2026/07/18 by Anna Hassine, Amit Goft, Boris Rotstein +1
Physics and Astronomy · #cond-mat.mes-hall
A single missing atom can drive a topological phase transition in a lattice that is otherwise trivial for all values of its parameters. We demonstrate this in a two-dimensional honeycomb lattice with anisotropic nearest-neighbor hopping ratio t'/t. The pristine lattice is topologically trivial for all t'/t by the Nielsen-Ninomiya fermion-doubling theorem: Dirac valleys appear in pairs whose topological charges cancel identically in any bulk invariant. A single vacancy breaks this cancelation, acting as an internal boundary with defect winding number ν3=∓ 1 for t'/t<2. At t'/t=2, the two Dirac valleys merge and annihilate; the number of active pseudospinor degrees of freedom drops from m=2 to m=1, violating the condition d+D+1=2m required for a non-trivial winding number. The winding number collapses to ν3=0: a topological phase transition within a fixed symmetry class (BDI), driven entirely by a bulk Lifshitz transition and observable only through the vacancy. The defect zero mode crosses over from algebraic (∼1/r) to stronger spatial confinement, with its inverse participation ratio reaching a sharp minimum at criticality. Wavefront dislocations in the local density of states provide a direct, spatially resolved image of ν3, accessible in graphene and in photonic and cold-atom analogs.