journal article·2018-08Open access

Holstein polaron in a valley-degenerate two-dimensional semiconductor

Mingu Kang, Sung Won Jung, Woo Jong Shin, Yeongsup Sohn, Sae Hee Ryu, Timur K. Kim, Moritz Hoesch, Keun Su Kim

Nature Materials· Volume 17· Issue 8

Abstract

Two-dimensional (2D) crystals have emerged as a class of materials with tunable carrier density1. Carrier doping to 2D semiconductors can be used to modulate many-body interactions2 and to explore novel composite particles. The Holstein polaron is a small composite particle of an electron that carries a cloud of self-induced lattice deformation (or phonons)3-5, which has been proposed to play a key role in high-temperature superconductivity6 and carrier mobility in devices7. Here we report the discovery of Holstein polarons in a surface-doped layered semiconductor, MoS2, in which a puzzling 2D superconducting dome with the critical temperature of 12 K was found recently8-11. Using a high-resolution band mapping of charge carriers, we found strong band renormalizations collectively identified as a hitherto unobserved spectral function of Holstein polarons12-18. The short-range nature of electron-phonon (e-ph) coupling in MoS2 can be explained by its valley degeneracy, which enables strong intervalley coupling mediated by acoustic phonons. The coupling strength is found to increase gradually along the superconducting dome up to the intermediate regime, which suggests a bipolaronic pairing in the 2D superconductivity.
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Research context

OpenAlex topics: 2D Materials and Applications · Electronic and Structural Properties of Oxides · Topological Materials and Phenomena

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References (40)

