$T_c$ (higher than the liquid hydrogen temperature), on conditions without high pressure and external strain which can be modified by strain and doping [@Penev-NL16; @M.Gao; @RC.Xiao].

Several types of borophene have been synthesized on Ag(111) [@mannix2015synthesis; @ZZhang; @BFeng; @BFeng2]. A similar striped phase, named as $\beta_{12}$ borophene, has an essentially flat structure that weakly interacts with the Ag(111) substrate. In particular, the existence of the Dirac cones with ultrahigh Fermi velocity, in $\beta_{12}$ borophene clearly proved using the angle-resolved photoemission spectroscopy (ARPES) experiment as well as by first-principles calculations [@Boro].

This novel two-dimensional material was first proposed by Boustani, who predicted that the quasi-planar 2D boron sheet could be constructed from a basic unit of puckered $B_7$ cluster by using the systematic ab initio density functional method $B_7$ cluster [@Boustani1; @Boustani2]. The first experimental evidence of the atomic-thin boron sheets was performed by Piazza [ *et al.*]{} in the planar $B_{36}$ cluster with a central hexagonal hole [@Piazza14].

As proposed by Tang and Ismail-Beigi, the mixed hexagonal-triangular 2D boron sheet ($\alpha$-borophene) was thought to be more stable than one composed only of buckled triangular motifs [@Tang2007; @Tang2009; @Tang2010]. Using the first-principle particle-swarm optimization global algorithm, Zeng’s group showed that another 