arXiv subjects

Wojciech J. Jankowski

Publications and source records attributed to Wojciech J. Jankowski.

At least 19 recordsLinked to original sources

arXiv2026

Frustrated Topological Orbital Magnetism

By studying the interplay of geometric frustration with Aharonov-Bohm fluxes in three dimensions, we unveil a rich playground exhibiting topological semimetallic ground states with orbital magnetic dipole, quadrupole and ferrotoroidic orders, akin to spin patterns in classical spin ices - a class of phenomena which we dub frustrated topological orbital magnetism. We demonstrate that the ground-state toroidizations underpinned by non-Abelian topological nodal lines induce measurable current-induced Hall phenomena. We further find that distinct 2-in-2-out and 3-in-1-out frustrated orbital current patterns can be associated with topological Weyl node charges, and corresponding anisotropic linear and nonlinear Hall effects. We propose signatures for experimental validation of distinct frustrated topological orbital magnetic orders in candidate materials.

cond-mat.mes-hall↗

arXiv2026

Multistate Torsion in Zitterbewegung

We derive nonlinear Zitterbewegung velocity of electrons augmented by band torsion in crystals. The equation of motion with multistate quantum geometric tensors and torsion culminates in transient nonlinear photocurrent responses distinct from the recently measured resonant steady-state photovoltaic effects induced by circularly polarized light. Tomography protocols for measuring the multistate quantum geometric torsion tensors are proposed.

cond-mat.mes-hall↗

arXiv2026

Quantum Geometry of Altermagnetic Magnons Probed by Light

Magnons with momentum-dependent chirality are a key signature of altermagnets. We identify bicircular light as a smoking-gun optical probe for chiral altermagnetic magnons, selectively targeting their quantum geometry induced by an alternation of magnonic chirality. We show that in $d$-wave altermagnets, under a canting magnetic field, the altermagnetic magnons realize a nontrivial quantum geometry, resulting in an enhancement of the nonlinear second-order light-magnon interactions. We find that the scattering of bicircular pulses probes the present magnonic quantum geometry, even if the magnonic topology is trivial. Hence, our findings establish bicircular Raman response as an optical effect of choice to identify altermagnetic magnons. As such, we propose a universal experimental protocol to distinguish altermagnets from antiferromagnets by detecting their magnon chirality patterns with light, independently of the underlying magnon topology.

cond-mat.mes-hall↗

arXiv2026

Nonlinear Odd Viscoelastic Effect

We uncover a class of nonlinear odd viscoelastic effects in three spatial dimensions. We show that these dissipationless effects arise upon combining geometric distortions in two orthogonal directions, yielding momentum flow in the third direction. We demonstrate that the effect arises from nontrivial geometric tensors in quantum states, and can be scaled up with integer topological invariants. We further show that the effect fingerprints the multiband Hilbert-space geometry of the underlying quantum states, as encoded in the nonmetricity and three-state quantum geometric tensors. Our findings unravel the role of multistate geometry in viscoelastic phenomena, paving a path for experimental observation of uncharted nonlinear odd viscoelastic responses in quantum systems.

cond-mat.mes-hall↗

arXiv2026

Orbital magnetization reveals multiband topology

We demonstrate that nontrivial multiband topological invariants of electronic wavefunctions can be revealed through orbital magnetization responses to external magnetic fields. We find that decomposing orbital magnetization into energetic and quantum-geometric contributions allows one to deduce nontrivial multiband topology, provided knowledge of the energy spectrum. We showcase our findings in general effective models with multiband Euler topology. We moreover identify such multiband topological invariants in effective models of strontium ruthenate ($\text{Sr}_2 \text{Ru} \text{O}_4$), which may in principle be verified in the state-of-the-art doping-dependent magnetization measurements. Our reconstruction scheme for multiband invariants sheds a topological perspective on the multiorbital effects in materials realizing unconventional phenomenologies of orbital currents or multiband superconductivity.

