Thanks to the field effect electrostatic (electrochemical) doping it is possible to achieve both positive and negative shifts in the transition, as well as to tune other strongly correlated phenomena (such as Mott-Hubbard transition, charge-density-waves, insulator-to-metal transition and ferromagnetism).

I studied, via density functional theory calculations and its linear response extension, how field effect doping affects the transport properties of MoS2 nanolayers, the anomalous screening of the electric field at the interface of a conventional superconductor (NbN) and the failure of the Thomas-Fermi theory of high electric field screening. I have also studied the possibility of inducing a superconductive phase transition in diamond thin films via electrochemical gating.

## Field-effect induced superconductivity in hydrogenated diamond thin films:

I have investigated the possible occurrence of field-effect induced superconductivity in the hydrogenated (111) diamond surface by first-principles calculations. I have found that at a doping level as large as n = 6 × 10^{14} cm^{−2}, where the Fermi level crosses three valence bands, the electron-phonon interaction is λ = 0.81 and superconductivity emerges with T_{C} ≈ 29 − 36 K. Superconductivity is mostly supported by in-plane diamond phonon vibrations and to a lesser extent by some out-of-plane vibrations. The relevant electron-phonon scattering processes involve both intra and interband scattering so that superconductivity is multiband in nature.

Starting from the band-resolved electron-phonon spectral functions α^{2}F_{jj′} (ω) computed ab initio, I have iteratively solved the self-consistent isotropic Migdal-Eliashberg equations, in both the single-band and the multi-band formulations, in the approximation of a constant density of states at the Fermi level. In the single-band formulation, I have found T_{C} ≈ 40 K, which is enhanced between 4% and 8% when the multi-band nature of the system is taken into account.

*References*:

- D.Romanin, Th. Sohier, D.Daghero, F.Mauri, R.S.Gonnelli and M. Calandra,
*Electric field exfoliation and high-TC superconductivity in field-effect hole-doped hydrogenated diamond (111)*, Applied Surface Science**496**, 143709 (2019) ; - E. Piatti, D. Romanin, D. Daghero and R. S. Gonnelli,
*Two-dimensional hole transport in ion-gated diamond surfaces: A brief review*, Low Temperature Physics**45**, 1143 (2019) ; - D. Romanin, G. A. Ummarino and E. Piatti,
*Migdal-Eliashberg theory of multi-band high-temperature superconductivity in field-effect-doped hydrogenated (111) diamond*, Applied Surface Science**536**, 147723 (2021) .

## Superconductive proximity effect in the FET geometry:

The superconductive critical temperature can be enhanced or suppressed reversibly by field-effect doping. However the effective doping of the thin film does not involve the sample as a whole. In a field-effect architecture only a small part of the material under study, which directly faces the electrolyte, will be in principle affected by the transverse electric field and thus experience charge accumulation, while the underlying bulk will be unaffected. Therefore, we will have a perturbed superconductor on top of an undoped one, which will be coupled by superconductive proximity effect.

I have therefore employed density functional theory to study the extent of the region of the material affected by the electric field and showed that:

- In the case of NbN, for sufficiently high values of the electric field, we can observe an
*anomalous screening*of the electric field, which goes beyond the (non-linear) Thomas-Fermi theory ; - In the case of MgB
_{2}and Indium thin films, together with a promixity-effect extension of the multi-band Migdal-Eliashberg theory of superconductivity, I have shown how it is possible to tune the superconductive critical temperature T_{C}via field-effective doping .

*References*:

- E. Piatti, D. Romanin, R. S.Gonnelli and D. Daghero,
*Anomalous screening of an electrostatic field at the surface of niobium nitride*, Applied Surface Science**461**, 17-22 (2018) ; - G. A. Ummarino and D. Romanin,
*Proximity two bands Eliashberg theory of electrostatic field-effect doping in a superconducting film of MgB2*, J. Phys.: Condens. Matter**31**, 024001 (2018) ; - G. A. Ummarino and D. Romanin,
*Theoretical Explanation of Electric Field-Induced Superconductive Critical Temperature Shifts in Indium Thin Films*, physica status solidi b**257**, 1900651 (2020) .

## Field effect doping of MoS_{2} nanolayers:

Gated molybdenum disulfide (MoS_{2}) exhibits a rich phase diagram upon increasing electron doping. Using density functional theory and the solution of the semiclassical Boltzmann transport equation:

- I have shown 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 (Lishfitz transitions) ;
- I have identified the opening of additional intervalley scattering channels connecting the simultaneously filled K/K’ and Q/Q’ valleys in the Brillouin zone, which are triggered by the two Lifshitz transitions induced by the filling of the high-energy Q/Q’ valleys upon increasing electron doping .

*References*:

- E. Piatti, D. Romanin and R. S. Gonnelli,
*Mapping multi-valley Lifshitz transitions induced by field-effect doping in strained MoS2 nanolayers*, J. Phys.: Condens. Matter**31**, 114002 (2019) ; - D. Romanin, Th. Brumme, D. Daghero, R. S. Gonnelli and E. Piatti,
*Strong band-filling-dependence of the scattering lifetime in gated MoS2 nanolayers induced by the opening of intervalley scattering channels*, Journal of Applied Physics**128**, 063907 (2020) .