Mapping multi-valley Lifshitz transitions induced by field-effect doping in strained MoS₂ nanolayers

Abstract

Gate-induced superconductivity at the surface of nanolayers of semiconducting transition metal dichalcogenides (TMDs) has attracted a lot of attention in recent years, thanks to the sizeable transition temperature, robustness against in-plane magnetic fields beyond the Pauli limit, and hints to a non-conventional nature of the pairing. A key information necessary to unveil its microscopic origin is the geometry of the Fermi surface hosting the Cooper pairs as a function of field-effect doping, which is dictated by the filling of the inequivalent valleys at the K/K ′ and Q/Q ′ points of the Brillouin Zone. Here, we achieve this by combining Density Functional Theory calculations of the bandstructure with transport measurements on ion-gated 2H-MoS2 nanolayers. We show that, when the number of layers and the amount of strain are set to their experimental values, the Fermi level crosses the bottom of the high-energy valleys at Q/Q ′ at doping levels where characteristic kinks in the transconductance are experimentally detected. We also develop a simple 2D model which is able to quantitatively describe the broadening of the kinks observed upon increasing temperature. We demonstrate that this combined approach can be employed to map the dependence of the Fermi surface of TMD nanolayers on field-effect doping, detect Lifshitz transitions, and provide a method to determine the amount of strain and spin-orbit splitting between sub-bands from electric transport measurements in real devices.

Two-dimensional hole transport in ion-gated diamond surfaces: A brief review (Review article)

“…The onset of superconductivity thus corresponds to a sudden jump in the DOS, N (0), that occurs when the second valence band crosses the Fermi level and that strongly boosts the electron-phonon coupling to λ ≈ 0.3. The situation is similar to that observed, for instance, in MoS 2 [67,77] where the superconducting transition does not appear until the Fermi level crosses both the spin-orbit split sub-bands at the Q point.…”

“…From the n 2Ddependence of L so , the authors also extracted the dependence of the Rashba spin-orbit splitting ∆ so , which was found to increase by over 4 times as n 2D was increased (see Fig.5c) even though the intrinsic Rashba coupling strength decreased (anomalous / negative differential Rashba splitting) [93,94]. Notably, the maximum gate-induced ∆ so ≃ 24.5 meV is larger than those reported for most 2D hole systems [47], and is comparable to those of 2D electron systems such as HgTe quantum wells [95] or the high-energy valleys of electron-doped MoS 2 [77].…”

Enhanced Electron-Phonon Interaction in Multivalley Materials

“…Superconductivity provides an example of a physical phenomenon for which the enhanced EPC mechanism that we have identified may be at play. It appears that much of the existing data on gate-induced superconductivity observed in some of the TMDs (e.g., WS 2 and MoS 2 ) is consistent with having the superconducting instability setting in only when multiple valleys are occupied [25,81]. Having multiple valleys occupied would explain, for instance, why gate-induced superconductivity in WS 2 starts occurring at a lower electron density than in MoS 2 [22,24,38] because, as we discussed above, the energy difference between the K and Q valleys is smaller in WS 2 than in MoS 2 .…”

Special issue on novel superconducting and magnetic materials

“…Finally in Ref. 28 Piatti, Romanin and Gonnelli map, in a combined experimental-theoretical work that Sandro would have certainly appreciated, the field-induced insulator metal transition in MoS 2 .…”