arXiv subjects

Stepan S. Tsirkin

Publications and source records attributed to Stepan S. Tsirkin.

At least 19 recordsLinked to original sources

arXiv2026

Anatomy of Spin--Orbit Torques in Monolayer Fe$_3$GeTe$_2$ and Fe$_3$GaTe$_2$: Insights from atomistic and momentum-space decompositions

We present a systematic first-principles study of the spin-orbit torques in the ferromagnetic monolayers Fe$_3$GeTe$_2$ (FGT) and Fe$_3$GaTe$_2$ (FGaT). Despite sharing the same crystal structure (point group $D_{3h}$) and predominantly Fe~$3d$ spin-polarized bands, the two materials exhibit markedly different current-induced torques. We reveal these differences by computing the full angular dependence of the torkance---the torque per unit applied electric field---using linear-response theory with symmetry-adapted spin--orbit-coupled Wannier functions. FGaT may be viewed as a hole-doped analogue of FGT, since Ga contributes one valence electron fewer than Ge. Although the work functions differ by only about $28$~meV, the band filling near $K$ and $K'$ changes substantially: the density of states at $\varepsilon_F$ is reduced by a factor of three and its spin polarization reverses from majority in FGT to minority in FGaT. These electronic changes are reflected in the torques resolved by time-reversal parity, sublattice, and momentum. In particular, we identify pronounced hidden torques in FGaT and relate the suppression of its fourth-harmonic Fermi-sea component to the evolution of momentum-space pockets. Finally, we discuss the emergence of such self-torques, which are not captured by the conventional picture of current-induced spin accumulation, within a symmetry-based phenomenological framework. Our results provide microscopic insight into current-induced torques in two-dimensional ferromagnets and offer guidance for defect and van der Waals engineering of layered magnetic materials.

cond-mat.mtrl-sci↗

arXiv2026

First-Principles Wannier Representation of Proximity Effects

Proximity effects in layered heterostructures are usually represented by static parameters fitted to first-principles bands, which discards the energy dependence of the virtual hybridization, the momentum transfer, and the spatial structure. We overcome this limitation by deriving a dynamical proximity operator $\mathcal{V}(\mathbf{k},\mathbf{k}';ω)$ directly from density functional theory, downfolding the Kohn-Sham Hamiltonian of the heterostructure onto a fixed low-energy target Wannier subspace and reproducing its spectrum exactly within that subspace. The construction separates direct matrix elements from virtual hybridization through all remaining states. In graphene on hBN/Co(0001), virtual hybridization generates more than $99\%$ of the proximity exchange and gives it a resonant frequency dependence set by the Co $d$ states. In graphene/PtSe$_2$ it resolves a sublattice-selective intervalley coupling with a $\sqrt{3}\times\sqrt{3}$ charge modulation, and in graphene/WSe$_2$ a bond-resolved Rashba coupling of $0.24$~meV, against below $1$~$μ$eV for the direct projection alone. Our results expose the limitations of static projections and establish a fitting-free microscopic foundation for low-energy modeling, spin-relaxation theory, and transport calculations.

cond-mat.mes-hall↗

arXiv2026

Study of the Nonlinear Dependence of Anomalous Hall Conductivity on Magnetization in Weak Itinerant Ferromagnet ZrZn2

As opposed to the ordinary Hall effect, the anomalous Hall effect (AHE) remained unexplained for decades, and, amazingly, some misconceptions have survived even now, in particular, the claim that AHE is linearly related to the net magnetization. Karplus and Luttinger provided a quantum-mechanical explanation of AHE by explicitly including the SOC and the Berry curvature of electronic bands. They did address the question of linearity, but only in the relatively uncommon limit of the exchange coupling smaller than SOC. Now the linear relation in traditional ferromagnets is understood as a domain population effect: both AHE and magnetization are independently proportional to the domain disbalance. In this connection, it is interesting to check to what extent this relation will hold in {\em single-domain} itinerant ferromagnet, the closest case to that analyzed by Karplus and Luttinger? We answer this question by direct calculations, using the Karplus-Luttinger formula, of AHE in a prototypical itinerant ferromagnet, ZrZn$_2$. We show that in the zero-magnetization limit, $M\rightarrow 0$, the linear relation hold, but at rather small moments of $\sim 0.4\ μ_B$/Zr breaks down completely and even flips the sign.

