arXiv subjects

Tarik P. Cysne

Publications and source records attributed to Tarik P. Cysne.

At least 19 recordsLinked to original sources

arXiv2026

Real-Space Spectral Approach to Orbital Magnetization

We present a real-space spectral method for computing the orbital magnetization of crystals. Starting from the commutator form of the orbital magnetization operator, we formulate an energy-resolved spectral function that is amenable to exact Chebyshev polynomial expansions and yields the total magnetization upon integration up to the Fermi level. This avoids the need for computing eigenstates and ground-state projects, providing an efficient numerical framework that is applicable to very large systems even in the presence of disorder and temperature. Our approach is benchmarked on the Haldane model, finding results that are in excellent agreement with the modern $k$-space formulation of orbital magnetization. Leveraging this technique, we extend our study to systems with uncorrelated disorder and point defects, and further show that the bulk Chern number can be directly obtained from the magnetization spectral density. These results open a promising route to investigate orbital responses and topological transitions in real-space models of quantum materials with realistic complexity.

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arXiv2026

Staggered orbital magnetization from itinerant electrons: orbital antiferro- and ferrimagnetic phases

Because electronic orbital angular momentum in solids is inherently non-local, its contribution to magnetism is usually cast in terms of a net orbital magnetization. Here, we show that itinerant electrons can generate orbital magnetic phases with ferromagnetic, antiferromagnetic, or ferrimagnetic orders. We demonstrate this possibility in a honeycomb lattice, using both the standard and a modified Haldane model. Employing real-space formulations, we decompose the itinerant orbital magnetization into sublattice contributions, $M_A$ and $M_B$. Their net ($M_z=M_A+M_B$) and staggered ($M_z^s=M_A-M_B$) combinations are then used to identify the orbital order. By varying the sublattice potential and the Fermi energy, we find distinct regimes: a (PT)-symmetric orbital antiferromagnet in the modified Haldane model, an orbital ferromagnet in the standard Haldane model, ferrimagnetic metallic states where net and staggered orbital magnetizations coexist, and insulating regimes in which the ferro- and antiferromagnetic orbital characters can be interchanged. These findings are explained by a low-energy theory in terms of two distinct valley mechanisms: valley-dependent Dirac masses in the standard Haldane model and valley-dependent energy shifts in its modified version.

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arXiv2026

Real-space topology and charge order in the Haldane-Holstein Model

We study the half-filled Haldane-Holstein model, where a paradigmatic Chern insulator is coupled to fully dynamical phonons, and provide an unbiased characterization of how retarded electron-phonon interactions destabilize Chern topology. Using determinant quantum Monte Carlo, we find that increasing the coupling drives an abrupt, first-order transition from a Chern insulator to a staggered charge-density wave that acts as a dynamical sublattice (Semenoff) mass. The transition is simultaneously signaled by a nearly quantized many-body Bott index and a real-space local Chern marker constructed from the interacting Green's function, both of which collapse as the charge order parameter becomes extensive. Spectral and open-boundary calculations reveal concomitant gap closing and the loss of boundary spectral weight at the critical coupling. Despite the generic phase problem induced by broken time-reversal symmetry, we show that it remains mild in the low-frequency regime and that the average phase factor sharply tracks the Chern insulator-charge density wave boundary. Our results establish a concrete route by which electron-phonon coupling can trigger a discontinuous collapse of Chern topology and provide experimentally relevant signatures for correlated topological platforms.

