arXiv subjects

Luis Elcoro

Publications and source records attributed to Luis Elcoro.

At least 19 recordsLinked to original sources

arXiv2026

Spin point group symmetry and classification of non-relativistic spin splitting in non-collinear magnetic structures: Identification of high-order spin splitting types (l=5,7, and 9)

A comprehensive study of the possible types of non-relativistic spin splitting of electronic bands in coplanar and non-coplanar magnetic structures is presented on the basis of spin-group theory. First, we tabulate all non-equivalent spin point groups (SpPGs) which can be expressed as a direct product of a nontrivial part and a spin-only group limited to be the intrinsic (trivial) one, or augmented by the time-reversal (TR) operation. This tabulation, which includes the listing of symmetry operations for 1249 nonequivalent SpPGs, is now available as an online database SPGENPOS in the Bilbao Crystallographic Server (BCS). This extends previous enumerations, in which the possible presence of TR in the magnetic point group was not taken into account, thus overlooking the full SpPG symmetry associated with the numerous magnetic structures which have a magnetic space group of type IV. For each of the listed coplanar and non-coplanar SpPGs, the spin-splitting that is symmetry allowed is analyzed in detail using the program STENSOR also in the BCS. Except for the SpPGs that include the operation 1', i.e., the combined operation of TR and space inversion, all other coplanar and non-coplanar SpPGs allow spin splitting at some order in a power expansion of the electron wave vector components. We find that, depending on the SpPG, spin-splitting terms can appear with the lowest-order monomials ranging from l=0 to 9, with the exception of l=8. This contrasts with the collinear case, where the lowest order is not higher than l=6, and where TR forbids any spin splitting. For the newly identified spin textures with powers l=5, 7, and 9, which are possible in some noncentrosymmetric SpPGs, the functional form of the spin splitting in terms of the components of the crystal momentum is given. One example of a real material, LaMnAu5, showing l=5 spin splitting is identified.

cond-mat.mtrl-sci↗

arXiv2026

Automatic calculation of symmetry-adapted tensors under spin-group symmetry. STENSOR, a new tool of the Bilbao Crystallographic Server

We present STENSOR, a new computational tool integrated into the Bilbao Crystallographic Server, designed for the automatic calculation of symmetry-adapted tensors under spin group symmetry. The program requires either a file containing the structural data of the magnetic compound or the generators of the oriented spin point group, together with the so-called generalized Jahn symbol associated to the tensor of interest. The user can propose any arbitrary tensor type or select a particular one from a predefined list. The program output returns the symmetry-adapted tensor under the spin point group and also under the magnetic point group, which is also calculated. The comparison of these two tensor forms allows to distinguish the coefficients that are due to spin-orbit coupling effects from those that have a non-relativistic origin and thus are usually more important. A couple of examples are given to illustrate the operation of the program.

cond-mat.mtrl-sci↗

arXiv2025

Revisiting the Abundance of Topological Materials

The classification of topological materials is revisited using advanced computational workflows that integrate hybrid density functional theory calculations with exact Hartree-Fock exchange. Unlike previous studies, our workflow optimizes atomic configurations obtained from the Materials Project Database, followed by precise electronic structure calculations. Our results based on hybrid density functional theory calculations reveal that only 15\% of materials are topologically nontrivial, which is in stark contrast to the previously reported 30\% based on semi-local exchange and correlation functionals. This discrepancy underscores the critical dependence of topological classifications on accurate atomic and electronic structures, rendering the abundance of topological materials much lower than generally assumed.

cond-mat.mtrl-sci↗

arXiv2025

Stable Real-Space Invariants and Topology Beyond Symmetry Indicators

We introduce stable real-space invariants (SRSIs), topological invariants defined from adiabatic deformations between Wannier states, generalizing previously discovered local and composite real-space invariants. SRSIs are $\mathbb{Z}$- and $\mathbb{Z}_n$-valued ($n=2,4$) linear combinations of Wannier state multiplicities characterizing the stable equivalence of atomic insulators. We enumerate all SRSIs in nonmagnetic space groups with and without spin-orbit coupling. $\mathbb{Z}$SRSIs are in one-to-one correspondence with momentum-space symmetry data and thus determine symmetry indicators of topology (SIs). $\mathbb{Z}_n$SRSIs capture real-space information beyond momentum-space symmetry data and SIs. Applying SRSIs to split elementary band representations (EBRs) whose symmetry data decomposes into positive sums of other EBR symmetry data, we diagnose the topology of all 211 cases across 51 space groups except for 8 exceptions in 5 space groups. Our results solidify Topological Quantum Chemistry beyond SIs and momentum-space symmetry data. Finally, we use SRSIs to diagnose an obstructed atomic insulator in a realistic material.