cond-mat.mtrl-sci↗

arXiv2025

Optical spatial dispersion via Wannier interpolation

We present a numerical implementation, based on Wannier interpolation, of a Kubo-Greenwood formalism for computing the spatially dispersive optical conductivity in crystals at first order in the wave vector of light. This approach is more efficient than direct $\textit{ab initio}$ methods because, with less computational cost, it allows for a much finer sampling of reciprocal space, resulting in better resolved spectra. Moreover, Wannier interpolation avoids errors arising from truncation of the sums over conduction bands when evaluating the spatially dispersive optical matrix elements. We validate our method by computing the optical activity spectrum of selected crystals, both polar (GaN) and chiral (trigonal Te, trigonal Se, and $α$-quartz), and comparing with existing literature.

cond-mat.mtrl-sci↗

arXiv2025

Symmetry Origin and Microscopic Mechanism of Electrical Magnetochiral Anisotropy in Tellurium

Non-linear transport effects in response to external magnetic fields, i.e. electrical magnetochiral anisotropy (eMChA), have attracted much attention for their importance to study quantum and spin-related phenomena. Indeed, they have permitted the exploration of topological surface states and charge-to-spin conversion processes in low-symmetry systems. Nevertheless, despite the inherent correlation between the symmetry of the material under examination and its non-linear transport characteristics, there is a lack of experimental demonstration to delve into this relationship and to unveil their microscopic mechanisms. Here, we study eMChA in chiral elemental Tellurium (Te) along different crystallographic directions, establishing the connection between the different eMChA components and the crystal symmetry of Te. We observed different longitudinal eMChA components with collinear current and magnetic field, demonstrating experimentally the radial angular momentum texture of Te. We also measured a transverse non-linear resistance which, as the longitudinal counterpart, scales bilinearly with current and magnetic fields, illustrating that they are different manifestations of the same effect. Finally, we study the scaling law of the eMChA, evidencing that extrinsic scattering from dynamic sources is the dominant microscopic mechanism. These findings underscore the efficacy of symmetry-based investigations in understanding and predicting non-linear transport phenomena, with potential applications in spintronics and energy harvesting.

cond-mat.mes-hall↗

arXiv2024

Unveiling intrinsic bulk photovoltaic effect in atomically thin ReS2

The bulk photovoltaic effect (BPVE) offers a promising avenue to surpass the efficiency limitations of current solar cell technology. However, disentangling intrinsic and extrinsic contributions to photocurrent remains a significant challenge. Here, we fabricate high-quality, lateral devices based on atomically thin ReS2 with minimal contact resistance, providing an optimal platform for distinguishing intrinsic bulk photovoltaic signals from other extrinsic photocurrent contributions originating from interfacial effects. Our devices exhibit large bulk photovoltaic performance with intrinsic responsivities of 1 mA/W in the visible range, without the need for external tuning knobs such as strain engineering. Our experimental findings are supported by theoretical calculations. Furthermore, our approach can be extrapolated to investigate the intrinsic BPVE in other non-centrosymmetric van der Waals materials, paving the way for a new generation of efficient light-harvesting devices.

