arXiv subjects

Yuval Abulafia

Publications and source records attributed to Yuval Abulafia.

4 recordsLinked to original sources

arXiv2025

Topological Winding Numbers from Wavefront Dislocations in Local Electronic Density

Topological materials are characterized by integer invariants that underpin robust quantized electronic properties, as exemplified by the Chern number in the integer quantum Hall effect. Yet, for most candidate systems, the observable linked to the topological invariant remains unknown, precluding direct verification of their topological nature. We present a general method to identify topological materials by connecting the local electronic density~$\delta\rho(\bm{r})$ to Atiyah-Singer index theorems. This method offers a concrete protocol for determining the winding number, the topological invariant associated with chiral-symmetric Hamiltonians. It also identifies a contour-independent wavefront dislocation pattern in $\delta\rho(\bm{r})$ arising from interference induced by topological defects and demonstrates its application to numerical simulations and to existing STM data. The method clearly distinguishes topological states from non-topological ones through a unified, standardized filtering step, offering a definitive approach for identifying and characterizing quantum topological states and opening the door to their use as robust, entangleable building blocks in quantum technologies.

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 $δρ\left(\boldsymbol{r}\right)$. 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 $δρ\left(\boldsymbol{r}\right)$, 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↗