arXiv subjects

Frank Schindler

Publications and source records attributed to Frank Schindler.

At least 19 recordsLinked to original sources

arXiv2026

Temporal Localisation of Waves from Imaginary Line-Gap Topology

For non-Hermitian Hamiltonians, gain, loss, and non-reciprocity produce complex eigenvalues which, in turn, facilitate different kinds of topological phases. One example is the imaginary line-gap phase, where eigenvalues cannot lie on the real line. This notion was recently shown to explain the robust temporal localisation of waves in photonic quantum walks and time-varying metamaterials. In these systems, waves localise around a time interface between topologically inequivalent mediums. At the core of this phenomenon is a $\mathcal{PT}$-symmetric two-mode model, where the non-trivial topology arises due to the $\mathbb{Z}_2$ classification of the AI symmetry class. In this work, we study two-mode models in all non-Hermitian symmetry classes. We find that robust temporal localisation generically follows as a physical consequence of imaginary line-gap topology according to a simple diagnostic: at least one of time-reversal symmetry ($\mathcal{T}^{\hspace{0.05em}2} = 1$) and particle-hole symmetry ($\mathcal{C}^2 = 1$) must be present. Our results provide a comprehensive symmetry-based guide to the observation of the topologically protected temporal localisation of waves.

physics.optics↗

arXiv2026

Topological Dislocation Response in Elementary Semiconductors

We study elementary semiconductors and insulators that are symmetric under spatial inversion: silicon, diamond, germanium, and black phosphorene. These materials are ideal candidates for realizing obstructed atomic insulators, which differ from trivial atomic insulators by a quantized spatial shift of their electronic Wannier centers with respect to the atomic lattice. We use symmetry indicator invariants that allow the prediction of non-trivial responses to crystal dislocations in these materials. We find that edge dislocations generically exhibit a non-trivial response, while screw dislocations always display a trivial response. With the aid of numerical simulations of realistic tight-binding models, we confirm the presence of mid-gap polarization bands localized along dislocations in silicon, diamond, and germanium.

cond-mat.mes-hall↗

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.

cond-mat.mes-hall↗

arXiv2026

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↗

arXiv2026

Topology from Decoherence

Decoherence is conventionally regarded as an obstacle to realizing topological quantum phases. This has motivated extensive efforts to suppress noise in candidate topological materials and devices. Here, we show that decoherence can instead induce topological phenomena. We demonstrate this in a lattice system subject to environment-induced dephasing. The noise-averaged dynamics, governed by an interacting quantum master equation, realize a topological phase characterized by a winding number and the non-Hermitian skin effect. The dynamical consequence is striking: the correlated nature of the stochastic noise yields asymmetric diffusion, whose direction is fixed by the winding number and is reversible only through a topological phase transition. This effect is induced purely by interactions, distinguishing it from previous studies of free, effectively single-particle systems. It also disappears upon postselecting measurement outcomes, confirming that it is a genuinely open-system phenomenon with no effective Hamiltonian description. Remarkably, the model remains analytically tractable. Our results establish correlated quantum noise as a route to topology in open many-body systems, beyond free-particle and non-Hermitian Hamiltonian paradigms.

quant-ph↗

arXiv2026

Anomalous suppression of quantum chaos between two integrable limits

Level statistics in non-integrable quantum many-body systems with time reversal symmetry are expected to follow the Gaussian Orthogonal Ensemble (GOE), a hallmark of quantum chaos. However, we show that the interacting Su-Schrieffer-Heeger model exhibits a clear suppression of the mean level-spacing ratio $\langle r\rangle$ from the GOE value $\approx 0.535$, persisting deep in the nonintegrable regime. This challenges the conventional association between non-integrability and fully chaotic spectral statistics. Using exact diagonalization supported by semi-analytical arguments, we trace this anomaly to incomplete hybridization of many-body band states inherited from the noninteracting band structure. The resulting restructuring of the spectrum weakens level repulsion without restoring integrability. We show the robustness of this mechanism in extensions of the model which break chiral and inversion symmetry.

cond-mat.stat-mech↗

arXiv2026

Topological Localisation in Time from PT Symmetry

Time has entered the domain of topological phases in the field of non-Hermitian physics. Previous studies have relied on periodic modulation in time to make an intuitive connection to established spatial topological invariants, albeit with energy and momentum exchanged. This connection has revealed the potential for topological interface states along the time axis, analogous to those in spatial models. In this work, we uncover a theoretical framework describing such topological interface states along the time axis, with no underlying connection to spatial models nor need for periodic driving. This new framework uncovers that this phenomenon -- the robust localisation of waves at an interface -- appears in every system that has parity-time symmetry and two coupled modes or bands, regardless of its spatial dimensionality. The topological nature of this localisation is understood by the identification of certain topological phases that are specific to parity-time-symmetric models of two coupled modes. Our theoretical framework can be applied to all existing experimental observations, notably including photonic time crystals, and serves as a foundation for future experiments in areas in which the topological localisation of waves in time has yet to be studied.