cond-mat.mes-hall↗

arXiv2024

The Wannier Function Software Ecosystem for Materials Simulations

Over the last two decades, following the early developments on maximally localized Wannier functions, an ecosystem of electronic-structure simulation techniques and software packages leveraging the Wannier representation has flourished. This environment includes codes to obtain Wannier functions and interfaces with first-principles simulation software, as well as an increasing number of related post-processing packages. Wannier functions can be obtained for isolated or extended systems (both crystalline and disordered), and can be used to understand chemical bonding, to characterize electric polarization, magnetization, and topology, or as an optimal basis set, providing very accurate interpolations in reciprocal space or large-scale Hamiltonians in real space. In this review, we summarize the current landscape of techniques, materials properties and simulation codes based on Wannier functions that have been made accessible to the research community, and that are now well integrated into what we term a \emph{Wannier function software ecosystem}. First, we introduce the theory and practicalities of Wannier functions, starting from their broad domains of applicability to advanced minimization methods using alternative approaches beyond maximal localization. Then we define the concept of a Wannier ecosystem and its interactions and interoperability with many quantum simulations engines and post-processing packages. We focus on some of the key properties and capabilities that are empowered by such ecosystem\textemdash from band interpolations and large-scale simulations to electronic transport, Berryology, topology, electron-phonon couplings, dynamical mean-field theory, embedding, and Koopmans functionals\textemdash concluding with the current status of interoperability and automation. [...]

cond-mat.mtrl-sci↗

arXiv2024

Electrical magnetochiral anisotropy in trigonal tellurium from first principles

Structural chirality gives rise to characteristic responses that change sign with the handedness of the crystal structure. One example is electrical magnetochiral anisotropy (eMChA), a change in resistivity that depends linearly on the applied current and on the magnetic field. Motivated by recent measurements of a strong eMChA in $p$-doped trigonal tellurium, we carry out an \textit{ab initio} study of the eMChA response in this material as a function of temperature and doping concentration. We use the semiclassical Boltzmann transport formalism within the constant relaxation-time approximation to express the bulk eMChA response tensor in terms of the energy dispersion, intrinsic magnetic moment, and Berry curvature of the conduction Bloch states. We find that the orbital Zeeman coupling dominates the calculated response, with smaller contributions coming from the spin Zeeman coupling and from the Berry curvature, and that the effect is maximal when both the current and magnetic field are along the trigonal axis. The calculated data shows a reasonable agreement with the experiments. We provide the open-source code to facilitate further \textit{ab initio} studies of eMChA in other materials.

cond-mat.mtrl-sci↗

arXiv2024

Origin of spin reorientation and intrinsic anomalous Hall effect in the kagome ferrimagnet TbMn6Sn6

TbMn$_6$Sn$_6$ has attracted a lot of recent interest for a variety of reasons, most importantly, because of the hypothesis that it may support quantum-limit Chern topological magnetism, derived from the kagome geometry. Besides, TbMn$_6$Sn$_6$ features a highly unusual magnetic reorientation transition about 100 K below the Curie point, whereby all spins in the system, remaining collinear, rotate by 90$^\circ$. In this work, we address both issues combining experiment, mean-field theory and first-principle calculations. Both magnetic reorientation and the unusual temperature dependence of the anomalous Hall conductivity (AHC) find quantitative explanation in the fact that Mn and Tb, by virtue of the Mermin-Wagner theorem, have very different spin dynamics, with Tb spins experiencing much more rapid fluctuation. We were able to cleanly extract the intrinsic AHC from our experiment, and calculated the same microscopically, with good semiquantitative agreement. We have identified the points in the band structure responsible for the AHC and showed that they are not the kagome-derived Dirac points at the K-corner of the Brillouin zone, as conjectured previously.

cond-mat.str-el↗

arXiv2024

Odd non-linear conductivity under spatial inversion in chiral Tellurium

Electrical transport in non-centrosymmetric materials departs from the well-established phenomenological Ohm's law. Instead of a linear relation between current and electric field, a non-linear conductivity emerges along specific crystallographic directions. This non-linear transport is fundamentally related to the lack of spatial inversion symmetry. However, the experimental implications of an inversion symmetry operation on the non-linear conductivity remain to be explored. Here, we report on a large, non-linear conductivity in chiral Tellurium. By measuring samples with opposite handedness, we demonstrate that the non-linear transport is odd under spatial inversion. Furthermore, by applying an electrostatic gate, we modulate the non-linear output by a factor of 300, reaching the highest reported value excluding engineered heterostructures. Our results establish chiral Te as an ideal compound not just to study the fundamental interplay between crystal structure, symmetry operations and non-linear transport, but also to develop wireless rectifiers and energy-harvesting chiral devices.

