arXiv subjects

Yoonseok Hwang

Publications and source records attributed to Yoonseok Hwang.

At least 19 recordsLinked to original sources

arXiv2026

Exciton Alchemy: Chern Excitons from Trivial Bands

Exciton topology is commonly inherited from the topology of the underlying electronic bands. Recent theoretical work, however, has shown that the exciton Chern number can in general receive an additional contribution from the topology of the exciton envelope wave function, allowing, in principle, interaction-induced topological excitons even when the constituent electronic bands are topologically trivial. Here, we provide an explicit realization of this case by constructing a two-dimensional exciton model with topologically trivial conduction and valence bands that nevertheless hosts a Chern exciton diagnosed by inversion symmetry. Starting from a real-space limit of exponentially localized Wannier states for the conduction and valence bands, we identify the essential ingredients responsible for the emergent exciton topology and formulate a simple construction recipe. Our work demonstrates that interactions alone can generate nontrivial exciton topology, independent of the topology of the underlying electronic bands, and establishes a general framework for designing interaction-induced topological excitons.

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arXiv2026

Fragile Topology is Unstable Under Translation Refinement

Fragile topological phases become trivial upon the addition of suitable trivial bands, distinguishing them from stable topological phases. Nevertheless, various response phenomena and material realizations have been proposed for fragile phases. At the same time, many of these phenomena can also occur in atomic insulators, leaving open the question of what properties are specific to fragile phases. Enlarging the unit cell offers a natural perspective on this question. Band folding increases the number of bands in a manner analogous to adding trivial bands. In this work, we establish a systematic framework for determining the stability of fragile topology under unit-cell enlargement. We first establish a systematic criterion for trivialization under enlargements compatible with space-group symmetry, grounded in a physical electron-positron picture and formulated through a Hilbert-basis analysis of momentum-space symmetry data. We then show that, for all two-dimensional wallpaper groups, with or without spin-orbit coupling and/or time-reversal symmetry, every symmetry-indicated fragile phase is adiabatically connected to an atomic insulator in a suitable finite supercell and can therefore be trivialized by an arbitrarily small symmetry-preserving perturbation. Our results reveal that fragile topology has only finite stability under translation-symmetry refinement. This highlights that the fate of a fragile phase can depend on translation-symmetry-breaking perturbations, such as charge-density-wave ordering, and suggests that physical signatures insensitive to translation refinement are unlikely to uniquely characterize fragile topology.

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arXiv2026

Quantum Oscillation Signatures of $\mathbb{Z}_2$ Monopole Charge in Nodal-Ring Semimetals

Topological semimetals host band nodes characterized by quantized invariants that can appear in bulk responses, yet some invariants remain hidden from standard probes. In particular, band nodes can carry secondary topological charges whose transport signatures are still largely unexplored. Here we study three-dimensional nodal-line semimetals in which nodal rings carry both the Berry phase $w_1\pi$ and a $\mathbb{Z}_2$ monopole charge $w_2$. We show that magnetic quantum oscillations, usually treated as a probe of $w_1$, can directly diagnose $w_2$, with the relevant signal selected by the magnetic-field direction. For a field along the ring axis, the inner and outer extremal orbits of the toroidal Fermi surface both encircle the $w_2$-enforced thread and exhibit a topological phase shift $\nu w_2\pi$ in the $\nu$th harmonic, which is accessible through standard phase-resolved quantum-oscillation analysis. By contrast, for a field applied perpendicular to the ring axis, the relevant extremal orbit exhibits the usual $\pi$ phase shift associated with the Berry phase $w_1\pi$, independent of $w_2$. For weak doping, three-dimensional ABC-stacked graphdiyne is predicted to exhibit the proposed oscillations in a field range accessible with present-day high-field facilities.

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arXiv2026

Composite Quantum Geometry and Semiclassical Dynamics

We derive semiclassical equations of motion for general composite bound states in insulators and semiconductors, covering excitations such as excitons and trions. For neutral composites we find that a uniform external electric field does not couple to a Berry curvature term, contrary to the naive expectation from single-electron dynamics. Instead, a distinct quantum geometric quantity appears generically in the equations of motion. This quantity is the difference between inequivalent Berry connections that can be defined for the composite, generalising the concept of the quantum geometric dipole previously studied for excitons. In the case of charged composites such as trions, we find an additional Berry curvature contribution to the equations of motion. As we demonstrate, however, there is an infinite family of inequivalent composite Berry curvatures, and so care must be taken to make the correct choice that describes the physical dynamics. We explain how this choice should be made dependent on the definition of a spatial centre for the composite. We end by discussing composite dynamics that have no single-electron counterpart. We find that trions in magic-angle twisted bilayer graphene undergo a transverse drift under an applied electric field and that this is driven not only by the Berry curvature contribution but also by the quantum geometric dipole. The interplay of these two geometric contributions further imprints itself on the trion's internal dynamics, causing its dipole moment to oscillate in time.