physics.optics↗

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.

cond-mat.mes-hall↗

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.

cond-mat.mes-hall↗

arXiv2026

A pedestrian's guide to the topological phases of free fermions

These lecture notes explain the classification of some simple fermionic topological phases of matter in a pedestrian manner, with an aim to be maximally pedagogical = doing things in excruciating detail. We focus on a many-body perspective, even if many of the models we work with are non-interacting. We start out with symmetry protected topological (SPT) phases of free fermions that are protected by U(1) symmetry = topological insulators. We then look at fermion topological phases that don't even need a symmetry = topological superconductors, and explain how their classification changes in presence of spinless time-reversal symmetry. We close by perturbatively checking which of the 1D topological phases we had found are stable to interactions.

cond-mat.str-el↗

arXiv2026

Exciton Berryology

In translationally invariant semiconductors that host exciton bound states, one can define an infinite number of possible exciton Berry connections. These correspond to the different ways in which a many-body exciton state, at fixed total momentum, can be decomposed into free electron and hole Bloch states that are entangled by an exciton envelope wave function. Inspired by the modern theory of polarization, we define an exciton projected position operator whose eigenvalues single out two unique choices of exciton Berry phase and associated Berry connection - one for electrons, and one for holes. We clarify the physical meaning of these exciton Berry phases and provide a discrete Wilson loop formulation that allows for their numerical calculation without a smooth gauge. As a corollary, we obtain a gauge-invariant expression for the exciton polarisation at a given total momentum, i.e. the mean separation of the electron and hole within the exciton wave function. In the presence of crystalline inversion symmetry, the electron and hole exciton Berry phases are quantized to the same value and we derive how this value can be expressed in terms of inversion eigenvalues of the many-body exciton state. We then consider $C_2 \mathcal{T}$ symmetry, for which no symmetry eigenvalues are available as it is anti-unitary, and confirm that the exciton Berry phase remains quantized and still diagnoses topologically distinct exciton bands. The notion of shift excitons, whose exciton Wannier states are displaced from those of the non-interacting bands by a quantized amount, can therefore be generalised beyond symmetry indicators.

cond-mat.mes-hall↗

arXiv2026

Berry Curvature of Low-Energy Excitons in Rhombohedral Graphene

We investigate low energy excitons in rhombohedral pentalayer graphene encapsulated by hexagonal boron nitride (hBN/R5G/hBN), focusing on the regime at the experimental twist angle $θ= 0.77^\circ$ and with an applied electric field. We introduce a new low-energy two-band model of rhombohedral graphene that captures the band structure more accurately than previous models while keeping the number of parameters low. Using this model, we show that the centres of the exciton Wannier functions are displaced from the moiré unit cell origin by a quantised amount - they are instead localised at $C_3$-symmetric points on the boundary. We also find that the exciton shift is electrically tunable: by varying the electric field strength, the exciton Wannier centre can be exchanged between inequivalent corners of the moiré unit cell. Our results suggest the possibility of detecting excitonic corner or edge modes, as well as novel excitonic crystal defect responses in hBN/R5G/hBN. Lastly, we find that the excitons in hBN/R5G/hBN inherit excitonic Berry curvature from the underlying electronic bands, enriching their semiclassical transport properties. Our results position rhombohedral graphene as a compelling tunable platform for probing exciton topology in moiré materials.

cond-mat.mes-hall↗

arXiv2026

Microscopic theory of Chern polarization via crystalline defect charge

The modern theory of polarization does not apply in its original form to systems with non-trivial band topology. Chern insulators are one such example. Defining polarization for them is complicated because they are insulating in the bulk but exhibit metallic edge states. Wannier functions formed a key ingredient of the original modern theory of polarization, but it has been considered that these cannot be applied to Chern insulators since they are no longer exponentially localized and the Wannier center, obtained from the Zak phase, is no longer gauge invariant. In this article, we provide an unambiguous definition of absolute polarization for a Chern insulator in terms of the Zak phase. We obtain our expression by studying the non-quantized fractional charge bound to lattice dislocations. Our expression can be computed directly from bulk quantities and makes no assumption on the edge state filling. It is fully consistent with previous results on the quantized charge bound to dislocations in the presence of crystalline symmetry. At the same time, our result is more general since it also applies to Chern insulators which do not have crystalline symmetries other than translations.

