arXiv subjects

Lumen Eek

Publications and source records attributed to Lumen Eek.

16 recordsLinked to original sources

arXiv2026

Decorated electronic kagome lattice in twisted bilayer germanene

Artificial kagome lattices provide a route to electronic flat bands, geometric frustration, and correlation driven phases, but their realization in atomically controlled two-dimensional materials remains scarce. Here, we show that commensurate twisted bilayer germanene on Ge2Pt produces two electronically distinct large-angle moir\'e phases. Scanning tunneling microscopy measurements and density functional theory calculations reveal that commensurate twisted bilayers that are odd under an exchange of sublattices are semiconducting, whereas the twisted bilayers with an even parity are metallic. The twisted bilayers with an even parity host an empty state resonance that exhibits an emergent decorated kagome structure with a C3 symmetry. These results establish large-angle twisted germanene as a platform for engineering kagome-like electronic states in a buckled two-dimensional material.

cond-mat.mes-hall↗

arXiv2026

Emergent $\mathbb{Z}$-type topology in a quasi-one-dimensional extended QWZ model

We investigate the emergence of zero-dimensional topological end states in nanoribbons described by the Qi-Wu-Zhang (QWZ) model and its extensions with longer-range couplings. While dimensional reduction from two to one dimension is often assumed to preserve the symmetry classification of the parent system, here an additional symmetry can emerge originating from the real-space geometry of the ribbon. This symmetry acts as a chiral symmetry, combining orbital and spatial transformations, and promotes the effective one-dimensional system from symmetry class D to class BDI. We demonstrate that the existence of such a symmetry depends both on the long and end termination of the ribbon and exhibits an even-odd effect with respect to ribbon width, revealing that the commonly studied rectangular ribbons constitute a special high-symmetry case. For the conventional QWZ model, we derive analytic expressions for the topological phase boundaries of finite-width nanoribbons and characterize the resulting hybridization-gap phases through ($\mathbb{Z}_2 $) and winding-number invariants. We further show that extended QWZ models with longer-range couplings support phases with multiple topological end states and higher winding numbers. These phases arise through distinct mechanisms, including the hybridization of multiple edge modes inherited from higher-Chern-number bulk phases. Our results demonstrate that both long and end termination can fundamentally alter the topological classification of confined Chern insulators, highlighting the interplay between crystalline geometry, emergent symmetries, and dimensional reduction.

cond-mat.mes-hall↗

arXiv2026

Universality of dimensional crossovers in topological insulators

We investigate dimensional crossovers in minimal tight-binding models of three-dimensional (3D) topological insulators subject to geometric confinement. While thin films are commonly understood to host a crossover from a 3D strong topological insulator to a two-dimensional (2D) quantum spin Hall phase via hybridization of surface states, we demonstrate that this picture is incomplete once bulk confinement effects and boundary termination are fully taken into account. Using lattice models, we show that reducing the system size induces a strongly non-monotonic dependence of the topology on thickness and microscopic parameters, leading to a sequence of topological phase transitions that is highly sensitive to surface termination. In particular, we find a cascade of dimensional reduction from a 3D topological insulator to a 2D quantum spin Hall phase and ultimately to a one-dimensional phase consisting of end states of Kramers pairs protected by inversion symmetry. Remarkably, we show that both the 2D and 1D topological phases can emerge even when the corresponding 3D bulk phase is topologically trivial. Our results reveal an unexpected universality in the phase diagrams of 3D-to-2D and 2D-to-1D crossovers, pointing toward a unified framework for topology under dimensional reduction.

cond-mat.mes-hall↗

arXiv2026

Fractality-induced photonic topological insulators

Fractal lattices have recently emerged as a promising setting for topological wave physics, but in most realizations the topological character is inherited from externally engineered couplings, gauge fields, or temporal modulation rather than from the fractal geometry itself. Here, we experimentally realize a photonic higher-order topological insulator in which the topology is induced solely by the self-similar geometry of a Sierpi\'nski-gasket lattice. Following the isospectral reduction method recently proposed by Eek \textit{et al.}~\cite{Eek2025}, we show that the fractal waveguide array with uniform nearest-neighbor couplings can be mapped onto an effective breathing Kagome model that supports corner states. We selectively excite these modes with a weakly coupled detuned auxiliary waveguide and directly observe robust corner localization in real space, whereas an otherwise equivalent uniform triangular lattice exhibits only bulk diffraction under the same protocol. Spectral analysis and open-boundary calculations associate the observed states with nontrivial $C_3$ rotational topology, and disorder measurements further show that the corner localization persists over a finite range of random and symmetry-preserving disorder. Our results establish fractal geometry itself as a mechanism for generating topological boundary states in photonic lattices.