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arXiv2026

Orbital Hall effect from orbital magnetic moments of Bloch states: the role of a new correction term

We present a rigorous derivation of the matrix elements of the orbital magnetic moment (OMM) of Bloch states. Our calculations include the Berry connection term in the k-derivatives of Bloch states, which was omitted in previous works. The resulting formula for the OMM matrix elements applies to any non-degenerate Bloch states within Hilbert space. We identify two new contributions: the first restores gauge covariance for non-degenerate states, while the second, being itself gauge covariant, can provide significant quantitative corrections depending on the system under study. We examine their impact on the orbital Hall effect in two bilayer systems: a 2H transition metal dichalcogenide bilayer and a biased bilayer graphene. In both cases, these new terms reduce the orbital Hall conductivity plateau compared with results that neglect them, suggesting that multi-layered van der Waals materials may be particularly susceptible to the derived OMM corrections. Our findings may contribute to the formal understanding of electronic OMM transport and to the conceptual foundations of the emerging field of orbitronics.

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arXiv2025

Orbitronics in Two-dimensional Materials

Orbitronics explores the control and manipulation of electronic orbital angular momentum in solid-state systems, opening new pathways for information processing and storage. One significant advantage of orbitronics over spintronics is that it does not rely on spin-orbit coupling, thereby broadening the range of non-magnetic materials that can be utilized for these applications. It also introduces new topological features related to electronic orbital angular momentum, and clarifies some long-standing challenges in understanding experiments that rely on the conventional concept of valley transport. This review highlights recent advances in orbitronics, particularly in relation to two-dimensional materials. We examine the fundamental principles underlying the generation, transport, and dynamics of orbital angular momentum to illustrate how the unique properties of two-dimensional materials can promote orbitronic phenomena. We also outline potential future research directions and address some outstanding questions in this field.

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arXiv2025

Topological Phases in Fractals: Local Spin Chern Marker in the Sierpinski carpet Kane-Mele-Rashba Model

We study the spectral properties and local topology of the Kane-Mele-Rashba model on a Sierpinski Carpet (SC) fractal, constructed from a rectangular flake with an underlying honeycomb arrangement and open boundary conditions. When the system parameters correspond to a topologically trivial phase, the energy spectrum is characterized solely by bulk states that are not significantly modified by the system's fractality. For parameters corresponding to the quantum spin Hall insulator (QSHI) phase, in addition to bulk states, the energy spectrum exhibits in-gap topological states that are strongly influenced by the fractal geometry. As the fractal generation increases, the in-gap topological states acquire a staircase profile, which translates into sharp peaks in the density of states. We also show that both the QSHI and the trivial phase exhibit a large gap in the valence-projected spin spectrum, allowing the use of the local spin Chern marker (LSCM) to index the local topology of the system. Fractality does not affect this gap, allowing the application of LSCM to higher fractal generations. Our results explore the LSCM versatility, showing its potential to access local topology in complex geometries such as fractal systems.

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arXiv2025

Anisotropic resonance energy transfer with strained phosphorene

We analyze the resonance energy transfer (RET) rate between quantum emitters (QEs) near a phosphorene/SiC interface under the effects of uniaxial strain. Using a low-energy tight-binding model, we describe the electronic structure of strained phosphorene in an experimentally feasible situation. Due to the anisotropic electronic structure of phosphorene, we demonstrate that the RET rate drastically depends on the direction in which the QEs are separated relative to the phosphorene lattice. More specifically, we obtain a large variation in the RET rate when the QEs are separated along the zigzag direction, in contrast to a rather small variation when separated along the armchair direction of phosphorene's crystalline structure. Furthermore, our results reveal that the RET rate can be highly modulated by uniaxial strain in phosphorene when considering emitters placed along the zigzag direction. Finally, by means of a simple toy model, we also show that this anisotropy in the RET rate is a general characteristic produced by anisotropic 2D materials.