Show source-provided references
1. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).10.1126/science.1102896 ↗
2. Li, L. J. et al. Controlling many-body states by the electric-field effect in a two-dimensional material. Nature 529, 185–189 (2016).10.1038/nature16175 ↗
3. Landau, L. D. On the motion of electrons in a crystal lattice. Phys. Z. Sowjet. 3, 664–665 (1933).
4. Fröhlich, H. Electrons in lattice fields. Adv. Phys. 3, 325–361 (1954).10.1080/00018735400101213 ↗
5. Holstein, T. Studies on polaron motion. Ann. Phys. 8, 343–389 (1959).10.1016/0003-4916(59)90003-X ↗
6. Alexandrov, A. S. Polarons in Advanced Materials (Springer, Dordrecht, 2007).10.1007/978-1-4020-6348-0 ↗
7. Hulea, I. N. et al. Tunable Fröhlich polarons in organic single-crystal transistors. Nat. Mater. 5, 982–986 (2006).10.1038/nmat1774 ↗
8. Ye, J. T. et al. Superconducting dome in a gate-tuned band insulator. Science 338, 1193–1196 (2012).10.1126/science.1228006 ↗
9. Lu, J. M. et al. Evidence for two-dimensional Ising superconductivity in gated MoS2. Science 350, 1353–1357 (2015).10.1126/science.aab2277 ↗
10. Saito, Y. et al. Superconductivity protected by spin-valley locking in ion-gated MoS2. Nat. Phys. 12, 144–149 (2016).10.1038/nphys3580 ↗
11. Costanzo, D., Jo, S., Berger, H. & Morpurgo, A. F. Gate-induced superconductivity in atomically thin MoS2 crystals. Nat. Nanotech. 11, 339–344 (2016).10.1038/nnano.2015.314 ↗
12. Engelsberg, S. & Schrieffer, J. R. Coupled electron–phonon system. Phys. Rev. 131, 993–1008 (1963).10.1103/PhysRev.131.993 ↗
13. Meden, V., Schönhammer, K. & Gunnarsson, O. Electron-phonon interaction in one dimension: exact spectral properties. Phys. Rev. B 50, 11179–11182 (1994).10.1103/PhysRevB.50.11179 ↗
14. Wellein, G. & Fehske, H. Polaron band formation in the Holstein model. Phys. Rev. B 56, 4513–4517 (1997).10.1103/PhysRevB.56.4513 ↗
15. Bonča, J., Trugman, S. A. & Batistić, I. Holstein polaron. Phys. Rev. B 60, 1633–1642 (1999).10.1103/PhysRevB.60.1633 ↗
16. Hohenadler, M., Aichhorn, M. & von der Linden, W. Spectral function of electron-phonon models by cluster perturbation theory. Phys. Rev. B 68, 184304 (2003).10.1103/PhysRevB.68.184304 ↗
17. Goodvin, G. L., Berciu, M. & Sawatzky, G. A. Green’s function of the Holstein polaron. Phys. Rev. B 74, 245104 (2006).10.1103/PhysRevB.74.245104 ↗
18. Berciu, M. & Sawatzky, G. A. Light polarons and bipolarons for a highly inhomogeneous electron–boson coupling. Eur. Phys. Lett. 81, 57008 (2008).10.1209/0295-5075/81/57008 ↗
19. Damascelli, A., Hussain, Z. & Shen, Z.-X. Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys. 75, 473–541 (2003).10.1103/RevModPhys.75.473 ↗
20. Perfetti, L. et al. Mobile small polarons and the Peierls transition in the quasi-one-dimensional conductor K0.3MoO3. Phys. Rev. B 66, 075107 (2002).10.1103/PhysRevB.66.075107 ↗
21. Shen, K. M. et al. Angle-resolved photoemission studies of lattice polaron formation in the cuprate Ca2CuO2Cl2. Phys. Rev. B 75, 075115 (2007).10.1103/PhysRevB.75.075115 ↗
22. Moser, S. et al. Tunable polaronic conduction in anatase TiO2. Phys. Rev. Lett. 110, 196403 (2013).10.1103/PhysRevLett.110.196403 ↗
23. Lee, J. J. et al. Interfacial mode coupling as the origin of the enhancement of T c in FeSe films on SrTiO3. Nature 515, 245–248 (2014).10.1038/nature13894 ↗
24. Chen, C., Avila, J., Frantzeskakis, E., Levy, A. & Asensio, M. C. Observation of a two-dimensional liquid of Fröhlich polarons at the bare SrTiO3 surface. Nat. Commun. 6, 8585 (2015).10.1038/ncomms9585 ↗
25. Wang, Z. et al. Tailoring the nature and strength of electron-phonon interactions in the SrTiO3(001) 2D electron liquid. Nat. Mater. 15, 835–839 (2016).10.1038/nmat4623 ↗
26. Koschorreck, M. et al. Attractive and repulsive Fermi polarons in two dimensions. Nature 485, 619–622 (2012).10.1038/nature11151 ↗
27. Zeng, H., Dai, J., Yao, W., Xiao, D. & Cui, X. Valley polarization in MoS2 monolayers by optical pumping. Nat. Nanotech. 7, 490–493 (2012).10.1038/nnano.2012.95 ↗
28. Mak, K. F., He, K., Shan, J. & Heinz, T. F. Control of valley polarization in monolayer MoS2 by optical helicity. Nat. Nanotech. 7, 494–498 (2012).10.1038/nnano.2012.96 ↗
29. Kaasbjerg, K., Thygesen, K. S. & Jacobsen, K. W. Phonon-limited mobility in n-type single-layer MoS2 from first principles. Phys. Rev. B 85, 115317 (2012).10.1103/PhysRevB.85.115317 ↗
30. Yu, P. Y. & Cardona, M. Fundamentals of Semiconductors 4th edn (Springer, Heidelberg, 2010).10.1007/978-3-642-00710-1 ↗
31. Eknapakul, T. et al. Electronic structure of a quasi-freestanding MoS2 monolayer. Nano Lett. 14, 1312 (2014).10.1021/nl4042824 ↗
32. Zhang, Y. et al. Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2. Nat. Nanotech. 9, 111–115 (2014).10.1038/nnano.2013.277 ↗
33. Riley, J. M. et al. Negative electronic compressibility and tunable spin splitting in WSe2. Nat. Nanotech. 10, 1043–1047 (2015).10.1038/nnano.2015.217 ↗
34. Kang, M. et al. Universal mechanism of band-gap engineering in transition-metal dichalcogenides. Nano Lett. 17, 1610–1615 (2017).10.1021/acs.nanolett.6b04775 ↗
35. Brumme, T., Calandra, M. & Mauri, F. First-principles theory of field-effect doping in transition-metal dichalcogenides: structural properties, electronic structure, Hall coefficient, and electrical conductivity. Phys. Rev. B 91, 155436 (2015).10.1103/PhysRevB.91.155436 ↗
36. Hohenadler, M. et al. Photoemission spectra of many-polaron systems. Phys. Rev. B 71, 245111 (2005).10.1103/PhysRevB.71.245111 ↗
37. Verdi, C., Caruso, F. & Giustino, F. Origin of crossover from polarons to Fermi liquids in transition metal oxides. Nat. Commun. 8, 15769 (2017).10.1038/ncomms15769 ↗
38. Covaci, L. & Berciu, M. Holstein polaron: the effect of coupling to multiple-phonon modes. Eur. Phys. Lett. 80, 67001 (2007).10.1209/0295-5075/80/67001 ↗
39. Mishchenko, A. S., Nagaosa, N. & Prokof’ev, N. Diagrammatic Monte Carlo method for many-polaron problems. Phys. Rev. Lett. 113, 166402 (2014).10.1103/PhysRevLett.113.166402 ↗
40. Covaci, L. & Berciu, M. Polaron formation in the presence of Rashba spin–orbit coupling: implications for spintronics. Phys. Rev. Lett. 102, 186403 (2009).10.1103/PhysRevLett.102.186403 ↗