cond-mat.mes-hall↗

arXiv2026

Magnetononlinear Hall effect from multigap topology in metal-organic frameworks

We unveil that non-Abelian multigap band topology characterized by nontrivial Euler class invariants induces observable magnetononlinear Hall transport phenomena. We demonstrate these effects in a highly-tunable class of recently synthesized two-dimensional kagome N-heterocyclic carbene (NHC) metal-organic frameworks. We showcase the controllability of the nonlinear effect upon applying external voltage, changing temperature, and chemical substitutions that preserve the bulk topology and associated edge states. Our findings therefore reveal an uncharted presence of Euler class topology in metal-organic materials that can be experimentally deduced through measurable magnetotransport.

cond-mat.mes-hall↗

arXiv2026

Topological Optical Chirality Dichroism

We report on a universal topological dichroism of chiral three-dimensional systems in response to the chirality of light. We show that chiral topological invariants result in integer-quantized dichroic excitation rate differences. Moreover, we demonstrate that such topological effects arise more generally from coupling optical chirality to higher tensor Berry curvatures and Dixmier-Douady invariants of quantum states, including Hopf indices. We finally propose an experimental setup that leverages superchiral light as a smoking-gun probe of chiral band topologies in three-dimensional materials. Our findings establish an optical route for probing to date unobserved chiral electronic band topologies.

cond-mat.mes-hall↗

arXiv2026

Topological Acoustic Diode

We show that certain three-dimensional topological phases can act as acoustic diodes realizing nonlinear odd acoustoelastic effects. Beyond uncovering topologically-induced anomalous acoustic second-harmonic generation and rectification, we demonstrate how such nonlinear responses are uniquely captured by the momentum-space nonmetricity tensor in the quantum state Hilbert-space geometry. In addition to completing the classification of quantum geometric observables in the quadratic response regime, our findings reveal unexplored avenues for experimental realizations of acoustic diodes using effective $θ$ vacua of axion insulators adaptable for topological engineering applications.

cond-mat.mes-hall↗

arXiv2025

Quantum Geometric Bounds in Non-Hermitian Systems

We identify quantum geometric bounds for observables in non-Hermitian systems. We find unique bounds on non-Hermitian quantum geometric tensors, generalized two-point response correlators, conductivity tensors, and optical weights. We showcase these findings in topological systems with non-Hermitian Chern numbers. We demonstrate that the non-Hermitian geometric constraints on response functions naturally arise in open quantum systems governed by out-of-equilibrium Lindbladian dynamics. Our findings are relevant to experimental observables and responses under the realistic setups that fall beyond the idealized closed-system descriptions.

quant-ph↗

arXiv2025

Quantum geometric bounds in spinful systems with trivial band topology

We derive quantum geometric bounds in spinful systems with spin topology characterized by a single $\mathbb{Z}$ index protected by a spin gap. Our bounds provide geometric conditions on the spin topology, distinct from the known quantum geometric bounds associated with Wilson loops and nontrivial band topologies. As a result, we obtain broader bounds in time-reversal symmetric systems with a nontrivial $\mathbb{Z}_2$ index and also bounds in systems with a trivial $\mathbb{Z}_2$ index, where the quantum metric should be otherwise unbounded. We benchmark these findings with first-principles calculations in elemental bismuth realizing a nontrivial even spin-Chern number. Moreover, we connect these bounds to optical responses and show their robustness in the presence of disorder within a real space marker formulation, demonstrating that spin-resolved quantum geometry is observable in realistic experimental settings of impure materials. Finally, we connect spin bounds to quantum Cramér-Rao bounds that are central to quantum metrology, showing that elemental Bi and other spin-topological phases hold promises for topological free fermion quantum sensors.

