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The coupling of the spin and the motion of charge carriers stems directly from the atomic structure of a conductor. It has become an important ingredient for the emergence of topological matter, and, in particular, topological superconductivity which could host non-abelian excitations such as Majorana modes or parafermions. These modes are sought after mostly in semiconducting platforms which are made of heavy atoms and therefore exhibit naturally a large spin-orbit interaction. Creating domain walls in the spin orbit interaction at the nanoscale may turn out to be a crucial resource for engineering topological excitations suitable for universal topological quantum computing. For example, it has been proposed for exploring exotic electronic states or for creating hinge states. Realizing this in natural platforms remains a challenge. In this work, we show how this can be alternatively implemented by using a synthetic spin orbit interaction induced by two lithographically patterned magnetically textured gates. By using a double quantum dot in a light material -- a carbon nanotube -- embedded in a microwave cavity, we trigger hopping between two adjacent orbitals with the microwave photons and directly compare the wave functions separated by the domain wall via the light-matter coupling. We show that we can achieve an engineered staggered spin-orbit interaction with a change of strength larger than the hopping energy between the two sites.
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Time-reversal (T) symmetry breaking is a fundamental physics concept underpinning a broad science and technology area, including topological magnets, axion physics, dissipationless Hall currents, or spintronic memories. A best known conventional model of macroscopic T-symmetry breaking is a ferromagnetic order of itinerant Bloch electrons with an isotropic spin interaction in momentum space. Anisotropic electron interactions, on the other hand, have been a domain of correlated quantum phases, such as the T-invariant nematics or unconventional superconductors. Here we report discovery of a broken-T phase of itinerant Bloch electrons with an unconventional anisotropic spin-momentum interaction, whose staggered nature leads to the formation of two ferromagnetic-like valleys in the momentum space with opposite spin splittings. We describe qualitatively the effect by deriving a non-relativistic single-particle Hamiltonian model. Next, we identify the unconventional staggered spin-momentum interaction by first-principles electronic structure calculations in a four-sublattice antiferromagnet Mn5Si3 with a collinear checkerboard magnetic order. We show that the staggered spin-momentum interaction is set by nonrelativistic spin-symmetries which were previously omitted in relativistic physics classifications of spin interactions and topological quasiparticles. Our measurements of a spontaneous Hall effect in epilayers of antiferromagnetic Mn5Si3 with vanishing magnetization are consistent with our theory predictions. Bloch electrons with the unconventional staggered spin interaction, compatible with abundant low atomic-number materials, strong spin-coherence, and collinear antiferromagnetic order open unparalleled possibilities for realizing T-symmetry broken spin and topological quantum phases.
The intrinsic spin Hall effect plays an important role in spintronics applications, such as spin-orbit torque-based memory. The bulk space group symmetry determines the form of the bulk spin current conductivity tensor. This paper considers materials for which the local point group symmetry of individual atoms is lower than the global (bulk) symmetry. This enables a position-dependent spin current response, with additional tensor components allowed relative to the bulk response. We present a general method to compute the position-dependent intrinsic spin Hall conductivity, with similar computational effort relative to computing the bulk spin Hall conductivity. We also present the general symmetry-constrained form of the position-dependent spin current response. We apply this method to 1T-WTe$_2$, which exhibits a conventional spin Hall conductivity tensor component $sigma^y_{xz}$ and a staggered unconventional component $sigma^z_{xz}$. The magnitude of these two components, around 100 and 20 $(rm Omegacdot cm)^{-1}$, respectively, are comparable to the spin-orbit torque exerted on adjacent ferromagnets in experiments. We then consider orthorhombic PbTe, in which both uniform and staggered spin current conductivity are one order of magnitude larger.
This work introduces a generalization of the form of the spin-orbit interaction, the generalized spin-orbit interaction (GSOI). It expresses the magnetic field induced by two charged particles moving with a non-zero relative velocity as a field defined at all points in space, and exists in the reference frames of both particles. This is in contrast to spin-orbit interaction theory, in which the generated magnetic field is defined at only one point in space, and exists in the reference frame of one of the two particles. At the macroscopic scale, it is shown that the GSOI theory implies the same form of the O{}rsted magnetic field produced by a current-carrying wire. However, the theory is incompatible with the microscopic form of the Biot-Savart equation that implies that a charged particle induces a magnetic field by having a non-zero velocity. The implications of the GSOI theory on properties of the O{}rsted magnetic field in current-carrying atomically thin two-dimensional materials, such as graphene, are discussed. The framework established in this paper aims at re-imagining classical physical concepts in light of an advanced microscopic understanding.
We present in-depth measurements of the electronic band structure of the transition-metal dichalcogenides (TMDs) MoS2 and WS2 using angle-resolved photoemission spectroscopy, with focus on the energy splittings in their valence bands at the K point of the Brillouin zone. Experimental results are interpreted in terms of our parallel first-principles computations. We find that interlayer interaction only weakly contributes to the splitting in bulk WS2, resolving previous debates on its relative strength. We additionally find that across a range of TMDs, the band gap generally decreases with increasing magnitude of the valence-band splitting, molecular mass, or ratio of the out-of-plane to in-plane lattice constant. Our results provide an important reference for future studies of electronic properties of MoS2 and WS2 and their applications in spintronics and valleytronics devices.
Tellurium (Te) has attracted great research interest due to its unique crystal structure since 1970s. However, the conduction band of Te is rarely studied experimentally because of the intrinsic p-type nature of Te crystal. By atomic layer deposited dielectric doping technique, we are able to access the conduction band transport properties of Te in a controlled fashion. In this paper, we report on a systematic study of weak-antilocalization (WAL) effect in n-type two-dimensional (2D) Te films. We find that the WAL agrees well with Iordanskii, Lyanda-Geller, and Pikus (ILP) theory. The gate and temperature dependent WAL reveals that Dyakonov-Perel (DP) mechanism is dominant for spin relaxation and phase relaxation is governed by electron-electron (e-e) interaction. Large phase coherence length near 600nm at T=1K is obtained, together with gate tunable spin-orbit interaction (SOI). Transition from weak-localization (WL) to weak-antilocalization (WAL) depending on gate bias is also observed. These results demonstrate that newly developed solution-based synthesized Te films provide a new controllable strong SOI 2D semiconductor with high potential for spintronic applications.
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