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arXiv2025

Topological characterization of modified Kane-Mele-Rashba models via local spin Chern marker

In this work, we use the local spin Chern marker (LSCM) recently introduced by Baù and Marrazzo [Phys. Rev. B 110, 054203 (2024)] to analyze the topology of the ground-state electronic wave functions in a finite honeycomb lattice flake described by three distinct models. The models considered here are characterized by strong Rashba spin-orbit interaction, which leads to non-conservation of the spin operator, i.e., $[\mathcal{H},\hat{s}_z]\neq 0$. The three spin-orbit couplings associated with the topological aspects of the models are: 1) Standard Kane-Mele coupling, 2) Sublattice-dependent Kane-Mele coupling, and 3) In-plane ($\hat{s}_y$) polarized Kane-Mele coupling. These couplings occur in graphene grown on suitable substrates and are relevant for modeling its van der Waals heterostructures. A particular topological phase diagram characterizes each of these spin-orbit interactions, and our calculations of LSCM successfully capture its general features. We also performed a detailed analysis of the spectral properties of the energy and valence-projected spin matrix eigenvalues, which shows that both exhibit a gap that protects the marker. Our results expand the applicability of the spin Chern number method to a class of Hamiltonians with experimental relevance and may contribute to future research on the real-space topology of realistic materials.

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arXiv2024

Controlling the orbital Hall effect in gapped bilayer graphene in the terahertz regime

We study the orbital Hall effect (OHE) in the AC regime using bilayer graphene (BLG) as a prototypical material platform. While the unbiased BLG has gapless electronic spectra, applying a perpendicular electric field creates an energy band gap that can be continuously tuned from zero to high values. By exploiting this flexibility, we demonstrate the ability to control the behavior of AC orbital Hall conductivity. Particularly, we demonstrate that the orbital Hall conductivity at the neutrality point changes its signal at a critical frequency, the value of which is proportional to the perpendicular electric field. For BLG with narrow band gaps, the active frequency region for the AC OHE may extend to a few terahertz, which is experimentally accessible with current technologies. We also consider the introduction of a perpendicular magnetic field in the weak coupling regime using first-order perturbation theory to illustrate how the breaking of time-reversal symmetry enables the emergence of AC charge Hall effect in the charge-doped situation and modifies the AC orbital Hall conductivity. Our calculations suggest that BLG with narrow bandgaps is a practical candidate for investigating time-dependent orbital angular momentum transport.

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arXiv2024

Transport of orbital currents in systems with strong intervalley coupling: the case of Kekulé distorted graphene

We show that orbital currents can describe the transport of orbital magnetic moments of Bloch states in models where the formalism based on valley current is not applicable. As a case study, we consider Kekulé distorted graphene. We begin by analyzing the band structure in detail and obtain the orbital magnetic moment operator for this model within the framework of the modern theory of magnetism. Despite the simultaneous presence of time-reversal and spatial-inversion symmetries, such operator may be defined, although its expectation value at a given energy is zero. Nevertheless, its presence can be exposed by the application of an external magnetic field. We then proceed to study the transport of these quantities. In the Kekulé-$O$ distorted graphene model, the strong coupling between different valleys prevents the definition of a bulk valley current. However, the formalism of the orbital Hall effect together with the non-Abelian description of the magnetic moment operator can be directly applied to describe its transport in these types of models. We show that the Kekulé-$O$ distorted graphene model exhibits an orbital Hall insulating plateau whose height is inversely proportional to the energy band gap produced by intervalley coupling. Our results strengthen the perspective of using the orbital Hall effect formalism as a preferable alternative to the valley Hall effect

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arXiv2023

The impact of Rashba spin-orbit coupling in charge-ordered systems

We study the impact of the Rashba spin-orbit coupling (RSOC) on the stability of charge-density wave (CDW) in systems with large electron-phonon coupling (EPC). Here, the EPC is considered in the framework of the Holstein model at the half-filled square lattice. We start obtaining the phase diagram of the Rashba-Holstein model using the Hartree-Fock mean-field theory, and identifying the boundaries of the CDW and Rashba metal phases. As our main result, we notice that the RSOC disfavors the CDW phase, driving the system to a correlated Rashba metal. Proceeding, we employ a cluster perturbation theory (CPT) approach to investigate the phase diagram beyond the Hartree-Fock approximation. The quantum correlations captured by CPT indicate that the RSOC is even more detrimental to CDW than previously anticipated. That is, the Rashba metal region is observed to be expanded in comparison to the mean-field case. Additionally, we investigate pairing correlations, and the results further strengthen the identification of critical points.