cond-mat.mes-hall↗

arXiv2024

Non-Hermitian Linear Electrooptic Effect in 3D materials

Here, we present an in-depth theoretical analysis of the linear electrooptic effect in low-symmetry three-dimensional (3D) conductive materials with large Berry curvature dipoles. Our study identifies two distinct kinetic contributions to the linear electrooptic effect: a gyrotropic Hermitian (conservative) piece and a non-Hermitian term that can originate optical gain. We concentrate on the study of 3D materials belonging to the 32 ($D_3$) point group subject to a static electric bias along the trigonal axis. Our investigation shows that doped trigonal tellurium has promising properties, with its gyrotropic electrooptic response offering the potential for realizing electrically-biased electromagnetic isolators and inducing significant optical dichroism. Most notably, it is demonstrated that under sufficiently large static electric bias, tellurium's non-Hermitian electrooptic response may lead to optical gain. Using first-principles calculations, it is shown that n-doped tellurium is particularly promising, as it can host significantly larger Berry curvature dipoles than the more common p-doped tellurium.

physics.optics↗

arXiv2023

Ab initio study of the nonlinear optical properties and d.c. photocurrent of the Weyl semimetal TaIrTe$_4$

We present a first principles theoretical study employing nonlinear response theory to investigate the d.c. photocurrent generated by linearly polarized light in the type-II Weyl semimetal TaIrTe4. We report the low energy spectrum of several nonlinear optical effects. At second-order, we consider the shift and injection currents. Assuming the presence of a built-in static electric field, at third-order we study the current-induced shift and injection currents, as well as the jerk current. We discuss our results in the context of a recent experiment measuring an exceptionally large photoconductivity in this material [J. Ma et at., Nat. Mater. 18, 476 (2019)]. According to our results, the jerk current is the most likely origin of the large response. Finally, we propose means to discern the importance of the various mechanisms involved in a time-resolved experiment.

cond-mat.mes-hall↗

arXiv2023

Covariant derivatives of Berry-type quantities: Application to nonlinear transport

The derivatives of the Berry curvature $Ω$ and intrinsic orbital magnetic moment m in momentum space are relevant to various problems, including the nonlinear anomalous Hall effect and magneto-transport within the Boltzmann-equation formalism. To investigate these properties using first-principles methods, we have developed a Wannier interpolation scheme that evaluates the ''covariant derivatives'' of the non-Abelian $Ω$ and m matrices for a group of bands within a specific energy range of interest. Unlike the simple derivative, the covariant derivative does not involve couplings within the groups and preserves the gauge covariance of the $Ω$ and m matrices. In the simulation of nonlinear anomalous Hall conductivity, the resulting ''Fermi-sea'' formula for the Berry curvature dipole are more robust and converges faster with the density of the integration k-grid than the ''Fermi-surface'' formula implemented earlier. The developed methodology is made available via the open-source code WannierBerri and we demonstrate the efficiency of this method through first-principles calculations on trigonal Tellurium.

cond-mat.mtrl-sci↗

arXiv2022

On the separation of Hall and Ohmic nonlinear responses

The symmetric and antisymmetric parts of the linear conductivity describe the dissipative (Ohmic) and nondissipative (Hall) parts of the current. The Hall current is always transverse to the applied electric field regardless of its orientation; the Ohmic current is purely longitudinal in cubic crystals, but in lower-symmetry crystals it has a transverse component whenever the field is not aligned with a principal axis. In this work, we extend that analysis beyond the linear regime. We consider all possible ways of partitioning the current at any order in the electric field without taking symmetry into account, and find that the Hall vs Ohmic decomposition is the only one that satisfies certain basic requirements. A general prescription is given for achieving that decomposition, and the case of the quadratic conductivity is analyzed in detail. By performing a symmetry analysis we find that in five of the 122 magnetic point groups the quadratic dc conductivity is purely Ohmic and even under time reversal, a type of response that is entirely disorder mediated.

