arXiv subjects

G. Q. Garcia

Publications and source records attributed to G. Q. Garcia.

14 recordsLinked to original sources

arXiv2026

Distributed Topological Charge and Spinorial Holonomy in Yukawa-Regularized Graphene Disclinations

Conical geometries provide the standard description of disclinations, but they concentrate the curvature at a singular apex. We introduce a Yukawa-type regularization that replaces this singularity by a smooth curvature distribution while preserving the asymptotic topology of the defect. Exact expressions are obtained for the conformal factor, curvature, and enclosed topological charge. The resulting geometry exhibits a scale-dependent topological charge and a corresponding radius-dependent holonomy, establishing a direct connection between distributed curvature and geometric phases. We further investigate the dynamics of massless Dirac quasiparticles in this background and show that the regularized core modifies the spin connection while preserving the asymptotic topological signature of the defect. These results provide a finite-core extension of the conventional conical description and offer a natural framework for studying geometric and topological effects in graphene-like systems.

cond-mat.mes-hall↗

arXiv2026

Holonomic quantum computation on graphene from Atiyah-Singer index theorem

We investigate the emergence of geometric phases in graphene-based nanostructures through the lens of the Atiyah-Singer index theorem. By modeling low-energy quasiparticles in curved graphene geometries as Dirac fermions, we demonstrate that topological defects arising from the insertion of pentagonal or heptagonal carbon rings generate effective gauge fields that induce quantized Berry phases. We derive a compact expression for the geometric phase in terms of the genus and number of open boundaries of the structure, providing a topological classification of zero-energy modes. This framework enables a deeper understanding of quantum holonomies in graphene and their potential application in holonomic quantum computation. Our approach bridges discrete lattice models with continuum index theory, yielding insights that are both physically intuitive and experimentally accessible.

cond-mat.mes-hall↗

arXiv2026

Zero modes and geometric phase for 2D Weyl fermions on Lifshitz backgrounds

Here we investigate analytical properties of Weyl fermions in (2+1)-dimensional Lifshitz spacetimes. In particular, we are interested in obtaining geometric phases and verifying the existence of well-behaved fermionic zero modes. Using the Dirac phase method, we show how geometric phases naturally arise from the coupling between the fermionic fields and the Lifshitz geometry. We also present exact solutions of the zero modes by rewriting the Weyl equation as a system of supersymmetric equations.

hep-th↗

arXiv2026

Elastic field causing noncommutativity

We study how a uniform torsion background, modeling a continuous density of screw dislocations and induces effective spatial noncommutativity and reshapes the energy spectrum of a free quantum particle. Within the geometric theory of defects, the metric yields a first-order (magnetic-like) coupling in the transverse dynamics, equivalent to an effective magnetic field $B_{eff}$ proportional to $p_z Omega$, where $Omega$ encodes the torsion strength. In the strong-coupling (Landau) regime, the planar coordinates obey [x,y] != 0 and the spectrum organizes into Landau-like levels with a slight electric-field-driven tilt and a uniform shift. Thus, increasing $Omega$ drives the system continuously toward the familiar Landau problem in flat space, with torsion setting the noncommutativity scale and controlling the approach to the Landau limit.

cond-mat.mes-hall↗

arXiv2025

New Solutions for Topological Defects with Continuous Distributions:A Conformal Metric Perspective

We present new exact solutions for two-dimensional geometries generated by continuous distributions of topological defects within a conformal metric framework. By reformulating Einstein's equations in two dimensions as a Poisson equation for the conformal factor, we analyze how smooth defect densities -- such as Gaussian, exponential, and power-law profiles -- regularize curvature singularities and encode nontrivial topological information. Each distribution yields a well-defined geometry that interpolates between localized curvature near the defect core and asymptotic flatness. We compute the Ricci scalar and total curvature, confirming consistency with the Gauss-Bonnet theorem. Our results provide a unified geometric description of regularized disclination-like defects and offer insights into analog gravity, crystalline materials, and two-dimensional systems with emergent curvature.

gr-qc↗

arXiv2025

Geometric and Topological Aspects of Quadrupoles of Disclinations: Conformal Metrics and Self-Forces

We study the geometric and physical effects of quadrupolar configurations of disclinations using a conformal metric approach in $(2+1)$ dimensions. Two cases are considered: a linear quadrupole, inducing anisotropic curvature with a $\cos(2θ)$ as profile, and a square quadrupole, yielding a more isotropic field with higher angular harmonics. We solve the Poisson equation for the conformal factor and compute the corresponding Green functions. Using these configurations, we evaluated the electrostatic and magnetostatic self-energies and self-forces for linear sources. The results reveal how symmetry and curvature influence self-interaction effects, with the magnetostatic self-force exhibiting a sign reversal compared to the electrostatic case. Connections with previous models of dislocations and cosmic strings are discussed, with potential applications in graphene, nematics, and gravitational analogs.