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arXiv2023

Ultrathin films of black phosphorus as suitable platforms for unambiguous observation of the orbital Hall effect

Phosphorene, a monolayer of black phosphorus, is a two-dimensional material that lacks a multivalley structure in the Brillouin zone and has negligible spin-orbit coupling. This makes it a promising candidate for investigating the orbital Hall effect independently of the valley or spin Hall effects. To model phosphorene, we utilized a DFT-derived tight-binding Hamiltonian, which is constructed with the pseudo atomic orbital projection method. For that purpose, we use the PAOFLOW code with a newly implemented internal basis that provides a fairly good description of the phosphorene conduction bands. By employing linear response theory, we show that phosphorene exhibits a sizable orbital Hall effect with strong anisotropy in the orbital Hall conductivity for the out-of-plane orbital angular momentum component. The magnitude and sign of the conductivity depend upon the in-plane direction of the applied electric field. These distinctive features enable the observation of the orbital Hall effect in this material unambiguously. The effects of strain and of a perpendicularly applied electric field on the phosphorene orbital-Hall response are also explored. We show that a supplementary electric field applied perpendicular to the phosphorene layer in its conductive regime gives rise to an induced in-plane orbital magnetization.

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arXiv2023

Controlling electric and magnetic Purcell effects in phosphorene via strain engineering

We investigate the spontaneous emission lifetime of a quantum emitter near a substrate coated with phosphorene under the influence of uniaxial strain. We consider both electric dipole and magnetic dipole-mediated spontaneous transitions from the excited to the ground state. The modeling of phosphorene is performed by employing a tight-binding model that goes beyond the usual low-energy description. We demonstrate that both electric and magnetic decay rates can be strongly tuned by the application of uniform strain, ranging from a near-total suppression of the Purcell effect to a remarkable enhancement of more than 1300% due to the high flexibility associated with the puckered lattice structure of phosphorene. We also unveil the use of strain as a mechanism to tailor the most probable decay pathways of the emitted quanta. Our results show that uniaxially strained phosphorene is an efficient and versatile material platform for the active control of light-matter interactions thanks to its extraordinary optomechanical properties.

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arXiv2023

Connecting Higher-Order Topology with the Orbital Hall Effect in Monolayers of Transition Metal Dichalcogenides

Monolayers of transition metal dichalcogenides (TMDs) in the 2H structural phase have been recently classified as higher-order topological insulators (HOTI), protected by $C_3$ rotation symmetry. In addition, theoretical calculations show an orbital Hall plateau in the insulating gap of TMDs, characterized by an orbital Chern number. We explore the correlation between these two phenomena in TMD monolayers in two structural phases: the noncentrosymmetric 2H and the centrosymmetric 1T. Using density functional theory, we confirm the characteristics of 2H-TMDs and reveal that 1T-TMDs are identified by a $\mathbb{Z}_4$ topological invariant. As a result, when cut along appropriate directions, they host conducting edge-states, which cross their bulk energy-band gaps and can transport orbital angular momentum. Our linear response calculations thus indicate that the HOTI phase is accompanied by an orbital Hall effect. Using general symmetry arguments, we establish a connection between the two phenomena with potential implications for spin-orbitronics.

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arXiv2023

Orbital magnetoelectric effect in nanoribbons of transition metal dichalcogenides

