In 2-dimensional multivalley semiconductors, at low doping, even a moderate electron-electron interaction enhances the response to any perturbation inducing a valley polarization. If the valley polarization is due to the electron-phonon coupling, the electron-electron interaction results in an enhancement of the superconducting critical temperature. By performing first principles calculations beyond DFT, we prove that this effect accounts for the unconventional doping-dependence of the superconducting transition-temperature (Tc) and of the magnetic susceptibility measured in LixZrNCl. Finally we discuss what are the conditions for a maximal Tc enahnacement in weakly doped 2-dimensional semiconductors.The quest for high T c superconductivity has mainly focused on strongly correlated materials in proximity of electronic instabilities like the Mott transition (cuprates [1]) or fragile magnetic states (iron pnictides [2, 3]). Heavily doped three dimensional (3D) covalently bonded semiconductors, like diamond [4], silicon [5] and SiC [6, 7] have been considered as an alternative, that, however, has lead, so far, to fairly low T c (< 10 K). In 3D, the density of states at the Fermi level slowly grows with doping. As T c increases with the density of states [8], a large number of carriers has to be introduced to achieve a large T c . This demanding requirement could be released in 2 dimensional (2D) semiconductors, such as transition metal dichalcogenides [9][10][11][12], cloronitrides [13,14] or other layered materials with massive Dirac fermions, where the doping can be controlled by intercalation [13,14] or field-effect [11,12,15]. In 2D, the density of states is a constant function of the Fermi energy ( F ) and, in principle, T c is expected to be insensitive on doping. Surprisingly, measurements on Li x ZrNCl [13,14,16], a weakly-doped multivalley 2D semiconductor, revealed that T c not only does not increase with doping but even decreases. Here we show that the e-e interaction is responsible for such a puzzling behavior. In particular, in a weakly-doped 2D multivalley semiconductor, e-e manybody effects enhance the response to any perturbation inducing a valley polarization. If the valley polarization is due to the electron-phonon coupling, the e-e interaction will lead to a large increase of T c . We demonstrate that this effect explains the high T c in Li x ZrNCl and its unconventional behavior [16] as a function of doping. Finally, by finding the conditions for a maximal Tc enhancement, we show how weakly-doped 2D semiconductors are an alternative route towards high Tc superconductivity.The electronic structure of multivalley semiconductors has minima (maxima) in the conduction (valence) band that are named valleys. In the low doping limit, the equivalent g v valleys are occupied by few electrons or holes and the electronic structure is described by the effective mass theory. The resulting model Hamiltonian is that of a multicomponent electron gas of mass m * and density n where the valley index plays the r...

The effect of the exchange interaction on the vibrational properties and on the electronphonon coupling were investigated in several recent works. In most of the case, exchange tends to enhance the electron-phonon interaction, although the motivations for such behaviour are not completely understood. Here we consider the class of weakly doped two-dimensional multivalley semiconductors and we demonstrate that a more global picture emerges. In particular we show that in these systems, at low enough doping, even a moderate electron-electron interaction enhances the response to any perturbation inducing a valley polarization. If the valley polarization is due to the electron-phonon coupling, the electron-electron interaction results in an enhancement of the superconducting critical temperature. We demonstrate the applicability of the theory by performing random phase approximation and first principles calculations in transition metal chloronitrides. We find that exchange is responsible for the enhancement of the superconducting critical temperature in Li x ZrNCl and that much larger T c s could be obtained in intercalated HfNCl if the synthesis of cleaner samples could remove the Anderson insulating state competing with superconductivity.