Multi-Valley Superconductivity in Ion-Gated MoS₂ Layers

Abstract

Layers of transition metal dichalcogenides (TMDs) combine the enhanced effects of correlations associated with the two-dimensional limit with electrostatic control over their phase transitions by means of an electric field. Several semiconducting TMDs, such as MoS, develop superconductivity (SC) at their surface when doped with an electrostatic field, but the mechanism is still debated. It is often assumed that Cooper pairs reside only in the two electron pockets at the K/K' points of the Brillouin Zone. However, experimental and theoretical results suggest that a multivalley Fermi surface (FS) is associated with the SC state, involving six electron pockets at Q/Q'. Here, we perform low-temperature transport measurements in ion-gated MoS flakes. We show that a fully multivalley FS is associated with the SC onset. The Q/Q' valleys fill for doping ≳ 2 × 10 cm, and the SC transition does not appear until the Fermi level crosses both spin-orbit split sub-bands Q and Q. The SC state is associated with the FS connectivity and promoted by a Lifshitz transition due to the simultaneous population of multiple electron pockets. This FS topology will serve as a guideline in the quest for new superconductors.

Broken adiabaticity induced by Lifshitz transition in MoS2 and WS2 single layers

“…These Fermi surfaces clearly depict the transformation from the one-valley to multi-valley electronic band structure as the electron and hole densities are elevated, in close agreement with the experiments [18,33]. The abrupt appearance of the Γ and Σ valleys (e.g., for MoS 2 when charge density is around ±0.08 e/unit cell) represents the standard case of the Lifshitz transition, which is believed to be responsible for the superconductivity in MoS 2 [18]. Here I show that this sudden change in the electron density of states induces the significant dynamical effects in the EPC contributing to the phonon frequency of the Raman-active phonon modes.The calculated doping-induced frequency shifts of the E 2g and A 1g optical phonon modes in MoS 2 and WS 2 single layers are shown in Figs.…”

“…Moreover, the theoretical considerations have predicted the importance of the NA coupling in charge transfer dynamics of TMDs heterostructures [13,14] as well as in exciton-mediated Raman scattering of MoS 2 [15]. Additionally, the effect beyond adiabatic approximation, namely, the phonon-mediated superconductive state was shown to exist in single-and few-layer MoS 2 when multiple conduction valleys are partially occupied [16][17][18]. Considering the plethora of exceptional charge-induced optical properties [19][20][21][22] and good carrier mobility in doped singlelayer TMDs [23], as well as the pivotal role of the EPC in these features, it is of paramount importance to decipher the role of the NA effects and the EPC in the corresponding Raman spectra.Here I show that the vibrational spectra of singlelayer MoS 2 and WS 2 , as prototypical examples of semiconducting TMDs, doped with electrons and holes are indeed governed by strong NA effects.…”

“…Considering the plethora of exceptional charge-induced optical properties [19][20][21][22] and good carrier mobility in doped singlelayer TMDs [23], as well as the pivotal role of the EPC in these features, it is of paramount importance to decipher the role of the NA effects and the EPC in the corresponding Raman spectra.Here I show that the vibrational spectra of singlelayer MoS 2 and WS 2 , as prototypical examples of semiconducting TMDs, doped with electrons and holes are indeed governed by strong NA effects. Namely, when more than one valley of either valence or conduction electronic bands are simultaneously partially occupied or empty a Lifshitz transition occurs (i.e., an abrupt change of the Fermi surface) [18] which then activates the significant dynamical part of the EPC. The latter is manifested as a considerable redshift of the A 1g optical phonon frequency along with the large corresponding NA correction.…”

“…Consequently, the latter demonstrates how the Raman spectroscopy could be utilized in order to extract the right amount of carrier density required for one-to multi-valley transformations in TMDs and similar semiconductors. Also, since both superconductive state and the breakdown of the adiabaticity occur at the outset of the Lifshitz transition, it is likely that the nonadiabatic channels are open in the superconductivity of the TMDs, and thus the framework beyond the standard Migdal-Eliashberg theory [34] might be necessary to explain the corresponding superconductive pairing as well as the discrepancy between 4 the theoretically-and experimentally-obtained transition temperature T c [18].In what follows, I investigate the impact of the EPCinduced electron-hole pair (EHP) scattering processes [4,9] on phonons in TMDs. In Figs.…”

Superconducting dome driven by intervalley phonon scattering in monolayer MoS2

“…The former has shown novel tribological [1], catalytic [2,3], and photovoltaic [4] properties. Recently, several experimental groups have reported a gate-induced superconducting state at the surface of gated MoS 2 flakes [5][6][7][8]. Particularly, an interesting fielddoping-induced superconducting dome was observed in a temperature-doping phase diagram of monolayer MoS 2 [5].…”