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arXiv:2608.14353

Orbital Hall Effect in Weyl Semimetals from quantum geometric band interference

Chiara Pacella, Maximilian Ünzelmann, Ahmed Osman, Tim Figgemeier, Friedrich Reinert, Angel Rubio, Domenico Di Sante

cond-mat.mtrl-sciquant-phSubmitted Aug 14, 2026• Announced Aug 17, 2026
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Abstract

Orbital angular momentum (OAM) transport in solids, prominently manifested in the orbital Hall effect, has emerged as a fundamental phenomenon that can decisively exceed its spin-based counterparts. However, the microscopic mechanisms governing OAM dynamics remain only partially understood. In particular, the role of band geometry in orbital transport is still largely unresolved. Here we address this question in the TaAs family of Weyl semimetals, TaAs, TaP, NbAs, and NbP, whose well-established topology and associated OAM textures make them an ideal platform in this context. Using ab initio density functional theory, complemented by a minimal Weyl model based on adiabatic perturbation theory, we establish --- both numerically and analytically --- a direct link between OAM transport, band geometry, and topological electronic structure.

Comments
5 pages, 4 figures

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Orbital angular momentum (OAM) transport in solids, prominently manifested in the orbital Hall effect, has emerged as a fundamental phenomenon that can decisively exceed its spin-based counterparts. However, the microscopic mechanisms governing OAM dynamics remain only partially understood. In particular, the role of band geometry in orbital transport is still largely unresolved. Here we address this question in the TaAs family of Weyl semimetals, TaAs, TaP, NbAs, and NbP, whose well-established topology and associated OAM textures make them an ideal platform in this context. Using ab initio density functional theory, complemented by a minimal Weyl model based on adiabatic perturbation theory, we establish --- both numerically and analytically --- a direct link between OAM transport, band geometry, and topological electronic structure.
The discovery of integer quantum Hall effect and its subsequent theoretical formulation heralded a new paradigm of thinking in condensed matter physics, which has by now blossomed into the rapidly growing field of topological phases. In this work we investigate several mutually related topics in the framework of topological band theory. In Chapter 2, we study solutions to boundary states on a lattice and see how they are related to the bulk topology. To elicit a real space manifestation of the non-trivial topology, the presence of a physical edge is not strictly necessary. We study two other possibilities, namely the entanglement spectrum associated with an imaginary spatial boundary, and the localization centers of Wannier functions, in Chapters 3,4, and 5. Topological classification through discrete indices is so far possible only for systems described by pure quantum states - in the existing scheme, quantization is lost for systems in mixed states. In Chapter 6, we present a program through which discrete topological indices can be defined for topological band systems at finite temperature, based on Uhlmann's parallel transport of density matrices. The potential of topologocal insulators in realistic applications lies in the existence of Dirac nodes on its surface spectrum. Dirac physics, however, is not exclusive to TI surfaces. In a recently discovered class of materials known as Weyl semimetals, energy nodes which emit linear dispersions also occur in the bulk material. In Chapter 7, we study the possibility of resonance states induced by localized impurities near the nodal energy in Weyl semimetals, which will help us in understanding the stability of density-of-state suppression at the energy nodes. Finally, in Chapter 8, we apply the topological characterization developed for noninteracting particles to a class of interacting spin models in 3D, which are generalizations of Kitaev's honeycomb model, and identify several exotic quantum phases such as spin metals and spin semimetals
Quantum Simulation Many compounds have now been identified as Weyl semimetals, materials with an unusual electronic band structure characterized by the so-called Weyl points. Weyl points always appear in pairs, but the solid-state materials studied so far have at least four. Wang et al. engineered a Weyl semimetallic state with the minimum number of Weyl points (two) in a gas of ultracold atoms trapped in an optical lattice (see the Perspective by Goldman and Yefsah). To do that, the researchers had to create three-dimensional spin-orbit coupling in this system. The relative simplicity of the resulting band structure will make it easier to observe the unusual effects associated with this state. Science , this issue p. [271][1]; see also p. [234][2] [1]: /lookup/doi/10.1126/science.abc0105 [2]: /lookup/doi/10.1126/science.abg0892