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arXiv2026

Stable Wave-Function Zeros Indicate Exciton Topology

Excitons are bound states of electrons and holes whose band topology arises from an interplay between the topology of the underlying electronic bands and the structure of the electron-hole interaction. In crystalline solids, symmetry representations and topological invariants of the conduction and valence bands constrain the structure of the exciton envelope wave function. In particular, we show that crystalline symmetry can enforce stable zeros in the exciton wave function. These occur at high-symmetry momenta, including the optically accessible total momentum p=0. We work out how the stable zeros constrain both the relative exciton-band topology (the difference of exciton and non-interacting topological invariants) and the relative band topology (the difference of valence and conduction band invariants), all without requiring detailed knowledge of the band structure or interactions. We establish these results for two-band excitons in inversion- and rotation-symmetric systems in one and two dimensions, where the relevant topological invariants are the Berry phase in one dimension and the Chern number (modulo the rotation order) in two dimensions. In two dimensions, the exciton Chern number itself can also be constrained by zero patterns.

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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.

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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.

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arXiv2024

Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators

Crystalline symmetry can be used to predict bulk and surface properties of topological phases. For non-interacting cases, symmetry-eigenvalue analysis of Bloch states at high symmetry points in the Brillouin zone simplifies the calculation of topological quantities. However, when open boundaries are present, and only the point group part of the symmetry group remains, it is unclear how to utilize crystalline symmetries to diagnose band topology. In this work, we introduce topological crystalline markers to characterize bulk topology in $C_n$-symmetric ($n=2,3,4,6$) crystalline insulators and superconductors with and without translation symmetry. These markers are expressed using a crystalline symmetry operator and the ground state projector, and are defined locally in position space. First, we provide a general method to calculate topological markers in periodic systems with an arbitrary number of unit cells. This includes cases where momentum quantization does not span all necessary high-symmetry points for computing the topological quantities, which we address using twisted boundary conditions. Second, we map these markers to the Chern number, bulk polarization, and sector charge for two-dimensional $C_n$-symmetric insulators in symmetry classes A, AI, AII, and superconductors in class D. Finally, we show how to numerically calculate the markers in finite-size systems with translation-symmetry (and even rotation-symmetry) breaking defects, and how to diagnose the bulk topology from the marker. Our results demonstrate how to compute bulk topological crystalline invariants locally in position space, thereby providing broader scope to diagnosing bulk crystalline topology that works even in inhomogeneous systems where there is no global rotation symmetry.

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arXiv2024

Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators

Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ($\mathcal{T}$-) invariant (helical) 3D TCI$\unicode{x2014}$termed higher-order TCIs (HOTIs)$\unicode{x2014}$the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), "spin-Weyl" semimetals, and $\mathcal{T}$-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate that $β$-MoTe$_2$ realizes a spin-Weyl state and that $α$-BiBr hosts both 3D QSHI and T-DAXI regimes.

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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.

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arXiv2023

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.

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arXiv2023

Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators

Topological crystalline insulators (TCIs) can host anomalous surface states which inherits the characteristics of crystalline symmetry that protects the bulk topology. Especially, the diversity of magnetic crystalline symmetries indicates the potential for novel magnetic TCIs with distinct surface characteristics. Here, we propose a topological magnetic Dirac insulator (TMDI), whose two-dimensional surface hosts fourfold-degenerate Dirac fermions protected by either the $p'_c4mm$ or $p4'g'm$ magnetic wallpaper group. The bulk topology of TMDIs is protected by diagonal mirror symmetries, which give chiral dispersion of surface Dirac fermions and mirror-protected hinge modes. We propose candidate materials for TMDIs including Nd$_4$Te$_8$Cl$_4$O$_{20}$ and DyB$_4$ based on first-principles calculations, and construct a general scheme for searching TMDIs using the space group of paramagnetic parent states. Our theoretical discovery of TMDIs will facilitate future research on magnetic TCIs and illustrate a distinct way to achieve anomalous surface states in magnetic crystals.

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arXiv2023

Spin-momentum Locking and Topological Vector Charge Response with Conserved Spin

Spin-momentum locking plays a fundamental role in spintronics and, more broadly, is an important concept in condensed matter physics. In 2D and 3D, spin-momentum locking typically does not allow spin-conservation because the spin-1/2 operators of electrons anticommute. Instead, here we study spin-momentum locking terms with conserved, commuting pseudospins built from a combination of spin and orbitals. We find that 2D spin-momentum locking terms with conserved pseudospins generally lead to linearly dispersing modes at low-energy with anomalous charge and pseudospin currents. To cure the anomaly we show that such anomalous modes can be realized on the surface of a 3D Weyl semimetal (or an associated weak topological insulator) with a nonzero mixed spin-momentum quadrupole moment, which is determined by the momentum location and pseudospin eigenvalues of Weyl points at the Fermi level. Crucially, this mixed quadrupole moment captures a mixed pseudospin-charge bulk response that cancels the anomaly of surface modes, and can generate a giant 3D spin Hall effect, among other phenomena.

