MgB4 trilayer film: A four-gap superconductor

Abstract

Since the discovery of two-gap superconductivity in bulk ${\mathrm{MgB}}_{2}$, many efforts have been devoted to searching for multigap superconductors. Recently, a monolayer of ${\mathrm{MgB}}_{2}$ and a trilayer film of ${\mathrm{AlB}}_{4}$ were predicted to be robust three-gap superconductors. Here we investigate using the fully anisotropic Migdal-Eliashberg theory the superconducting behaviors in a series of boron-based monolayers and trilayer films that are dynamically stable but not synthesized experimentally heretofore. Remarkably, we find that the trilayer film of ${\mathrm{MgB}}_{4}$ has an exciting four-gap superconducting nature with a high transition temperature ${T}_{c}\ensuremath{\sim}52$ K. We demonstrate that this high-${T}_{c}$ four-gap superconductivity is closely related to the Fermi surface exhibiting an unusually strong electron-phonon coupling with evident four-region distribution characteristics. The electron-lattice coupling is dominated by the acoustic modes of a softening kink and the high-energy optical phonons around the Brillouin-zone center, of which the former ones place the system on the verge of a latent charge density wave state. To our knowledge, no material with more than three superconducting gaps has been reported. At the same time, we also show that the ${\mathrm{GaB}}_{4}$ trilayer film has a robust three-gap nature with ${T}_{c}\ensuremath{\sim}51$ K, and the trilayer films of ${\mathrm{BeB}}_{4}$ and ${\mathrm{LiB}}_{4}$ are two-gap superconductors with ${T}_{c}$'s of $\ensuremath{\sim}39$ and 32 K, respectively.