cond-mat.mes-hall↗

arXiv2025

Crystal tensor properties of magnetic materials with and without spin-orbit coupling. Application of spin point groups as approximate symmetries

Spin space groups, formed by operations where the rotation of the spins is independent of the accompanying operation acting on the crystal structure, are appropriate groups to describe the symmetry of magnetic structures with null spin-orbit coupling. Their corresponding spin point groups are the symmetry groups to be considered for deriving the symmetry constraints on the form of the crystal tensor properties of such idealized structures. These groups can also be taken as approximate symmetries (with some restrictions) of real magnetic structures, where spin-orbit and magnetic anisotropy are however present. Here we formalize the invariance transformation properties that must satisfy the most important crystal tensors under a spin point group. This is done using modified Jahn symbols, which generalize those applicable to ordinary magnetic point groups [Gallego et al., Acta Cryst. (2019) A75, 438-447]. The analysis includes not only equilibrium tensors, but also transport, optical and non-linear optical susceptibility tensors. The constraints imposed by spin collinearity and coplanarity within the spin group formalism on a series of representative tensors are discussed and compiled. As illustrative examples, the defined tensor invariance equations have been applied to some known magnetic structures, showing the differences of the symmetry-adapted form of some relevant tensors, when considered under the constraints of its spin point group or its magnetic point group. This comparison, with the spin point group implying additional constraints in the tensor form, can allow one to distinguish those magnetic-related properties that can be solely attributed to spin-orbit coupling from those that are expected even when spin-orbit coupling is negligible.

cond-mat.mtrl-sci↗

arXiv2024

2D Theoretically Twistable Material Database

The study of twisted two-dimensional (2D) materials, where twisting layers create moir\'e superlattices, has opened new opportunities for investigating topological phases and strongly correlated physics. While systems such as twisted bilayer graphene (TBG) and twisted transition metal dichalcogenides (TMDs) have been extensively studied, the broader potential of a seemingly infinite set of other twistable 2D materials remains largely unexplored. In this paper, we define "theoretically twistable materials" as single- or multi-layer structures that allow for the construction of simple continuum models of their moir\'e structures. This excludes, for example, materials with a "spaghetti" of bands or those with numerous crossing points at the Fermi level, for which theoretical moir\'e modeling is unfeasible. We present a high-throughput algorithm that systematically searches for theoretically twistable semimetals and insulators based on the Topological 2D Materials Database. By analyzing key electronic properties, we identify thousands of new candidate materials that could host rich topological and strongly correlated phenomena when twisted. We propose representative twistable materials for realizing different types of moir\'e systems, including materials with different Bravais lattices, valleys, and strength of spin-orbital coupling. We provide examples of crystal growth for several of these materials and showcase twisted bilayer band structures along with simplified twisted continuum models. Our results significantly broaden the scope of moir\'e heterostructures and provide a valuable resource for future experimental and theoretical studies on novel moir\'e systems.

cond-mat.mtrl-sci↗

arXiv2024

Two-dimensional Topological Quantum Chemistry and Catalog of Topological Materials

We adapt the topological quantum chemistry formalism to layer groups, and apply it to study the band topology of 8,872 entries from the computational two-dimensional (2D) materials databases C2DB and MC2D. In our analysis, we find 4,073 topologically non-trivial or obstructed atomic insulator entries, including 905 topological insulators, 602 even-electron number topological semimetals, and 1,003 obstructed atomic insulators. We thus largely expand the library of known topological or obstructed materials in two dimensions, beyond the few hundreds known to date. We additionally classify the materials into four categories: experimentally existing, stable, computationally exfoliated, and not stable. We present a detailed analysis of the edge states emerging in a number of selected new materials, and compile a Topological 2D Materials Database (2D-TQCDB) containing the band structures and detailed topological properties of all the materials studied in this work. The methodology here developed is implemented in new programs available to the public, designed to study the topology of any non-magnetic monolayer or multilayer 2D material.