cond-mat.mes-hall↗

arXiv2025

Enhancing the Hyperpolarizability of Crystals with Quantum Geometry

We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $π$-conjugated chains as representative model systems. First, we show that the crystalline-symmetry-protected topology of these chains imposes a lower bound on their quantum metric and hyperpolarizabilities. Second, we employ numerical simulations to reveal the tunability of nonlinear, quantum geometry-driven optical responses in various one-dimensional crystals in which band topology can be externally controlled. Third, we develop a semiclassical picture to deliver an intuitive understanding of these effects. Our findings offer a firm interpretation of otherwise elusive experimental observations of colossal hyperpolarizabilities and establish guidelines for designing topological materials of any dimensionality with enhanced nonlinear optical properties.

cond-mat.mes-hall↗

arXiv2025

Optical signatures of Euler superconductors

We study optical manifestations of multigap band topology in multiband superconductors with a nontrivial topological Euler class. We introduce a set of lattice models for non-Abelian superconductors with the Euler invariant signified by a nontrivial quantum geometry. We then demonstrate that the topological Bogoliubov excitations realized in these models provide for a characteristic first-order optical response distinct from those of the other known topological superconductors. We find that the spectral distribution of the optical conductivity universally admits a topological jump originating from the Euler class in the presence of $d$-wave superconducting pairings, and naturally differs from the features induced by the quantum geometry in the noninteracting bands without pairing terms. Further to uncovering observable signatures in first-order optical conductivities, we showcase that the higher-order optical responses of the non-Abelian Euler superconductor can result in enhanced nonlinear currents that fingerprint the exotic topological invariant. Finally, by employing a diagrammatic approach, we generalize our findings beyond the specific models of Euler superconductors.

cond-mat.supr-con↗

arXiv2025

Probing Tensor Monopoles and Gerbe Invariants in Three-Dimensional Topological Matter

We show that momentum-space tensor monopoles corresponding to nontrivial vector bundle generalizations, known as bundle gerbes, can be realized in bands of three-dimensional topological matter with nontrivial Hopf invariants. We provide a universal construction of tensor Berry connections in these topological phases, demonstrating how obstructions therein lead to $\mathbb{Z}$-quantized bulk magnetoelectric and nonlinear optical phenomena. We then pinpoint that these quantum effects are supported by intraband and interband torsion leading to nontrivial Dixmier-Douady classes in most known Hopf phases and in more general topological insulators realizing gerbe invariants falling beyond the tenfold classification of topological phases of matter. We furthermore provide an interacting generalization upon introducing many-body gerbe invariants by employing twisted boundary conditions. This opens an avenue to study gerbe invariants realized through higher-dimensional charge fractionalizations that can be electromagnetically probed.

cond-mat.mes-hall↗

arXiv2025

Anomalous geometric transport signatures of topological Euler class

We investigate Riemannian quantum-geometric structures in semiclassical transport features of two-dimensional multigap topological phases. In particular, we study nonlinear Hall-like bulk electric current responses and, accordingly, semiclassical equations of motion induced by the presence of a topological Euler invariant. We provide analytic understanding of these quantities by phrasing them in terms of momentum-space geodesics and geodesic deviation equations and further corroborate these insights with numerical solutions. Within this framework, we moreover uncover anomalous bulk dynamics associated with the second- and third-order nonlinear Hall conductivities induced by a patch Euler invariant. As a main finding, our results show how one can reconstruct the Euler invariant by coupling to electric fields at nonlinear order and from the gradients of the electric fields. Furthermore, we comment on the possibility of deducing the nontrivial non-Abelian Euler class invariant specifically in second-order nonlinear ballistic conductance measurements within a triple-contact setup, which was recently proposed to probe the Euler characteristics of more general Fermi surfaces. Generally, our results provide a route for deducing the topology in real materials that exhibit the Euler invariant by analyzing bulk electrical currents.