physics.optics↗

arXiv2026

Topology of honeycomb nanoribbons revisited

We present an in-depth study of end states in honeycomb nanoribbons, focusing on the interplay between nanoribbon termination, chiral symmetry, and complex next-nearest-neighbor hopping in the framework of the Haldane model. Although previous work has identified zero-dimensional end states in such systems, this analysis is incomplete. Here, we systematically investigate zigzag and armchair nanoribbons of various widths, using the multiband Zak phase to characterize the topological properties of the occupied bands. We show that the Zak phase is quantized only for certain ribbon terminations, and we elucidate how this termination dependence governs the existence and robustness of end states. Furthermore, we explore the effect of varying the complex next-nearest-neighbor hopping phase, demonstrating the breakdown of chiral symmetry, the evolution of the bulk gap, and the resulting depinning of end-state energies. Finally, we place our findings in the context of previous studies and discuss connections to the Kane-Mele model, including the role of Rashba spin-orbit coupling. Our work provides a more detailed analysis of topological end states in nanoribbons described by the Haldane and Kane-Mele models and offers a framework for their characterization in related systems.

cond-mat.mes-hall↗

arXiv2026

Fragile topology for six-fold rotation symmetry indicated by the concentric Wilson loop spectrum

We investigate topological phase transitions for the Haldane and Kane-Mele model in a lattice with $p6$ symmetry, which consists of triangles and hexagons arranged in a two-dimensional geometry. For the Haldane model, which breaks time-reversal symmetry, we calculate the Chern number using a multi-band non-Abelian Wilson loop formalism. By varying the hopping parameters in the triangles and hexagons independently, a large variety of topological phases emerge. In the presence of a next-next-nearest neighbor hopping, the phase diagram becomes even richer, with regions exhibiting high Chern numbers. Then, we consider the Kane-Mele model, for which time-reversal symmetry is preserved, and calculate the number of $\pi$-crossings in the Concentric Wilson Loop Spectrum (CWLS). This method is appropriate to determine the topological invariant for systems hosting time-reversal and rotational symmetry, but lacking all other symmetries. According to a classification based on $K$-theory, the CWLS invariant reveals topological properties even when more conventional invariants fail to detect them. The formalism was previously successfully applied to systems with 3- and 4-fold symmetry. Here, we surprisingly find that for the 6-fold-symmetry model investigated, the topology identified by this invariant is fragile, therefore questioning the claim that this should be the strong invariant missing in a complete classification of topological insulators.

cond-mat.mes-hall↗

arXiv2026

Enhanced spin-current generation in Dirac altermagnets through Klein tunneling

Altermagnets have recently emerged as a new platform for spintronics applications, offering spin-split electronic bands despite vanishing net magnetization. Here, we investigate spin-current generation in Dirac altermagnets and identify Klein tunneling as an efficient mechanism for enhancing spin transport. Using a low-energy Dirac model combined with scattering theory, we demonstrate that Klein tunneling in altermagnets is strongly spin-dependent and can be used to effectively control the electronic spin-current polarization by, for instance, adjusting the height, width and orientation of the potential barrier. Finally, we explore how the l-wave symmetry of the Dirac altermagnet shapes the spin-current polarization and transmission, focusing especially on the d- and g-wave cases. Particularly promising results are obtained for the g-wave Dirac altermagnet, as it is found that the presence of a potential barrier can significantly boost the spin-current polarization, even when the intrinsic polarization due to the spin-split band structure is vanishingly small. For a barrier implemented via electrostatic gating, such a mechanism would in turn allow the spin-current polarization to be switched on and off via a gate voltage.

