherent photoelectron spectroscopy of quantized electronic states on metal surfaces. _Science_ 277,

1480–1482 (1997). Article  Google Scholar  * Kisiel, M. et al. Suppression of electronic friction on Nb films in the superconducting state. _Nat. Mater._ 10, 119–122 (2011). Article  CAS 

Google Scholar  * Langer, M. et al. Giant frictional dissipation peaks and charge-density-wave slips at the NbSe2 surface. _Nat. Mater._ 13, 173–177 (2013). Article  Google Scholar  *

Kisiel, M. et al. Noncontact atomic force microscope dissipation reveals a central peak of SrTiO3 structural phase transition. _Phys. Rev. Lett._ 115, 046101 (2015). Article  CAS  Google

Scholar  * Stipe, B. C., Mamin, H. J., Stowe, T. D., Kenny, T. W. & Rugar, D. Noncontact friction and force fluctuations between closely spaced bodies. _Phys. Rev. Lett._ 87, 096801

(2001). Article  CAS  Google Scholar  * Volokitin, A. I. & Persson, B. N. J. Near-field radiative heat transfer and noncontact friction. _Rev. Mod. Phys._ 79, 1291–1329 (2007). Article 

CAS  Google Scholar  * Neupane, M. et al. Topological surface states and Dirac point tuning in ternary topological insulators. _Phys. Rev. B_ 85, 235406 (2012). Article  Google Scholar  *

Miyamoto, K. et al. Topological surface states with persistent high spin polarization across the Dirac point in Bi2Te2Se and Bi2Se2T. _Phys. Rev. Lett._ 109, 166802 (2012). Article  CAS 

Google Scholar  * Schouteden, K. et al. Moiré superlattices at the topological insulator Bi2Te3. _Sci. Rep._ 6, 20278 (2016). Article  CAS  Google Scholar  * Pivetta, M., Patthey, F.,

Stengel, M., Baldereschi, A. & Schneider, W. D. Local work function moiré pattern on ultrathin ionic films: NaCl on Ag(100). _Phys. Rev. B_ 72, 115404 (2005). Article  Google Scholar  *

Bose, S. et al. Image potential states as a quantum probe of graphene interfaces. _New J. Phys._ 12, 023028 (2010). Article  Google Scholar  * Volokitin, A. I., Persson, B. N. J. & Ueba,

H. Enhancement of noncontact friction between closely spaced bodies by two-dimensional systems. _Phys. Rev. B_ 73, 165423 (2006). Article  Google Scholar  * Cockins, L. et al. Energy levels

of few-electron quantum dots imaged and characterized by atomic force microscopy. _Proc. Natl Acad. Sci. USA_ 107, 9496–9501 (2010). Article  CAS  Google Scholar  * Kisiel, M. et al.

Mechanical dissipation from charge and spin transitions in oxygen-deficient SrTiO3 surfaces. _Nat. Commun._ 9, 2946 (2018). Article  Google Scholar  * Stomp, R. et al. Detection of

single-electron charging in an individual InAs quantum dot by noncontact atomic-force microscopy. _Phys. Rev. Lett._ 94, 056802 (2005). Article  Google Scholar  * Paulsson, M., Zahid, F.

& Datta, S. _Resistance of a Molecule_ 426 (CRC Press, 2002). * Volokitin, A. I. & Persson, B. N. J. in _Fundamentals of Friction and Wear on the Nanoscale_ (eds Gnecco, E. &

Meyer, E.) 426 (Springer, 2007). * Sarid, D. _Scanning Force Microscopy with Applications to Electric, Magnetic and Atomic Forces_ (Oxford Univ. Press, 1991). * Sessi, P. et al. Signatures

of Dirac fermion-mediated magnetic order. _Nat. Commun._ 5, 5349 (2014). Article  CAS  Google Scholar  * Olsen, J. L. _Electron Transport in Metals_ (Interscience, 1962). * Fatayer, S. et

al. Controlled fragmentation of single molecules with atomic force microscopy by employing doubly charged states. _Phys. Rev. Lett._ 121, 226101 (2018). Article  CAS  Google Scholar  *

Cleveland, J. P., Anczykowski, B., Schmid, A. E. & Elings, V. B. Energy dissipation in tapping-mode atomic force microscopy. _Appl. Phys. Lett._ 72, 2613–2615 (1998). Article  CAS 

Google Scholar  Download references ACKNOWLEDGEMENTS 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 AUTHORS AND AFFILIATIONS * Department of Physics, University of Basel, Basel, Switzerland D. Yildiz, M. Kisiel, U. Gysin & E. Meyer * Department of Physics, Istanbul

Technical University, Istanbul, Turkey O. Gürlü Authors * D. Yildiz View author publications You can also search for this author inPubMed Google Scholar * M. Kisiel View author publications

You can also search for this author inPubMed Google Scholar * U. Gysin View author publications You can also search for this author inPubMed Google Scholar * O. Gürlü View author

publications You can also search for this author inPubMed Google Scholar * E. Meyer View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS 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. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER’S NOTE

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION Supplementary Notes

1–4 and Figs. 1–8. RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE 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). https://doi.org/10.1038/s41563-019-0492-3 Download citation * Received: 16 January 2019 * Accepted: 27 August

2019 * Published: 14 October 2019 * Issue Date: November 2019 * DOI: https://doi.org/10.1038/s41563-019-0492-3 SHARE THIS ARTICLE Anyone you share the following link with will be able to

read this content: Get shareable link Sorry, a shareable link is not currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing

initiative