cond-mat.mtrl-sci↗

arXiv2022

Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators

In insulating crystals, it was previously shown that defects with two fewer dimensions than the bulk can bind topological electronic states. We here further extend the classification of topological defect states by demonstrating that the corners of crystalline defects with integer Burgers vectors can bind 0D higher-order end (HEND) states with anomalous charge and spin. We demonstrate that HEND states are intrinsic topological consequences of the bulk electronic structure and introduce new bulk topological invariants that are predictive of HEND dislocation states in solid-state materials. We demonstrate the presence of first-order 0D defect states in PbTe monolayers and HEND states in 3D SnTe crystals. We relate our analysis to magnetic flux insertion in insulating crystals. We find that $π$-flux tubes in inversion- and time-reversal-symmetric (helical) higher-order topological insulators bind Kramers pairs of spin-charge-separated HEND states, which represent observable signatures of anomalous surface half quantum spin Hall states.

cond-mat.mes-hall↗

arXiv2022

From triple-point materials to multiband nodal links

We study a class of topological materials which in their momentum-space band structure exhibit three-fold degeneracies known as triple points. Focusing specifically on $\mathcal{P}\mathcal{T}$-symmetric crystalline solids with negligible spin-orbit coupling, we find that such triple points can be stabilized by little groups containing a three-, four- or six-fold rotation axis, and we develop a classification of all possible triple points as type A vs. type B according to the absence vs. presence of attached nodal-line arcs. Furthermore, by employing the recently discovered non-Abelian band topology, we argue that a rotation-symmetry-breaking strain transforms type-A triple points into multiband nodal links. Although multiband nodal-line compositions were previously theoretically conceived and related to topological monopole charges, a practical condensed-matter platform for their manipulation and inspection has hitherto been missing. By reviewing the known triple-point materials with weak spin-orbit coupling, and by performing first-principles calculations to predict new ones, we identify suitable candidates for the realization of multiband nodal links in applied strain. In particular, we report that an ideal compound to study this phenomenon is Li$_2$NaN, in which the conversion of triple points to multiband nodal links facilitates largely tunable density of states and optical conductivity with doping and strain, respectively.

cond-mat.mes-hall↗

arXiv2022

Signatures of a topological Weyl loop in Co$_3$Sn$_2$S$_2$

The search for novel topological phases of matter in quantum magnets has emerged as a frontier of condensed matter physics. Here we use state-of-the-art angle-resolved photoemission spectroscopy (ARPES) to investigate single crystals of Co$_3$Sn$_2$S$_2$ in its ferromagnetic phase. We report for the first time signatures of a topological Weyl loop. From fundamental symmetry considerations, this magnetic Weyl loop is expected to be gapless if spin-orbit coupling (SOC) is strictly zero but gapped, with possible Weyl points, under finite SOC. We point out that high-resolution ARPES results to date cannot unambiguously resolve the SOC gap anywhere along the Weyl loop, leaving open the possibility that Co$_3$Sn$_2$S$_2$ hosts zero Weyl points or some non-zero number of Weyl points. On the surface of our samples, we further observe a possible Fermi arc, but we are unable to clearly verify its topological nature using the established counting criteria. As a result, we argue that from the point of view of photoemission spectroscopy the presence of Weyl points and Fermi arcs in Co$_3$Sn$_2$S$_2$ remains ambiguous. Our results have implications for ongoing investigations of Co$_3$Sn$_2$S$_2$ and other topological magnets.

cond-mat.str-el↗

arXiv2022

Signatures of Weyl fermion annihilation in a correlated kagome magnet

The manipulation of topological states in quantum matter is an essential pursuit of fundamental physics and next-generation quantum technology. Here we report the magnetic manipulation of Weyl fermions in the kagome spin-orbit semimetal Co$_3$Sn$_2$S$_2$, observed by high-resolution photoemission spectroscopy. We demonstrate the exchange collapse of spin-orbit-gapped ferromagnetic Weyl loops into paramagnetic Dirac loops under suppression of the magnetic order. We further observe that topological Fermi arcs disappear in the paramagnetic phase, suggesting the annihilation of exchange-split Weyl points. Our findings indicate that magnetic exchange collapse naturally drives Weyl fermion annihilation, opening new opportunities for engineering topology under correlated order parameters.

cond-mat.str-el↗