Second-order topological insulator in Bilayer borophene

TL;DR

The study tackles the challenge of realizing 2D higher-order topological insulators in realistic materials by identifying bilayer α5-borophene as a C2-protected 2D SOTI. Through first-principles calculations and tight-binding modeling, interlayer B–B covalent bonds stabilize the bilayer and open sizable direct bulk gaps, while the bulk quadrupole momentum and robust corner states reveal the second-order topology. This work provides a realistic SOTI candidate in borophene and offers a tunable platform to explore 2D higher-order topology via interlayer spacing and edge geometry. The findings highlight potential routes for borophene-based topological devices and deepen the understanding of how interlayer bonding influences topology in 2D materials.

Abstract

As the novel topological states, the higher-order topological insulators have attracted great attentions in the past years. However, their realizations in realistic materials, in particular in two dimensional systems, remains the big challenge due to the lack of adequate candidates. Here, based on the first-principle calculation and tight-binding model simulations, we identify the currently \emph{existing} bilayer $α_{5}$-phase borophenes as the two-dimensional second-order topological insulators, protected by the $C_{2}$-rotational symmetry. The formation of interlayer B-B covalent bonds, stabilizing the bilayer borophenes and opening the large direct bulk gaps ($\sim 0.55-0.62$ eV) at Fermi level, plays the key roles. The second-order topology is characterized by the bulk quantized quadrupole momentum. Our results enriches the candidates for the second-order topological insulators, and also provide a way to study topological states in borophenes.

Figures (14)

• Figure 1: (a) Top and side view of crystal structure of flat $\alpha_{5}$-phase boron monolayer. The black arrows represent the primitive lattice vectors. (b) The near-Fermi-level electronic band structure of $\alpha_{5}$-borophene. Part of parity values at $\Gamma$ and $M$ are marked. The black circle highlight the existence of Dirac-like crossing point in bulk.
• Figure 2: Top and side view of crystal structures. Upper panels: (a)-(c) AA-, AB- and AC- stacking $\alpha_{5}$-BLB. The pink and green spheres represent B atoms of upper and lower layers, respectively. Lower panels: The charge density difference relative to the monolayer case. The yellow and blue color indicate the gain and loss of charge. The long and short black arrows show the length of B-B bonds in the "vdW" area and "bonded" area, respectively.
• Figure 3: Upper panels are the band structures of (a) AA-, (b) AB- and (c) AC-stacking $\alpha_{5}$-BLB along high symmetric paths obtained from DFT and Wannier functions (only B-$p_{x}$, $p_{y}$, and $p_{z}$ orbits are shown), respectively. Solid black and red dashes indicate DFT and Wannier functions. Lower panels are the corresponding orbital-resolved band structures. The blue and red indicate the $p_{x}+p_{y}$, and $p_{z}$ states of boron, respectively. The Fermi levels are fixed at $0$.
• Figure 4: (a) and (b) Top views of the structure of AA-stacking $\alpha_{5}$-BLB. The black lines mark a near flat edges and a zigzag edge. (c) and (d) The edge states of the cylinder geometry with ZZ-I edge and flat edges, calculated by the Wannier interpolation method.
• Figure 5: The energy spectrum of four nanodisks with (a), (b) and (c) zigzag and (d) flat edges of AA-stacking $\alpha_{5}$-BLB calculated by DFT. The corner states are marked by red dots. The corresponding insets show the real-space distribution of the corner states.