arXiv subjects

Mikel García-Díez

Publications and source records attributed to Mikel García-Díez.

7 recordsLinked to original sources

arXiv2026

Building blocks of topological band theory for photonic crystals

We derive a framework for classifying topological bands in three-dimensional photonic band structures, where the zero frequency polarization singularity implied by Maxwell's equations complicates the direct application of existing symmetry-based approaches. Building on recent advances in the regularization of photonic bands, we use the recently introduced concept of stable real-space invariants (SRSIs) to show how photonic band structures can be unambiguously characterized in terms of equivalence classes of band representations. We classify topologically trivial photonic bands using SRSIs, treating them as the fundamental building blocks of 3D photonic band structures. This means that if certain bands cannot be constructed from these building blocks, they are necessarily topological. Furthermore, we distinguish between photonic and electronic band structures by analyzing which SRSI values are allowed in systems with and without polarization singularity. We also explore the impact of the polarization singularity on the behavior of Wilson loops, providing new insights into the topological classification of 3D photonic systems.

physics.optics↗

arXiv2025

Symmetry-breaking-induced topology in FeSe

FeSe has been one of the most intensively studied iron-based superconductors over the past two decades, exhibiting a wide range of phenomena such as unconventional superconductivity, nematic order, magnetism, orbital-selective correlations, and structural phase transitions. While topologically non-trivial phases have been identified in certain cases -- such as Te-doped FeSe and monolayer FeSe -- topology in bulk FeSe has largely remained unexplored. In this work, we propose a new route to realize topological phases directly in bulk FeSe. We demonstrate that breaking the tetragonal $C_4$ rotational symmetry, thereby lowering the crystal symmetry, can drive FeSe into a strong topological insulating phase. To support this, we perform density functional theory calculations and analyze the band structure using Topological Quantum Chemistry and symmetry-based indicators. Our results show that both uniaxial strain and temperature-induced structural changes lead to non-trivial band topology. Moreover, incorporating electronic correlations through dynamical mean field theory reveals that the topological characteristics near the Fermi level remain robust, as the relevant bands experience only moderate renormalization. These findings highlight strain as a promising mechanism to induce topological phases in FeSe

cond-mat.mtrl-sci↗

arXiv2025

Transversality-Enforced Tight-Binding Models for 3D Photonic Crystals aided by Topological Quantum Chemistry

Tight-binding models can accurately replicate the band structure and topology of crystalline systems. They have been widely used in solid-state physics due to their versatility and low computational cost. It is straightforward to build an accurate tight-binding model of any crystalline system using the crystal's maximally localized Wannier functions as a basis. Unfortunately, in 3D photonic crystals, the transversality condition of Maxwell's equations precludes the construction of a basis of maximally localized Wannier functions via usual techniques. As a result, building reliable tight-binding models of 3D photonic crystals has not been straightforward up to now. In this work, we show how to overcome this problem using topological quantum chemistry, allowing us to express the band structure of the photonic crystal as a difference of band representations. This can be achieved by introducing a set of auxiliary modes, as recently proposed in Christensen et al., Phys. Rev. X 12, 021066 (2022), which regularizes the Gamma-point obstruction arising from the transversality constraint of Maxwell's equations. The decomposition into elementary band representations allows us to isolate a set of pseudo-orbitals that permit us to construct an accurate transversality-enforced tight-binding model that matches the dispersion, symmetry content, and topology of the 3D photonic crystal under study. Moreover, we show how to introduce the effects of a gyrotropic bias in the framework, modeled via non-minimal coupling to a static magnetic field. Our work provides the first systematic method to analytically model the photonic bands of the lowest transverse modes over the entire Brillouin zone via a transversality-enforced tight-binding model.