cond-mat.mes-hall↗

arXiv2024

New magnetic topological materials from high-throughput search

We conducted a high-throughput search for topological magnetic materials on 522 new, experimentally reported commensurate magnetic structures from MAGNDATA, doubling the number of available materials on the Topological Magnetic Materials database. This brings up to date the previous studies which had become incomplete due to the discovery of new materials. For each material, we performed first-principle electronic calculations and diagnosed the topology as a function of the Hubbard U parameter. Our high-throughput calculation led us to the prediction of 250 experimentally relevant topologically non-trivial materials, which represent 47.89% of the newly analyzed materials. We present five remarkable examples of these materials, each showcasing a different topological phase: Mn${}_2$AlB${}_2$ (BCSID 1.508), which exhibits a nodal line semimetal to topological insulator transition as a function of SOC, CaMnSi (BCSID 0.599), a narrow gap axion insulator, UAsS (BCSID 0.594) a 5f-orbital Weyl semimetal, CsMnF${}_4$ (BCSID 0.327), a material presenting a new type of quasi-symmetry protected closed nodal surface and FeCr${}_2$S${}_4$ (BCSID 0.613), a symmetry-enforced semimetal with double Weyls and spin-polarised surface states.

cond-mat.mtrl-sci↗

arXiv2022

Catalogue of topological phonon materials

Phonons play a crucial role in many properties of solid state systems, such as thermal and electrical conductivity, neutron scattering and associated effects or superconductivity. Hence, it is expected that topological phonons will also lead to rich and unconventional physics and the search of materials hosting topological phonons becomes a priority in the field. In electronic crystalline materials, a large part of the topological properties of Bloch states can be indicated by their symmetry eigenvalues in reciprocal space. This has been adapted to the high-throughput calculations of topological materials, and more than half of the stoichiometric materials on the databases are found to be topological insulators or semi-metals. Based on the existing phonon materials databases, here we have performed the first catalogue of topological phonon bands for more than ten thousand three-dimensional crystalline materials. Using topological quantum chemistry, we calculate the band representations, compatibility relations, and band topologies of each isolated set of phonon bands for the materials in the phonon databases. We have also calculated the real space invariants for all the topologically trivial bands and classified them as atomic and obstructed atomic bands. In particular, surface phonon modes (dispersion) are calculated on different cleavage planes for all the materials. Remarkably, we select more than one thousand "ideal" non-trivial phonon materials to fascinate the future experimental studies. All the data-sets obtained in the the high-throughput calculations are used to build a Topological Phonon Database.

cond-mat.mtrl-sci↗

arXiv2022

Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries

Adding magnetic flux to a band structure breaks Bloch's theorem by realizing a projective representation of the translation group. The resulting Hofstadter spectrum encodes the non-perturbative response of the bands to flux. Depending on their topology, adding flux can enforce a bulk gap closing (a Hofstadter semimetal) or boundary state pumping (a Hofstadter topological insulator). In this work, we present a real-space classification of these Hofstadter phases. We give topological indices in terms of symmetry-protected Real Space Invariants (RSIs) which encode bulk and boundary responses of fragile topological states to flux. In fact, we find that the flux periodicity in tight-binding models causes the symmetries which are broken by the magnetic field to reenter at strong flux where they form projective point group representations. We completely classify the reentrant projective point groups and find that the Schur multipliers which define them are Arahanov-Bohm phases calculated along the bonds of the crystal. We find that a nontrivial Schur multiplier is enough to predict and protect the Hofstadter response with only zero-flux topology.

cond-mat.mes-hall↗

arXiv2022

Hierarchy of quasi-symmetries and degeneracies in chiral crystal materials CoSi

In materials, certain approximated symmetry operations can exist in a lower-order approximation of the effective model but are good enough to influence the physical responses of the system, and these approximated symmetries were recently dubbed "quasi-symmetries" \cite{guo_arxiv_2021}. In this work, we reveal a hierarchy structure of the quasi-symmetries and the corresponding nodal structures that they enforce via two different approaches of the perturbation expansions for the effective model in the chiral crystal material CoSi. In the first approach, we treat the spin-independent linear momentum (k) term as the zero-order Hamiltonian. Its energy bands are four-fold degenerate due to an SU(2)$\times$SU(2) quasi-symmetry. We next consider both the k-independent spin-orbit coupling (SOC) and full quadratic-k terms as the perturbation terms and find that the first-order perturbation leads to a model described by a self-commuting "stabilizer code" Hamiltonian with a U(1) quasi-symmetry that can protect nodal planes. In the second approach, we treat the SOC-free linear-k term and k-independent SOC term as the zero-order. They exhibit an SU(2) quasi-symmetry, which can be reduced to U(1) quasi-symmetry by a choice of quadratic terms. Correspondingly, a two-fold degeneracy for all the bands due to the SU(2) quasi-symmetry is reduced to two-fold nodal planes that are protected by the U(1) quasi-symmetry. For both approaches, including higher-order perturbation will break the U(1) quasi-symmetry and induce a small gap $\sim$ 1 meV for the nodal planes. These quasi-symmetry protected near degeneracies play an essential role in understanding recent quantum oscillation experiments in CoSi.

