arXiv subjects

Amit Goft

Publications and source records attributed to Amit Goft.

5 recordsLinked to original sources

arXiv2026

Vacancy-Induced Topological Phase Transition via Valley Annihilation in an Anisotropic Honeycomb Lattice

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 $\nu_3=\mp 1$ 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 $\nu_3=0$: 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 (${\sim}1/r$) 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 $\nu_3$, accessible in graphene and in photonic and cold-atom analogs.

cond-mat.mes-hall↗

arXiv2025

Engineering Topological Materials

The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering materials to realize desired topological properties. In this work, we introduce a general method for designing topological materials by embedding defects or spatial textures, which alter symmetry or dimension. This enables controlled navigation across the tenfold table, allowing one to induce topological phase transitions on demand. We illustrate this approach through several nontrivial examples, demonstrating how local defects can generate phases with different symmetries and topological invariants.

cond-mat.mes-hall↗

arXiv2025

Defects Potentials for Two-Dimensional Topological Materials

For non-topological quantum materials, introducing defects can significantly alter their properties by modifying symmetry and generating a nonzero analytical index, thus transforming the material into a topological one. We present a method to construct the potential matrix configuration with the purpose of obtaining a non-zero analytical index, akin to a topological invariant like a winding or Chern number. We establish systematic connections between these potentials, expressed in the continuum limit, and their initial tight-binding model description. We apply our method to graphene with an adatom, a vacancy, and both as key examples illustrating our comprehensive description. This method enables analytical differentiation between topological and non-topological zero-energy modes and allows for the construction of defects that induce topology.

cond-mat.mes-hall↗

arXiv2023

Wavefronts Dislocations Measure Topology in Graphene with Defects

We present a general method to identify topological materials by studying the local electronic density $\delta \rho \left(\boldsymbol{r}\right)$. More specifically, certain types of defects or spatial textures such as vacancies, turn graphene into a topological material characterised by invariant Chern or winding numbers. We show that these numbers are directly accessible from a dislocation pattern of $\delta \rho \left(\boldsymbol{r}\right)$, resulting from an interference effect induced by topological defects. For non topological defects such as adatoms, this pattern is scrambled by Friedel oscillations absent in topological cases. A Kekule distortion is discussed and shown to be equivalent to a vacancy.

cond-mat.mes-hall↗

arXiv2023

Defects in Graphene : A Topological Description

Specific types of spatial defects or potentials can turn monolayer graphene into a topological material. These topological defects are classified by a spatial dimension $D$ and they are systematically obtained from the Hamiltonian by means of its symbol $\mathcal{H} (\boldsymbol{k}, \boldsymbol{r}) $, an operator which generalises the Bloch Hamiltonian and contains all topological information. This approach, when applied to Dirac operators, allows to recover the tenfold classification of insulators and superconductors. The existence of a stable $\mathbb{Z}$-topology is predicted as a condition on the dimension $D$, similar to the classification of defects in thermodynamic phase transitions. Kekule distortions, vacancies and adatoms in graphene are proposed as examples of such defects and their topological equivalence is discussed.

cond-mat.mes-hall↗