Role of Substrate in Transition Metal Dichalcogenides Superconductivity
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ORIGINAL PAPER
Role of Substrate in Transition Metal Dichalcogenides Superconductivity Ioan Grosu1 Received: 28 May 2020 / Accepted: 19 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We analyze the effect of a substrate on zero temperature superconducting energy gap, on critical temperature, and on Geilikman-Kresin ratio in the case of transition metal dichalcogenides. The energy spectrum is modified due to the presence of the substrate. We assume a linear modification similar to the massless particles in graphene. When the substrate effect is removed we reobtain the previous results. Keywords Transition metal dichalcogenides · Substrate · Superconductivity · Superconducting gap · Critical temperature
1 Introduction The transition metal dichalcogenides are layered materials (quasi two-dimensional systems) where, at low temperatures, the s-wave superconductivity is present. The superconducting phase coexists with the charge density waves (CDW ) [1]. The transition metal dichalcogenides reveal some similar properties with high temperature superconductors such as a linear temperature dependence of the normal resistivity and high anisotropic transport properties. Other experiments [2] reveal a marginal Fermi liquid lifetime behavior of the quasi-particles. Here the elementary quasi-particles are Dirac fermions which exist in a region where CDW gap vanishes [3]. The superconducting state appear due to the Cooper pairing between the Dirac particles, and the attraction mechanism comes from acoustic phonons through a piezoelectric coupling. However, the Dirac electrons play an important role in understanding the superconducting properties in other materials such as graphene [4–11]. The possibility of an unconventional superconducting phase in transition metal dichalcogenides, a mixture of a spin singlet and a spin triplet, was predicted in [12]. The competition between superconductivity and CDW in layered metallic transition metal dichalcogenides was analyzed also in [13]. The topological properties of the superconducting state have Ioan Grosu
[email protected] 1
Department of Physics, “Babes-Bolyai” University, 400084 Cluj-Napoca, Romania
been discussed in [14]. An exhaustive discussion of s-wave superconductivity in transition metal dichalcogenides has been made by Uchoa et al. [15]. The results obtained here have similarities with those of graphene. In this paper, following the model given in [15], we will analyze several superconducting properties of transition metal dichalcogenides, taking into account the case when the transition metal dichalcogenide is grown on a substrate. In this case an additional energy gap E0 opens in the energy spectrum. In the case of graphene this behavior was proved by Zhou et al. [16, 17], leading to a dispersion relation called massive gapped spectrum. When one departs from the Dirac point the dispersion relation changes, passing towards the massless gapped spectrum [18]. The effect of the gap on various properties of graphene was
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