Abstract
When considering a Li-intercalated hexagonal boron nitride bilayer (Li-hBN), the vertex corrections of electron–phonon interaction cannot be omitted. This is evidenced by the very high value of the ratio λωD/εF ≈ 0.46, where λ is the electron–phonon coupling constant, ωD is the Debye frequency, and εF represents the Fermi energy. Due to nonadiabatic effects, the phonon–induced superconducting state in Li-hBN is characterized by much lower values of the critical temperature (TLOVCC ∈ {19.1, 15.5, 11.8} K, for μ* ∈ {0.1, 0.14, 0.2}, respectively) than would result from calculations not taking this effect into account (TMEC∈ {31.9, 26.9, 21} K). From the technological point of view, the low value of TC limits the possible applications of Li-hBN. The calculations were carried out under the classic Migdal–Eliashberg formalism (ME) and the Eliashberg theory with lowest-order vertex corrections (LOVC). We show that the vertex corrections of higher order (λ3) lower the value of TLOVCC by a few percent.
Highlights
Low-dimensional systems such as graphene [1,2,3,4,5], silicene [6], borophene [7,8], and phosphorene [9,10,11] are mechanically stable only when placed on a substrate [12,13,14]
Note that retardation and strong-coupling effects for Li-intercalated hexagonal boron nitride bilayer (Li-hexagonal boron nitride (hBN)) are of the same order as in Li-MoS2 bilayer compounds [49], Li-black phosphorene bilayers [48], and Li-blue phosphorene bilayers [47], i.e., 0.068, 0.094, and 0.099, respectively
One can give arguments that support the results presented in this paper: (1) First of all, it should be noted that the very high value of the ratio λωD/εF does not mean that higher-order vertex corrections are or even more important than the lowest-order corrections
Summary
Low-dimensional systems such as graphene [1,2,3,4,5], silicene [6], borophene [7,8], and phosphorene [9,10,11] are mechanically stable only when placed on a substrate [12,13,14]. It is assumed that the best substrate for graphene is hexagonal boron nitride (hBN) with a honeycomb crystal structure in which boron (B) and nitrogen (N) atoms alternatingly occupy the hexagonal lattice nodes. A decade later, the twodimensional form of hBN was obtained at the University of Manchester [32]
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