Universal Increase in the Superconducting Critical Temperature of Two-Dimensional Semiconductors at Low Doping by the Electron-Electron Interaction

Abstract

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...

Spin susceptibility and electron-phonon coupling of two-dimensional materials by range-separated hybrid density functionals: Case study ofLixZrNCl

“…21 that all phonons strongly coupled to electrons and having phonon momentum q = K, K ′ (intervalley phonons) act as pseudo-magnetic fields, namely induce an asymmetry in the valley occupation, without breaking the spin degeneracy, at least as long as there is no net magnetization. Thus the intervalley distortion shifts the two valleys, changes the occupation per valley but preserves the absence of a magnetization in each valley.…”

“…21), a condition necessary to have the intravalley electronelectron scattering dominating over the intervalley one.…”

“…Under this assumption, only the intravalley electronelectron interaction remains and the RPA susceptibility can be calculated analytically, by using the LDA/PBE effective mass of undoped ZrNCl and the environmental dielectric constant, ǫ M = 5.59 19,20,44 , used in Ref. 21.…”

“…Indeed the bottom of the conduction band of ZrNCl is composed of two perfectly parabolic bands at points K and K ′ = 2K in the Brillouin zone. The interlayer interaction is extremely weak [18][19][20][21] . Upon Li intercalation, the semiconducting state is lost and superconductivity emerges.…”

“…In a previous work 21 , the behavior of χ s and T c as a function of doping was investigated by using local functionals and a 2D two-valley electron gas model solved within the random phase approximation (RPA). In this framework, it was found that the electron-electron interaction enhances the electron-phonon matrix elements of those intervalley phonons inducing an unbalance in the valley occupations.…”