Studies of the 3D quantum Hall effect (QHE) have primarily emphasized transport features that mimic the well-established 2D QHE. In this work, we show that qualitatively new features arise when an in-plane magnetic field is applied to a 3D Weyl semimetal in the quantum Hall regime. An unexpected Hall quantum oscillation, distinct from the Weyl-orbit oscillation, coexists with the QHE, along with an unquantized two-terminal magnetoresistance. Moreover, unconventional antichiral transmission enables a peculiar disorder-robust negative longitudinal resistance. Quantization tunable by the lead configuration is further found in this transport geometry. A unique type of nonlocal quantum backscattering channels underlies these phenomena. Our work demonstrates a breakdown of the topological characterization of transport even with 3D Chern numbers and reveals hidden 3D QHE transport properties. It opens a new class of transport measurements and phenomena.
Weyl semimetals are three-dimensional (3D) gapless topological phases with Weyl cones in the bulk band. According to lattice theory, Weyl cones must come in pairs, with the minimum number of cones being two. A semimetal with only two Weyl cones is an ideal Weyl semimetal (IWSM). Here we report the experimental realization of an IWSM band by engineering 3D spin-orbit coupling for ultracold atoms. The topological Weyl points are clearly measured via the virtual slicing imaging technique in equilibrium and are further resolved in the quench dynamics. The realization of an IWSM band opens an avenue to investigate various exotic phenomena that are difficult to access in solids.
We explore the topological properties of double-Weyl semimetals with cold atoms in optical lattices. We first propose a tight-binding model of simulating the double-Weyl semimetal with a pair of double-Weyl points by engineering the atomic hopping in a three-dimensional optical lattice. We show that the double-Weyl points with topological charges of $\ifmmode\pm\else\textpm\fi{}2$ behave as the sink and source of Berry flux in momentum space connecting by two Fermi arcs and they are stabilized by the C4h{C}_{4h}C4h​ point-group symmetry. By applying a realizable C4{C}_{4}C4​ breaking term, we find that each double-Weyl point splits into two single-Weyl points and obtain rich phase diagrams in the parameter space spanned by the strengths of an effective Zeeman term and the C4{C}_{4}C4​ breaking term, which contains a topological and a normal insulating phase and two topological Weyl semimetal phases with eight and four single-Weyl points, apart from the double-Weyl semimetal phase. Furthermore, we demonstrate with numerical simulations that (i) the mimicked double- and single-Weyl points can be detected by measuring the atomic transfer fractions after a Bloch oscillation; (ii) the Chern number of different quantum phases in the phase diagram can be extracted from the center shift of the hybrid Wannier functions, which can be directly measured with time-of-flight imaging; (iii) the band topology of the C4{C}_{4}C4​-symmetric Bloch Hamiltonian can be detected simply from measuring the spin polarization at the high-symmetry momentum points with a condensate in the optical lattice. The proposed system would provide a promising platform for elaborating the intrinsic exotic physics of double-Weyl semimetals and the related topological phase transitions.
Weyl semimetals are three-dimensional, topologically protected, gapless phases which show exotic phenomena such as Fermi arc surface states or negative magnetoresistance. It is an open question whether interparticle interactions can turn the topological semimetal into a topologically nontrivial Mott-insulating phase. We investigate an experimentally motivated model for Weyl physics of cold atoms in optical lattices, with the main focus on interaction effects and topological properties, by means of dynamical mean-field theory. We characterize topological phases by numerically evaluating the Chern number via the Ishikawa-Matsuyama formula for interacting phases. Within our studies, we find that the Chern numbers become trivial when interactions lead to insulating behavior. For a deeper understanding of the Weyl-semimetal-to-Mott-insulator topological phase transition, we evaluate the topological properties of quasiparticle bands as well as so-called blind bands. Finally, we consider a system with an open boundary along one spatial direction in order to study correlation effects of surface states. In a narrow regime close to the topological phase transition, we find a correlation-induced state in which the surface becomes metallic while the bulk is semimetallic.