cond-mat.mes-hall↗

arXiv2026

Tensor-network methodology for real-space super-moir\'e excitons

Computing excitonic spectra in quasicrystal and super-moir\'e systems constitutes a formidable challenge due to the exceptional size of the excitonic Hilbert space. Here, we demonstrate a tensor-network method for the real-space Bethe-Salpeter Hamiltonian, allowing us to access the spectra of an excitonic $10^{18}$-dimensional Hamiltonian, and enabling the direct computation of bound-exciton spectral functions for systems exceeding one billion lattice sites, several orders of magnitude beyond the capabilities of conventional approaches. Our method combines a tensor-network encoding of the real-space Bethe-Salpeter Hamiltonian with a Chebyshev tensor network algorithm. This strategy bypasses explicit storage of the Hamiltonian while preserving full real-space resolution across widely different length scales. We demonstrate our methodology for one- and two-dimensional super-moir\'e systems, achieving the simultaneous resolution of atomistic and mesoscopic structures in the excitonic spectra in billion-size systems, showing exciton miniband formation and moir\'e-induced spatial confinement. Our results establish a real-space methodology enabling the simulation of excitonic physics in large-scale quasicrystal and super-moir\'e quantum matter.

cond-mat.str-el↗

arXiv2025

Real-Space Imaging of Moir\'e-Confined Excitons in Twisted Bilayer MoS$_2$

Twisted two-dimensional semiconductors generate a moir\'e landscape that confines excitons (bound electron-hole pairs) into programmable lattices, offering routes to efficient light sources, sensing, and room-temperature information processing. However, direct real-space imaging of confined excitonic species within a moir\'e unit cell remains challenging; existing claims are inferred from spatially averaged far-field signals that are intrinsically insufficient to resolve nanometre-scale variations. Here, we imaged excitons across the moir\'e of a 2$^{\circ}$ twisted bilayer MoS$_2$ with nanometre resolution using room-temperature photocurrent atomic force microscopy. We directly resolved site-selective confinement: direct and indirect excitons localize at different stacking registries of the moir\'e, with contrast governed by alignment between site-selective generation and confinement minima. A Wannier-based moir\'e-exciton model reproduces the measured energies and the moir\'e-induced localization of the exciton wavefunction. These species-specific, unit-cell-resolved measurements constrain microscopic models of moir\'e excitons, provide benchmarks for excitonic order, and establish a device-compatible route to engineering excitonic lattices in van der Waals heterostructures.

cond-mat.mes-hall↗

arXiv2025

Electric field-induced spin-valley locking in twisted bilayer buckled honeycomb materials

A twisted honeycomb bilayer exhibits a moir\'e superstructure that is composed of a hexagonal arrangement of AB and BA stacked domains separated by domain boundaries. In the case of twisted bilayer graphene, the application of an electric field normal to the bilayer leads to the opening of inverted band gaps in the AB and BA stacked domains. The inverted band gaps result in the formation of a two-dimensional triangular network of counterpropagating valley protected helical domain boundary states, also referred to as the quantum valley Hall effect. Owing to spin-orbit coupling and buckling, the quantum valley Hall effect in twisted bilayer silicene and germanene is more complex than in twisted bilayer graphene. We found that there is a range of electric fields for which the spin degree of freedom is locked to the valley degree of freedom of the electrons in the quantum valley Hall states, resulting in a stronger topological protection. For electric fields smaller than the aforementioned range the twisted bilayer does not exhibit the quantum valley Hall effect, whereas for larger electric fields the spin-valley locking is lifted and the emergent quantum valley Hall states are only valley-protected.

cond-mat.mes-hall↗

arXiv2025

Twist-modulated magnetic interactions in bilayer van der Waals materials

The ability to control magnetic interactions at the nanoscale is crucial for the development of next-generation spintronic devices and functional magnetic materials. In this work, we investigate theoretically, by means of many-body perturbation theory, how interlayer twisting modulates magnetic interactions in bilayer van der Waals systems composed of two ferromagnetic layers. We demonstrate that the relative strengths of the interlayer Heisenberg exchange interaction, the Dzyaloshinskii-Moriya interaction, and the anisotropic exchange interaction can be significantly altered by varying the twist angle between the layers, thus leading to tunable magnetic textures. We further show that these interactions are strongly dependent on the chemical potential, enabling additional control via electrostatic gating or doping. Importantly, our approach is applicable to arbitrary twist angles and does not rely on the construction of a Moir\'e supercell, making it particularly efficient even at small twist angles.

cond-mat.mes-hall↗

arXiv2025

Electric-field control of zero-dimensional topological states in ultranarrow germanene nanoribbons

