Wavefront-Dislocation Evolution via Quadratic Band Touching Annihilation

Abstract

Wavefront dislocations (WDs) -- phase singularities observed in quasiparticle interference (QPI) experiments -- have been widely interpreted as the definitive real-space signatures of Berry phases in graphene-family systems. Here, we disentangle the roles of topological charge and pseudospin texture in WD experiments. By investigating various way of the annihilation of quadratic band touchings (QBTs) in bilayer graphene and magneto-spin-orbit graphene systems, we demonstrate that WD evolution is governed exclusively by changes in the underlying pseudospin winding, while remaining insensitive to the topological charge (i.e., vorticity) of the band touching itself. Our results imply that WD measures wavefunction pseudospin texture rather than a diagnostic of topological charge and provide solid-state platforms in which WD evolution can be engineered and observed.

Figures (4)

• Figure 1: (a) STM setup for measuring the impurity-induced LDOS modulation $\Delta\rho(\mathbf r)$ (Friedel oscillations). (b) BA and AA stackings of BBHL, connected by layer sliding along a space--time-inversion-symmetric path. (c) Evolution of the energy dispersion near the $\mathbf K$ valley under sliding. In (c), dots mark touching nodes between the lower (red), middle (black), and upper (green) bands.
• Figure 2: FT--STS analysis of QBT annihilation during the layer sliding. (a) FT--STS map $\rho_{2A,1A}(\omega,\mathbf q)$ during the sliding. The color indicate phase; insets show the zoomed image. "C" marks the chosen pair used for filtering. (b--f) Corresponding intervalley-filtered real-space modulations $\rho^{\text{filtered}}_{l'\sigma',l\sigma}(\omega,\mathbf r)$ for representative stacking configurations; left labels indicate the STM and impurity channel. Numbers in the green boxes denote the WD charge, obtained by taking the difference between the numbers of green wavefront lines coming or going from the red circle. For plotting we use $\omega=0.2~\mathrm{eV}$ above half filling and $m=0.05~\mathrm{eV}$.
• Figure 3: Pseudospin textures versus sliding. (a--e) Evolution of $\mathbf{s}_{l'\sigma',l\sigma}$ along the constant-energy contour at $\omega=0.2~\mathrm{eV}$ for different stackings. The magnitude and phase of $\mathbf{s}_{l'\sigma',l\sigma}$ are encoded by the line thickness and color, respectively. Left labels specify STM and impurity channel, and numbers denote the pseudospin winding, which is unchanged for $l'=l$ but evolves for $l'\neq l$.
• Figure 4: WD patterns and pseudospin textures for QBT removal by a sublattice potential $m$. (a) Energy dispersion for different $m$; dashed lines mark $\omega=\pm 0.5~\mathrm{eV}$. (b,c) $\mathbf{s}_{2A,1A}$ on the corresponding constant-energy contours at (b) $\omega=-0.5~\mathrm{eV}$ and (c) $\omega=0.5~\mathrm{eV}$, and (d,e) $\rho^{\text{filtered}}_{2A,1A}$ at the same energies. Numbers in (b,c) indicate the pseudospin winding, while those in (d,e) denote the corresponding WD charge. Transferring the QBT to adjacent bands leaves both pseudospin windings and WDs unchanged.