Phonon-induced electronic degeneracy breaking: a SSAdNDP interpretation

TL;DR

The paper addresses how phonon perturbations can break electronic degeneracies near the Fermi level and how this can be interpreted chemically using SSAdNDP. By applying a frozen $E_{2g}$ phonon mode to MgB2, graphene, and hBN, the authors analyze concurrent changes in band structure and real-space bonding, bridging reciprocal-space information with multicenter bonding patterns. They find that significant bonding reorganization accompanies band splitting in MgB2, where 6c and 8c motifs redistribute occupancy, while graphene and hBN show degeneracy lifting without meaningful bonding changes near $E_f$. This work demonstrates that SSAdNDP offers a chemically intuitive, transferable framework to interpret vibrationally driven electronic effects in solids and to identify when degeneracy lifting has true chemical consequence.

Abstract

This work explores how phonon perturbations can induce the breaking of electronic degeneracies near the Fermi level and how this response can be interpreted from a chemical perspective through the SSAdNDP method. We apply this approach to a family of structurally similar yet electronically distinct hexagonal materials-MgB2, graphene, and hBN-to analyze how a single phonon mode simultaneously modifies the electronic structure (band dispersion) and the nature of chemical bonding (natural occupations and nodal patterns) in real space. Our results show that band splitting becomes physically relevant only when it is accompanied by an electronic redistribution, reflected in changes of the occupation numbers or bonding topology. Thus, SSAdNDP provides a direct bridge between reciprocal- and real-space representations, translating phenomena such as electron-phonon coupling into chemically intuitive reorganizations of multicenter bonds, and offering a unified framework to interpret vibrationally driven electronic effects in solids.

Figures (6)

• Figure 1: (a) General unit cell with A and B atoms. (b) $E_{2g}$ phonon mode in a hexagonal lattice
• Figure 2: MgB$_2$: Bonding configurations and their occupation numbers (ON) for the 6c case. The left side displays the unperturbed system, while the right side shows the system perturbed by an in-lattice $E_{2g}$ phonon. The color-coding links correspond to bond geometries in each scenario; a square represents a change in the ON, and triangles show bonds that remain stable.
• Figure 3: MgB$_2$: Comparison of the band structure for the (left) unperturbed and (right) perturbed system. The colors indicate the projections onto the $s, p_x$, and $p_y$ orbitals associated with the $\sigma$ bonds, while blue denotes the unique contribution from the $p_z$ orbitals.
• Figure 4: Bonding analysis and electronic structure of graphene under the $E_{2g}$ phonon perturbation. Top panels display the SSAdNDP bonding motifs for the (a) unperturbed equilibrium state and (b) the distorted structure. The orbitals are sorted by ON, revealing a topologically invariant network where bonding preferences remain unaltered. Bottom panels present the electronic band structure for the (c) unperturbed and (d) perturbed systems. The color gradient represents the atomic projection onto the in-plane $\sigma$ orbitals ($s, p_x, p_y$)
• Figure 5: Bonding analysis and electronic structure of h-BN under the $E_{2g}$ phonon perturbation. Top panels display the SSAdNDP bonding motifs for the (a) unperturbed equilibrium state and (b) the distorted structure. The orbitals are sorted by ON, revealing a topologically invariant network where bonding preferences remain unaltered. Bottom panels present the electronic band structure for the (c) unperturbed and (d) perturbed systems. The color gradient represents the atomic projection onto the in-plane $\sigma$ orbitals ($s,\; p_x,\; p_y$)