The orbital magnetoelectric effect (OME) generically refers to the appearance of an orbital magnetization induced by an applied electric field. Here, we show that nanoribbons of transition metal dichalcogenides (TMDs) with zigzag (ZZ) edges may exhibit a sizeable OME activated by an electric field applied along the ribbons' axis. We examine nanoribbons extracted from a monolayer (1L) and a bilayer (2L) of MoS$_2$ in the trigonal (H) structural phase. Transverse profiles of the induced orbital angular momentum accumulations are calculated to first order in the longitudinally applied electric field. Our results show that close to the nanoribbon's edge-state crossings energy, the orbital angular momentum accumulations take place mainly around the ribbons' edges. They have two contributions: one arising from the orbital Hall effect (OHE) and the other consists in the OME. The former is transversely anti-symmetric with respect to the principal axis of the nanoribbon, whereas the latter is symmetric, and hence responsible for the resultant orbital magnetization induced in the system. We found that the orbital accumulation originating from the OHE for the 1L-nanoribbon is approximately half that of a 2L-nanoribbon. Furthermore, while the OME can reach fairly high values in 1L-TMD nanoribbons, it vanishes in the 2L ones that preserve spatial inversion symmetry.The microscopic features that justify our findings are also discussed.

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arXiv2022

Generation and control of non-local chiral currents in graphene superlattices by orbital Hall effect

Graphene-based superlattices offer a new materials playground to exploit and control a higher number of electronic degrees of freedom, such as charge, spin, or valley for disruptive technologies. Recently, orbital effects, emerging in multivalley band structure lacking inversion symmetry, have been discussed as possible mechanisms for developing orbitronics. Here, we report non-local transport measurements in small gap hBN/graphene/hBN moiré superlattices which reveal very strong magnetic field-induced chiral response which is stable up to room temperature. The measured sign dependence of the non-local signal with respect to the magnetic field orientation clearly indicates the manifestation of emerging orbital magnetic moments. The interpretation of experimental data is well supported by numerical simulations, and the reported phenomenon stands as a formidable way of in-situ manipulation of the transverse flow of orbital information, that could enable the design of orbitronic devices.

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arXiv2022

Orbital Hall effect in bilayer transition metal dichalcogenides: From the intra-atomic approximation to the Bloch states orbital magnetic moment approach

Using an effective Dirac model, we study the orbital Hall effect (OHE) in bilayers of transition metal dichalcogenides with 2H stacking (2H-TMD). We use first-order perturbation theory in the interlayer coupling of the bilayer system to obtain analytical expressions for the orbital Hall conductivity in the linear response regime. We use two distinct descriptions of the orbital angular momentum (OAM) operator: The first one is the intra-atomic approximation that considers only the intrasite contribution to the OAM [Cysne et al. Phys. Rev. Lett. 126, 056601 (2021)]. The second one uses the Berry-phase formula of the orbital (valley) magnetic moment to describe the OAM operator [Bhowal and Vignale, Phys. Rev. B 103, 195309 (2021)]. This approach includes both intersite and intrasite contributions to the OAM. Our results suggest that the two approaches agree qualitatively in describing the OHE in bilayers of 2H-TMDs, although they present some quantitative differences. We also show that interlayer coupling plays an essential role in understanding the OHE in the unbiased bilayer of 2H-TMD. This coupling causes the Bloch states to become bonding (antibonding) combinations of states of individual layers, demanding the consideration of the non-Abelian structure of the orbital magnetic moment to the occurrence of OHE. As we discuss throughout the work, the emerging picture of transport of OAM in the unbiased bilayer of 2H-TMDs based on OHE is very different from the usual picture based on the valley Hall effect, shedding new lights on previous experimental results. We also discuss the effect of the inclusion of a gate-voltage bias in the bilayer system. Our work gives support to recent theoretical predictions on OHE in two-dimensional materials.

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arXiv2021

Orbital magnetoelectric effect in zigzag nanoribbons of p-band systems

Profiles of the spin and orbital angular momentum accumulations induced by a longitudinally applied electric field are explored in nanoribbons of $p$-band systems with a honeycomb lattice. We show that nanoribbons with zigzag borders can exhibit orbital magnetoelectric effects. More specifically, we have found that purely orbital magnetization oriented perpendicularly to the ribbon may be induced in these systems by means of the external electric field, when sublattice symmetry is broken. The effect is rather general and may occur in other multi-orbital materials.

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