Sliding-induced topological transitions in bilayer biphenylene

TL;DR

This work investigates how interlayer sliding in bilayer biphenylene reshapes electronic topology, including the arrangement of type-II Dirac cones and Lifshitz-like changes in the Fermi surface. A symmetry-guided approach parameterizes stackings by the sliding vector and classifies them into high-symmetry and low-symmetry groups, analyzing irreducible representations to predict crossing patterns. Combined first-principles DFT calculations and tight-binding modeling reveal four Dirac crossings in high-symmetry stackings, nodal lines from nonsymmorphic symmetries, and a sequence of Fermi-surface topologies that can be tracked by the Euler characteristic. The results show that electronic topology in bilayer biphenylene is tunable via sliding, offering a practical route to engineer Dirac-cone patterns and Fermi-sea connectivity for potential nanoelectronic and quantum-information applications.

Abstract

Sliding-induced topological transitions in biphenylene bilayers are investigated, considering various stacking configurations which are analyzed from a symmetry perspective and described in detail,highlighting the intricate patterns of type-II Dirac cone crossings. Topological changes in the Fermi surface are assessed via the Euler characteristic, linking each transition to its corresponding symmetry, which can be experimentally tested by conductance measurements. Moreover, the ability to tune these topological properties by sliding the layers provides a simpler and more effective way to observe such phenomena.

Figures (5)

• Figure 1: (a) Biphenylene monolayer structure with bond lengths $d_1=1.41$ Å, $d_2=1.45$ Å, and $d_3=1.46$ Å. (b) Type-II band structure of BPN monolayer with Dirac points at $E=0.26$ eV; valence (green) and conduction (blue) bands are shown. (c) Bilayer stacking configurations labeled $(\delta_x, \delta_y)$.
• Figure 2: Sliding diagram for the bilayer stackings: classification of the different space groups and Dirac cone patterns with respect to the displacements $\delta_x$ and $\delta_y$. Each square of the grid is colored according to the space group of the specific bilayer; the color code is shown in the bottom panel. Inside the square, a symbol indicates the type of band crossing at the double Dirac cone closest to the Fermi energy: circles (4 crossings), stars (2 crossings) and triangles (anticrossing), as indicated in the panel below the diagram.
• Figure 3: (a) Band structures for the biphenylene bilayers corresponding to the displacements $(\delta_{x},\delta_{y})$. Symbols and colors refer to the diagram of Fig. \ref{['FIGdiagram']}. (b) Electronic bands along the $Y$-$\Gamma$ line exhibiting the four crossings for HSS $(0.0,0.0)$ and LSS $(0.2,0.0)$, labeled with the corresponding irreps $\Delta_i$.
• Figure 4: Fermi surface (loops) for the HSS set. Blue and red solid lines represent electron-like and hole-like surfaces, respectively. Each stacking is accompanied by the corresponding group symmetry and Dirac cone type as colored circles.
• Figure A1: DFT (darker dots) and TB (solid lines) electronic bands for different bilayer stackings, TB energy contours evaluated at the first cone crossing and the respective surface cone plot for the stackings (a-b) HSS $(0.5,0.5)$ and $(0.0,0.5)$, and (c-d) LSS $(0.4,0.0)$ and $(0.3,0.5)$, respectively.