cond-mat.mes-hall↗

arXiv2025

Shift photocurrent vortices from topological polarization textures

Following the recent interest in van der Waals (vdW) ferroelectrics, topologically nontrivial polar structures have been predicted to form in twisted bilayers. However, these structures have proven difficult to observe experimentally. We propose that these textures may be probed optically by showing that topological polarization textures result in exotic nonlinear optical responses. We derive this relationship analytically using non-Abelian Berry connections and a quantum-geometric framework, supported by tight-binding and first-principles calculations. For the case of moiré materials without centrosymmetry, which form networks of polar merons and antimerons, the shift photoconductivity forms a vortex-like structure in real space. For a range of frequencies where transitions between topologically trivial bands occur at the Brillouin zone edge, the shift photocurrents are antiparallel to the in-plane electronic polarization field. Our findings highlight the interplay between complex polarization textures and nonlinear optical responses in vdW materials and provide a sought-after strategy for their experimental detection.

cond-mat.mes-hall↗

arXiv2025

Excitonic topology and quantum geometry in organic semiconductors

Excitons drive the optoelectronic properties of organic semiconductors which underpin devices including solar cells and light-emitting diodes. Here we show that excitons can exhibit topologically non-trivial states protected by inversion symmetry and identify a family of organic semiconductors realising the predicted excitonic topological phases. We also demonstrate that the topological phase can be controlled through experimentally realisable strains and chemical functionalisation of the material. Appealing to quantum Riemannian geometry, we predict that topologically non-trivial excitons have a lower bound on their centre-of-mass spatial spread, which can significantly exceed the size of a unit cell. Furthermore, we show that the dielectric environment allows control over the excitonic quantum geometry. The discovery of excitonic topology and excitonic Riemannian geometry in organic materials brings together two mature fields and suggests many new possibilities for a range of future optoelectronic applications.

cond-mat.mes-hall↗

arXiv2025

Topologically-enhanced exciton transport

Excitons dominate the optoelectronic response of many materials. Depending on the time scale and host material, excitons can exhibit free diffusion, phonon-limited diffusion, or polaronic diffusion, and exciton transport often limits the efficiency of optoelectronic devices such as solar cells or photodetectors. We demonstrate that topological excitons exhibit enhanced diffusion in all transport regimes. Using quantum geometry, we find that topological excitons are generically larger and more dispersive than their trivial counterparts, promoting their diffusion. We apply this general theory to organic polyacene semiconductors and show that exciton transport increases up to fourfold when topological excitons are present. We also propose that non-uniform electric fields can be used to directly probe the quantum metric of excitons, providing a rare experimental window into a basic geometric feature of quantum states. Our results provide a new strategy to enhance exciton transport in semiconductors and reveal that mathematical ideas of topology and quantum geometry can be important ingredients in the design of next-generation optoelectronic technologies.

cond-mat.mes-hall↗

arXiv2025

Optical manifestations and bounds of topological Euler class

We analyze quantum-geometric bounds on optical weights in topological phases with pairs of bands hosting nontrivial Euler class, a multigap invariant characterizing non-Abelian band topology. We show how the bounds constrain the combined optical weights of the Euler bands at different dopings and further restrict the size of the adjacent band gaps. In this process, we also consider the associated interband contributions to dc conductivities in the flat-band limit. We physically validate these results by recasting the bound in terms of transition rates associated with the optical absorption of light, and demonstrate how the Euler connections and curvatures can be determined through the use of momentum and frequency-resolved optical measurements, allowing for a direct measurement of this multiband invariant. Additionally, we prove that the bound holds beyond the degenerate limit of Euler bands, resulting in nodal topology captured by the patch Euler class. In this context, we deduce optical manifestations of Euler topology within $\vec{k} \cdot \vec{p}$ models, which include quantized optical conductivity, and third-order jerk photoconductivities. We showcase our findings with numerical validation in lattice-regularized models that benchmark effective theories for real materials and are realizable in metamaterials and optical lattices.

cond-mat.mes-hall↗