cond-mat.mes-hall↗

arXiv2021

Three-Dimensional Real Space Invariants, Obstructed Atomic Insulators and A New Principle for Active Catalytic Sites

Topologically trivial insulators come in two kinds: atomic, where the Wannier charge centers (WCCs) are localized on the atoms, and obstructed atomic, where the WCCs are located away from the atoms. The latter, which can exhibit interesting surface states and possibly have much larger band gaps than the topological insulators, have so far not been classified in three-dimensional (3D) crystalline materials. In this paper, we developed the 3D real space invariants (RSIs) for the 1651 Shubnikov space groups with the spin-orbit coupling and provide the full classification of 3D obstructed atomic insulators (OAIs) by the RSIs. We then apply the theory to the entire database of materials on the Topological Quantum Chemistry website and Topological Magnetic Materials website, obtaining all the OAIs so far existing in nature. We find that, out of the 34013 paramagnetic and 296 magnetic topologically trivial insulators, there are 3383 paramagnetic and 30 magnetic OAIs. All of them present a filling anomaly under certain open-boundary conditions and exhibit obstructed surface states (OSSs). We further refine the atomic insulator concept to obtain the orbital-selected OAIs (OOAIs), where the WCC of the system is located at a Wyckoff position occupied by an atom but forms a symmetric representation that does not belong to the outer-shell electrons of the given atom. In such a way, we obtain a further 121 OOAIs. Furthermore, we analyze the catalytic properties of one of the OAIs in a "proof of principle" experiment. By using the single crystal of 2H-MoS2 as a hydrogen evolution catalyst, we directly prove that the catalytic activities arise from the surfaces with OSSs. Additional potential applications of the 3D RSIs and OAIs in, for example, electrochemistry, asymmetric catalysis, superconductivity, and Josephson diode will be discussed.

cond-mat.mtrl-sci↗

arXiv2021

Filling-Enforced Obstructed Atomic Insulators

Topological band theory has achieved great success in the high-throughput search for topological band structures both in paramagnetic and magnetic crystal materials. However, a significant proportion of materials are topologically trivial insulators at the Fermi level. In this paper, we show that, remarkably, for a subset of the topologically trivial insulators, knowing only their electron number and the Wyckoff positions of the atoms we can separate them into two groups: the obstructed atomic insulator (OAI) and the atomic insulator (AI). The interesting group, the OAI, have a center of charge not localized on the atoms. Using the theory of topological quantum chemistry, in this work we first derive the necessary and sufficient conditions for a topologically trivial insulator to be a filling enforced obstructed atomic insulator (feOAI) in the 1651 Shubnikov space groups. Remarkably, the filling enforced criteria enable the identification of obstructed atomic bands without knowing the representations of the band structures. Hence, no ab-initio calculations are needed for the filling enforced criteria, although they are needed to obtain the band gaps. With the help of the Topological Quantum Chemistry website, we have performed a high-throughput search for feOAIs and have found that 957 ICSD entries (638 unique materials) are paramagnetic feOAIs, among which 738 (475) materials have an indirect gap. The metallic obstructed surface states of feOAIs are also showcased by several material examples.

cond-mat.mtrl-sci↗

arXiv2021

General Construction and Topological Classification of All Magnetic and Non-Magnetic Flat Bands

Exotic phases of matter emerge from the interplay between strong electron interactions and non-trivial topology. Owing to their lack of dispersion at the single-particle level, systems harboring flat bands are excellent testbeds for strongly interacting physics, with twisted bilayer graphene serving as a prime example. On the other hand, existing theoretical models for obtaining flat bands in crystalline materials, such as the line-graph formalism, are often too restrictive for real-life material realizations. Here we present a generic technique for constructing perfectly flat bands from bipartite crystalline lattices. Our prescription encapsulates and generalizes the various flat band models in the literature, being applicable to systems with any orbital content, with or without spin-orbit coupling. Using Topological Quantum Chemistry, we build a complete topological classification in terms of symmetry eigenvalues of all the gapped and gapless flat bands, for all 1651 Magnetic Space Groups. In addition, we derive criteria for the existence of symmetry-protected band touching points between the flat and dispersive bands, and we identify the gapped flat bands as prime candidates for fragile topological phases. Finally, we show that the set of all (gapped and gapless) perfectly flat bands is finitely generated and construct the corresponding bases for all 1651 Shubnikov Space Groups.