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arXiv2022

Unsupervised learning of topological phase diagram using topological data analysis

Topology and machine learning are two actively researched topics not only in condensed matter physics, but also in data science. Here, we propose the use of topological data analysis in unsupervised learning of the topological phase diagrams. This is possible because the quantum distance can capture the shape of the space formed by the Bloch wavefunctions as we sweep over the Brillouin zone. Therefore, if we minimize the volume of the space formed by the wavefunction through a continuous deformation, the wavefunctions will end up forming distinct spaces which depend on the topology of the wavefunctions. Combining this observation with the topological data analysis, which provides tools such as the persistence diagram to capture the topology of the space formed by the wavefunctions, we can cluster together Hamiltonians that give rise to similar persistence diagrams after the deformation. By examining these clusters as well as representative persistence diagrams in the clusters, we can draw the phase diagram as well as distinguish between topologically trivial and nontrivial phases. Our proposal to minimize the volume can be interpreted as finding geodesics in 1D Brillouin zone, and minimal surfaces in 2D and higher-dimensional Brillouin zones. Using this interpretation, we can guarantee the convergence of the minimization under certain conditions, which is an outstanding feature of our algorithm. We demonstrate the working principles of our machine learning algorithm using various models.

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arXiv2021

Geometric characterization of anomalous Landau levels of isolated flat bands

According to the Onsager's semiclassical quantization rule, the Landau levels of a band are bounded by its upper and lower band edges at zero magnetic field. However, there are two notable systems where the Landau level spectra violate this expectation, including topological bands and flat bands with singular band crossings, whose wave functions possess some singularities. Here, we introduce a distinct class of flat band systems where anomalous Landau level spreading (LLS) appears outside the zero-field energy bounds, although the relevant wave function is nonsingular. The anomalous LLS of isolated flat bands are governed by the cross-gap Berry connection that measures the wave-function geometry of multi bands. We also find that symmetry puts strong constraints on the LLS of flat bands. Our work demonstrates that an isolated flat band is an ideal system for studying the fundamental role of wave-function geometry in describing magnetic responses of solids.

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arXiv2021

General construction of flat bands with and without band crossings based on wave function singularity

In this work, we develop a systematic method of constructing flat-band models with and without band crossings. Our construction scheme utilizes the symmetry and spatial shape of a compact localized state (CLS) and also the singularity of the flat-band wave function obtained by a Fourier transform of the CLS (FT-CLS). In order to construct a flat-band model systematically using these ingredients, we first choose a CLS with a specific symmetry representation in a given lattice. Then, the singularity of FT-CLS indicates whether the resulting flat band exhibits a band crossing point or not. A tight-binding Hamiltonian with the flat band corresponding to the FT-CLS is obtained by introducing a set of basis molecular orbitals, which are orthogonal to the FT-CLS. Our construction scheme can be systematically applied to any lattice so that it provides a powerful theoretical framework to study exotic properties of both gapped and gapless flat bands arising from their wave function singularities.

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arXiv2021

Flat bands with band crossings enforced by symmetry representation

Flat bands have band crossing points with other dispersive bands in many systems including the canonical flat band models in the Lieb and kagome lattices. Here we show that some of such band degeneracy points are unavoidable because of the symmetry representation (SR) of the flat band under unitary symmetry. We refer to such a band degeneracy point of flat bands as a SR-enforced band crossing. SR-enforced band crossing is distinct from the conventional band degeneracy protected by symmetry eigenvalues or topological charges in that its protection requires both specific symmetry representation and band flatness of the flat band, simultaneously. Even $n$-fold rotation $C_n$ ($n=2,3,4,6$) symmetry, which cannot protect band degeneracy without additional symmetries due to its abelian nature, can protect SR-enforced band crossings in flat band systems. In two-dimensional flat band systems with $C_n$ symmetry, when the degeneracy of a SR-enforced band crossing is lifted by a $C_n$ symmetry-preserving perturbation, we obtain a nearly flat Chern band. Our theory not only explains the origin of the band crossing points of FBs existing in various models, but also gives a strict no-go theorem for isolated FBs in a given lattice arising from the SR.

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arXiv2021

Wave-function geometry of band crossing points in two-dimensions

Geometry of the wave function is a central pillar of modern solid state physics. In this work, we unveil the wave-function geometry of two-dimensional semimetals with band crossing points (BCPs). We show that the Berry phase of BCPs are governed by the quantum metric describing the infinitesimal distance between quantum states. For generic linear BCPs, we show that the corresponding Berry phase is determined either by an angular integral of the quantum metric, or equivalently, by the maximum quantum distance of Bloch states. This naturally explains the origin of the $π$-Berry phase of a linear BCP. In the case of quadratic BCPs, the Berry phase can take an arbitrary value between 0 and $2π$. We find simple relations between the Berry phase, maximum quantum distance, and the quantum metric in two cases: (i) when one of the two crossing bands is flat; (ii) when the system has rotation and/or time-reversal symmetries. To demonstrate the implication of the continuum model analysis in lattice systems, we study tight-binding Hamiltonians describing quadratic BCPs. We show that, when the Berry curvature is absent, a quadratic BCP with an arbitrary Berry phase always accompanies another quadratic BCP so that the total Berry phase of the periodic system becomes zero. This work demonstrates that the quantum metric plays a critical role in understanding the geometric properties of topological semimetals.

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