gr-qc↗

arXiv2025

Contribution of Geometry and Non-Abelian Gauge Fields to Aharonov-Bohm Scattering of Massless Fermions in Graphene with Disclinations

This work examines the effect of disclinations on the scattering of quasipaticles in graphene with the presence of a topological defect. Using the tight-binding method, the electronic properties of graphene with disclination are described, where the topological defects are introduced in the lattice via geometric theory. The massless Dirac equation is modified to account for the curvature induced by these defects, incorporating a gauge field. The results show that disclinations significantly affect the scattering process, altering phase shifts and interference patterns. The differential cross-section and its dependence on the scattering angle are analyzed, highlighting the role of geometric factors like the parameter α in shaping the scattering dynamics.

cond-mat.mes-hall↗

arXiv2024

Rotation effects on the graphene wormhole energy levels

In this work, we are interested in how spinning effects influence the electronic properties of the graphene wormhole. For this purpose, we have described the graphene by the wormhole background based on the model developed by González and his co-workers. By applying a coordinate transformation in the metric of graphene wormhole, we can introduce rotating effects. In the continuum limit, by solving the massless Dirac equation in the context of a rotating wormhole background, we obtain the Landau levels for the rotating graphene wormhole. We still have exposed the analogy between the graphene wormhole and fermions on the Gödel-type spacetime.

cond-mat.mes-hall↗

arXiv2024

Landau levels for massive disclinated graphene-based topological insulator

In this work, we investigate the massive Kane-Mele model for graphene in the presence of disclination and an external magnetic field, where graphene behaviors as a topological insulator. In the low-energy limit, the effective field equation for graphene is described by a Dirac equation with three different degrees of freedom. We succeed to decouple the set of eight components of the Dirac equation by using the spin projector \hat{C} in the disclinated geometry. As consequence, we obtain the Landau levels in this framework, in which we note the emergence of zero modes as edge states due to the inversion symmetry breaking. We also note that for different sites in sublattices \mathcal{A/B}, one can have different values of gap width.

cond-mat.mes-hall↗

arXiv2020

Graphene-based topological insulator in the presence of a disclination submitted to a uniform magnetic field

In this paper we investigate quasiparticles in graphene-based topological insulator with a wedge disclination in the presence of a uniform magnetic field. In particular, we consider a massive spinless model. The Landau levels are analytically found for the described system. We show that the Landau levels are lifted for a specific range of the parameter ν. In addition, we also show that, for appropriate parameter values, one finds gapless and gapped states.

cond-mat.mes-hall↗

arXiv2019

Graphene wormhole trapped by external magnetic field

In this work we study the behavior of massless fermions in a graphene wormhole and in the presence of an external magnetic field. The graphene wormhole is made from two sheets of graphene that play the roles of asymptotically flat spaces connected through a carbon nanotube with a zig-zag boundary. We solve the massless Dirac equation in this geometry and analyze its wave function. We show that the energy spectra of these solutions exhibit similar behavior to Landau levels.

hep-th↗

arXiv2017

Weyl fermions in a family of Gödel-type geometries with a topological defect

In this paper we study Weyl fermions in a family of Gödel-type geometries in Einstein general relativity. We also consider that these solutions are embedded in a topological defect background. We solve the Weyl equation and find the energy eigenvalues and eigenspinors for all three cases of Gödel-type geometries where a topological defect is passing through them. We show that the presence of a topological in these geometries contributes to modification of the spectrum of energy. The energy zero modes for all three cases of the Gödel geometries are discussed.

hep-th↗

arXiv2017

Evolution of Landau levels in graphene-based topological insulators in the presence of wedge disclinations

In this paper we consider modification of electronic properties of graphene-based topological insulator in the presence of wedge disclination and magnetic field by adopting the Kane-Mele model with intrinsic spin-orbit coupling. Using the properly defined Dirac-Weyl equation for this system, an exact solution for the Landau levels is obtained. The influence of the topological defect on the evolution of Landau levels is discussed.

cond-mat.str-el↗

arXiv2017

Fermions in Gödel-type background space-times with torsion and the Landau quantization

In this paper, we analyze Dirac fermions in Gödel-type background space-times with torsion. We also consider the Gödel-type spacetimes embedded in a topological defect background. We show that relativistic bound states solutions to the Dirac equation can be obtained by dealing with three cases of the Gödel-type solutions with torsion, where a cosmic string passes through these three cases of the space-time. We obtain the relativistic energy levels for all cases of the Gödel-type solutions with torsion with a cosmic string, where we show that there exists an analogy with the Landau levels for Dirac particles. We also show that the presence of torsion in the space-time yields new contributions to the relativistic spectrum of energies and that the presence of the topological defect modifies the degeneracy of the relativistic energy levels.

hep-th↗