cond-mat.mes-hall↗

arXiv2021

Catalogue of Flat-Band Stoichiometric Materials

Topological electronic flatten bands near or at the Fermi level are a promising avenue towards unconventional superconductivity and correlated insulating states. However, the related experiments are mostly limited to the engineered materials, such as moire systems. Here we present a catalogue of all the three-dimensional stoichiometric materials with flat bands around the Fermi level that exist in nature. We consider 55,206 materials from the Inorganic Crystal Structure Database catalogued using the Topological Quantum Chemistry website which provides their structural parameters, space group (SG), band structure, density of states and topological characterization. We combine several direct signatures and properties of band flatness to a high-throughput analysis of all crystal structures. In particular, we identify materials hosting line-graph or bipartite sublattices - either in two or three dimensions - likely leading to flat bands. From this trove of information, we create the Materials Flatband Database website, a powerful search engine for future theoretical and experimental studies. We use it to extract a curated list of 2,379 materials, with among them 345 promising candidates, potentially hosting flat bands whose charge centers are not strongly localized on the atomic sites. We showcase five representative materials: KAg[CN]2 in SG 163 $(P\bar{3}1c)$, Pb2Sb2O7 in SG 227 $(Fd\bar{3}m)$, Rb2CaH4 in SG 139 $(I4/mmm)$, Ca2NCl in SG 166 $(R\bar{3}m)$ and WO3 in SG 221 $(Pm\bar{3}m)$. We provide a theoretical explanation for the origin of their flat bands close to the Fermi energy using the $S$-matrix method introduced in a parallel work [Calugaru et al., Nature Physics 18, 185 (2022)].

cond-mat.str-el↗

arXiv2021

Topological Materials Discovery from Crystal Symmetry

Topological materials discovery has evolved at a rapid pace over the past 15 years following the identification of the first nonmagnetic topological insulators (TIs), topological crystalline insulators (TCIs), and 3D topological semimetals (TSMs). Most recently, through complete analyses of symmetry-allowed band structures - including the theory of Topological Quantum Chemistry (TQC) - researchers have determined crystal-symmetry-enhanced Wilson-loop and complete symmetry-based indicators for nonmagnetic topological phases, leading to the discovery of higher-order TCIs and TSMs. The recent application of TQC and related methods to high-throughput materials discovery has revealed that over half of all of the known stoichiometric, solid-state, nonmagnetic materials are topological at the Fermi level, over 85% of the known stoichiometric materials host energetically isolated topological bands, and that just under $2/3$ of the energetically isolated bands in known materials carry the stable topology of a TI or TCI. In this Review, we survey topological electronic materials discovery in nonmagnetic crystalline solids from the prediction of the first 2D and 3D TIs to the recently introduced methods that have facilitated large-scale searches for topological materials. We also discuss future venues for the identification and manipulation of solid-state topological phases, including charge-density-wave compounds, magnetic materials, and 2D few-layer devices.

cond-mat.mtrl-sci↗

arXiv2021

All Topological Bands of All Nonmagnetic Stoichiometric Materials

Topological Quantum Chemistry and Symmetry-Based Indicators have facilitated large-scale searches for materials with topological properties at the Fermi energy ($E_{F}$). We report the completion of a publicly accessible catalog of stable and fragile topology in all of the bands both at and away from $E_{F}$ in the 96,196 processable entries in the Inorganic Crystal Structure Database. Our calculations represent the completion of the symmetry-indicated band topology of known nonmagnetic materials, and enable the discovery of repeat-topological and supertopological materials, which include rhombohedral bismuth and Bi$_2$Mg$_3$. We find that 52.65% of all materials are topological at $E_{F}$, roughly $2/3$ of bands across all materials exhibit symmetry-indicated stable topology, and that 87.99% of all materials contain at least one stable or fragile topological band.

cond-mat.mtrl-sci↗

arXiv2020

Magnetic Topological Quantum Chemistry

For over 100 years, the group-theoretic characterization of crystalline solids has provided the foundational language for diverse problems in physics and chemistry. However, the group theory of crystals with commensurate magnetic order has remained incomplete for the past 70 years, due to the complicated symmetries of magnetic crystals. In this work, we complete the 100-year-old problem of crystalline group theory by deriving the small corepresentations, momentum stars, compatibility relations, and magnetic elementary band corepresentations of the 1,421 magnetic space groups (MSGs), which we have made freely accessible through tools on the Bilbao Crystallographic Server. We extend Topological Quantum Chemistry to the MSGs to form a complete, real-space theory of band topology in magnetic and nonmagnetic crystalline solids - Magnetic Topological Quantum Chemistry (MTQC). Using MTQC, we derive the complete set of symmetry-based indicators of electronic band topology, for which we identify symmetry-respecting bulk and anomalous surface and hinge states.

cond-mat.mes-hall↗