Reversible, all-electric control of symmetry-protected zero-dimensional modes has been a long-standing goal. In buckled honeycomb lattices, a perpendicular field couples to the staggered sublattice potential providing the required handle. We combine scanning tunneling microscopy and tight-binding theory to switch zero-dimensional topological end states reversibly on and off in ultranarrow germanene nanoribbons by tuning the electric field in the tunnel junction. Increasing the field switches off the end modes of topological two-hexagon wide ribbons, while the same field switches on zero-dimensional states in initially trivial three- and four-hexagon wide ribbons. This atomic scale platform realizes a proof-of-principle for a zero-dimensional topological field effect device, opening a path for ultrasmall memory, controllable qubits, and neuromorphic architectures.

cond-mat.mtrl-sci↗

arXiv2024

Latent Haldane Models

Latent symmetries, which materialize after performing isospectral reductions, have recently been shown to be instrumental in revealing novel topological phases in one-dimensional systems, among many other applications. In this work, we explore how to construct a family of seemingly complicated two-dimensional models that result in energy-dependent Haldane models upon performing an isospectral reduction. In these models, we find energy-dependent latent Semenoff masses without introducing a staggered on-site potential. In addition, energy-dependent latent Haldane masses also emerge in decorated lattices with nearest-neighbor complex hoppings. Using the Haldane model's properties, we then predict the location of the topological gaps in the aforementioned family of models and construct phase diagrams to determine where the topological phases lie in parameter space. This idea yielded, for instance, useful insights in the case of a modified version of $\alpha$-graphyne and hexagonal plaquettes with additional decorations, where the gap-closing energies can be calculated using the ISR to predict topological phase transitions.

cond-mat.mes-hall↗

arXiv2024

Haldane model on the Sierpi\'nski gasket

We investigate the topological phases of the Haldane model on the Sierpi\'nski gasket. As a consequence of the fractal geometry, multiple fractal gaps arise. Additionally, a flat band appears, and due to a complex next-nearest neighbour hopping, this band splits and multiple topological flux-induced gaps emerge. Owing to the fractal nature of the model, conventional momentum-space topological invariants cannot be used. Therefore, we characterise the system's topology in terms of a real-space Chern number. In addition, we verify the robustness of the topological states to disorder. Finally, we present phase diagrams for both a fractal gap and a flux-induced gap. Previous work on a similar system claims that fractality "squeezes" the well-known Haldane phase diagram. However, this result arises because a doubled system was considered with two Sierpi\'nski gaskets glued together. We consider only a single copy of the Sierpi\'nski gasket, keeping global self-similarity. In contrast with these previous results, we find intricate and complex patterns in the phase diagram of this single fractal. Our work shows that the fractality of the model greatly influences the phase space of these structures, and can drive topological phases in the multitude of fractal and flux-induced gaps, providing a richer platform than a conventional integer dimensional geometry.

cond-mat.mes-hall↗

arXiv2023

Emergent non-Hermitian models

The Hatano-Nelson and the non-Hermitian Su-Schrieffer-Heeger model are paradigmatic examples of non-Hermitian systems that host non-trivial boundary phenomena. In this work, we use recently developed graph-theoretical tools to design systems whose isospectral reduction -- akin to an effective Hamiltonian -- has the form of either of these two models. In the reduced version, the couplings and on-site potentials become energy-dependent. We show that this leads to interesting phenomena such as an energy-dependent non-Hermitian skin effect, where eigenstates can simultaneously localize on either ends of the systems, with different localization lengths. Moreover, we predict the existence of various topological edge states, pinned at non-zero energies, with different exponential envelopes, depending on their energy. Overall, our work sheds new light on the nature of topological phases and the non-Hermitian skin effect in one-dimensional systems.

quant-ph↗

arXiv2022

Field Theoretical Study of Disorder in Non-Hermitian Topological Models

Non-Hermitian systems have provided a rich platform to study unconventional topological phases.These phases are usually robust against external perturbations that respect certain symmetries of thesystem. In this work, we provide a new method to analytically study the effect of disorder, usingtools from quantum field theory applied to discrete models around phase-transition points. Weinvestigate two different one-dimensional models, the paradigmatic non-Hermitian SSH model andas-wave superconductor with imbalanced pairing. These analytic results are compared to numericalsimulations in the discrete models. An universal behavior is found for the two investigated models,namely that the systems are driven from a topological to a trivial phase for disorder strengths equalto about four times the energy scale of the model.

cond-mat.dis-nn↗