cond-mat.str-el↗

arXiv2026

Lindbladian versus Postselected Non-Hermitian Topology

The recent topological classification of non-Hermitian `Hamiltonians' is usually interpreted in terms of pure quantum states that decay or grow with time. However, many-body systems with loss and gain are typically better described by mixed-state open quantum dynamics, which only correspond to pure-state non-Hermitian dynamics upon a postselection of measurement outcomes. Since postselection becomes exponentially costly with particle number, we here investigate to what extent the most important example of non-Hermitian topology can survive without it: the non-Hermitian skin effect and its relationship to a bulk winding number in one spatial dimension. After defining the winding number of the Lindbladian superoperator for a quadratic fermion system, we systematically relate it to the winding number of the associated postselected non-Hermitian Hamiltonian. We prove that the two winding numbers are equal (opposite) in the absence of gain (loss), and provide a physical explanation for this relationship. When both loss and gain are present, the Lindbladian winding number typically remains quantized and non-zero, though it can change sign at a phase transition separating the loss and gain-dominated regimes. This transition, which leads to a reversal of the Lindbladian skin effect localization, is rendered invisible by postselection. We also identify a case where removing postselection induces a skin effect from otherwise topologically trivial non-Hermitian dynamics.

quant-ph↗

arXiv2025

Momentum-space modulated symmetries in the Luttinger liquid

The chiral Luttinger liquid develops quantum chaos as soon as a -- however slight -- nonlinear dispersion is introduced for the microscopic electronic degrees of freedom. For this nonlinear version of the model, we identify an infinite family of translation-invariant interaction potentials with corresponding modulated symmetries. These symmetries are highly unconventional: they are modulated in momentum space (and do not seem to have an easy physical interpretation). We develop a systematic understanding of these symmetries and study the resulting blocks in the Hamiltonian. In particular, this approach allows us to predict the analytic Hamiltonian block sizes and derive asymptotic scaling laws in the limit of large total momentum. These blocks are reminiscent of Hilbert space fragmentation in that, even though they are labeled by a symmetry, this symmetry is highly nonlocal and does not have a simple interpretation. We corroborate this result by studying entanglement entropy and level statistics.

cond-mat.str-el↗

arXiv2025

Nonlinear breathers with crystalline symmetries

Nonlinear lattice models can support "discrete breather" excitations that stay localized in space for all time. By contrast, the localized Wannier states of linear lattice models are dynamically unstable. Nevertheless, symmetric and exponentially localized Wannier states are a central tool in the classification of band structures with crystalline symmetries. Moreover, the quantized transport observed in nonlinear Thouless pumps relies on the fact that -- at least in a specific model -- discrete breathers recover Wannier states in the limit of vanishing nonlinearity. Motivated by these observations, we investigate the correspondence between nonlinear breathers and exponentially localised Wannier states for a family of discrete nonlinear Schrödinger equations with crystalline symmetries. We develop a formalism to analytically predict the breathers' spectrum, center of mass and symmetry data, and apply this to nonlinear generalizations of the Su-Schrieffer-Heeger chain and the breathing kagome lattice.

cond-mat.mes-hall↗

arXiv2024

Interaction-induced crystalline topology of excitons

We apply the topological theory of symmetry indicators to interaction-induced exciton band structures in centrosymmetric semiconductors. Crucially, we distinguish between the topological invariants inherited from the underlying electron and hole bands, and those that are intrinsic to the exciton wavefunction itself. Focusing on the latter, we show that there exists a class of exciton bands for which the maximally-localised exciton Wannier states are shifted with respect to the electronic Wannier states by a quantised amount; we call these excitons shift excitons. Our analysis explains how the exciton spectrum can be topologically nontrivial and sustain exciton edge states in open boundary conditions even when the underlying noninteracting bands have a trivial atomic limit. We demonstrate the presence of shift excitons as the lowest energy neutral excitations of the Su-Schrieffer-Heeger model in its trivial phase when supplemented by local two-body interactions, and show that they can be accessed experimentally in local optical conductivity measurements.

cond-mat.mes-hall↗

arXiv2024

Engineering Miniband Topology via Band-Folding in Moiré Superlattice Materials

The emergence of topologically non-trivial flat bands in moiré materials provides an opportunity to explore the interplay between topological physics and correlation effects, leading to the recent experimental realization of interacting topological phases, e.g. fractional Chern insulators. In this work, we propose a mechanism of band inversion induced by band-folding from the moiré superlattice potential for engineering topological minibands in moiré materials. We illustrate this mechanism via two classes of model Hamiltonians, namely the Rashba model and the Bernevig-Hughes-Zhang (BHZ) model, under the moiré superlattice potentials. Moiré minibands with non-trivial band topology, including Z2 number, mirror Chern number and fragile topology, have been found and the topological phase diagram is constructed for these moiré models. A general theory based on band representations in the morié Brillouin zone is also developed for a generalization of this mechanism to other space groups. Possible experimental realizations of our model Hamiltonian are discussed.

cond-mat.mes-hall↗