physics.optics↗

arXiv2025

Band representations in Strongly Correlated Settings: The Kitaev Honeycomb Model

In the study of quantum spin liquids, the Kitaev model plays a pivotal role due to the fact that its ground state is exactly known as well as the fact that it may be realized in strongly frustrated materials such as $α$-RuCl${}_3$. While topological insulators and superconductors can be investigated by means of topological band theory -- in particular the topological quantum chemistry (TQC) formalism -- the Kitaev model evades such a treatment, as it is not possible to set up a proper single-particle Green's function for it. We instead associate spin operators with ``orbitals'' that give rise to a band structure. It is thereby possible to analyze the corresponding excitation spectrum engendered by these localized excitations by means of TQC. Special attention is given to the low-energy topological edge mode spectrum. Our work sheds light on the question how the TQC formalism may be generalized to strongly correlated and topologically ordered systems like the Kitaev model.

cond-mat.str-el↗

arXiv2025

Origins of the anomalous Hall conductivity in the symmetry enforced Fe3GeTe2 nodal-line ferromagnet

Fe$_3$GeTe$_2$ has gained attention in the condensed matter community for its potential to be exfoliated into thin films with ferromagnetic (FM) order, thanks to its van der Waals layered structure and significant intrinsic anomalous Hall conductivity (AHC). In this work, we analyze the electronic structure and show that, contrary to prior claims, the bulk of the AHC cannot arise from gapped nodal lines. By studying the material's symmetry properties, both with and without spin-orbit coupling (SOC) and across paramagnetic and FM phases, we find that Fe$_3$GeTe$_2$ hosts mirror-symmetry-protected nodal lines, which support surface drumhead states. Additionally, we identify three key sources of AHC: nodal lines in the paramagnetic phase gapped by the FM order, Weyl points within specific energy ranges, and gaps between spin-up and spin-down bands caused by SOC. Finally, our calculations suggest that electron doping could increase the AHC up to four times compared to its value at the computed Fermi level.

cond-mat.mtrl-sci↗

arXiv2023

Axion Topology in Photonic Crystal Domain Walls

Axion insulators are 3D magnetic higher-order topological insulators protected by inversion-symmetry that exhibit hinge-localized chiral channels and induce quantized topological magnetoelectric effects. Recent research has suggested that axion insulators may be capable of detecting dark-matter axion-like particles by coupling to their axionic excitations. Beyond its fundamental theoretical interest, designing a photonic AXI offers the potential to enable the development of magnetically-tunable photonic switch devices through the manipulation of the axionic modes and their chiral propagation using external magnetic fields. Motivated by these facts, in this work, we propose a novel approach to induce axionic band topology in gyrotropic 3D Weyl photonic crystals gapped by supercell modulation. To quantize an axionic angle, we create domain-walls across inversion-symmetric photonic crystals, incorporating a phase-obstruction in the supercell modulation of their dielectric elements. This allows us to bind chiral channels on inversion-related hinges, ultimately leading to the realization of an axionic chiral channel of light. Moreover, by controlling the material gyrotropic response, we demonstrate a physically accessible way of manipulating the axionic modes through a small external magnetic bias, which provides an effective topological switch between different 1D chiral photonic fiber configurations. Remarkably, the unidirectional axionic hinge states supported by the photonic axion insulator are buried in a fully connected 3D dielectric structure, thereby being protected from radiation through the electromagnetic continuum. As a result, they are highly suitable for applications in guided-light communication, where the preservation and non-reciprocal propagation of photonic signals are of paramount importance.

physics.optics↗

arXiv2021

Cubic 3D Chern photonic insulators with orientable large Chern vectors

Time Reversal Symmetry (TRS) broken topological phases provide gapless surface states protected by topology, regardless of additional internal symmetries, spin or valley degrees of freedom. Despite the numerous demonstrations of 2D topological phases, few examples of 3D topological systems with TRS breaking exist. In this article, we devise a general strategy to design 3D Chern insulating (3D CI) cubic photonic crystals in a weakly TRS broken environment with orientable and arbitrarly large Chern vectors. The designs display topologically protected chiral and unidirectional surface states with disjoint equifrequency loops. The resulting crystals present the following novel characteristics: First, by increasing the Chern number, multiple surface states channels can be supported. Second, the Chern vector can be oriented along any direction simply changing the magnetization axis, opening up larger 3D CI/3D CI interfacing possibilities as compared to 2D. Third, by lowering the TRS breaking requirements, the system is ideal for realistic photonic applications where the magnetic response is weak.

cond-mat.mes-hall↗