Asymmetric Spin Splitting Research Articles

Tunable spin splitting of reflected vortex-beam of Weyl semimetal metasurface with stronger optical activity

This work investigated the spin splitting of a reflected beam with a vortex beam irradiating on a metasurface. This metasurface structure is the periodically rectangular-groove array of ionic crystal, where the array is a sub-wavelength grating with its periodical direction situated in the surface plane. In the grating structure, we embedded magnetic Weyl semimetals. Consequently, a stronger optical activity can be found, which originates from the unique electronic structure of Weyl semimetals and the orientation of the grating arrangement. By controlling the separation of Weyl points and grating orientation, we observe notable asymmetric spin splitting in different frequency ranges with distinctly unique distributions. Significant spin splitting was observed to be correlated with substantial Kerr rotation angles and reflectance differences, indicating strong optical activity. Additionally, with the increasing topological charges, the spin splitting increases significantly. Our results are useful for the manipulation of infrared radiations and infrared optical detection.

Goos–Hänchen shifts on spin representation

We analyze the Goos–Hänchen (GH) shift and longitudinal spin splitting (LSS) at a planar interface between two optical media in the spin representation. While these optical effects have been studied previously, we examine the direct and cross-reflected light fields, and their interference from the spin representation to reveal the physical mechanism of the GH shift and establish a quantitative relationship between it and LSS. Furthermore, we show that angular asymmetric spin splitting occurs under the spin representation when linearly polarized light with a phase difference of 180° and an amplitude ratio angle deviating from 45° impinges on the air–glass interface at Brewster’s angle. Finally, we reveal that the spin component field of the reflected light field for the total reflection case is different from that of the Brewster angle reflection, the most typical manifestation is that the intensity of the two spin component fields is not equal.

Giant asymmetric proximity-induced spin–orbit coupling in twisted graphene/SnTe heterostructure

We analyze the spin–orbit coupling effects in a 3∘-degree twisted bilayer heterostructure made of graphene and an in-plane ferroelectric SnTe, with the goal of transferring the spin–orbit coupling from SnTe to graphene, via the proximity effect. Our results indicate that the point-symmetry breaking due to the incompatible mutual symmetry of the twisted monolayers and a strong hybridization has a massive impact on the spin splitting in graphene close to the Dirac point, with the spin splitting values greater than 20 meV. The band structure and spin expectation values of graphene close to the Dirac point can be described using a symmetry-free model, triggering different types of interaction with respect to the threefold symmetric graphene/transition-metal dichalcogenide heterostructure. We show that the strong hybridization of the Dirac cone’s right movers with the SnTe band gives rise to a large asymmetric spin splitting in the momentum space. Furthermore, we discover that the ferroelectricity-induced Rashba spin–orbit coupling in graphene is the dominant contribution to the overall Rashba field, with the effective in-plane electric field that is almost aligned with the (in-plane) ferroelectricity direction of the SnTe monolayer. We also predict an anisotropy of the in-plane spin relaxation rates. Our results demonstrate that the group-IV monochalcogenides MX (M = Sn, Ge; X = S, Se, Te) are a viable alternative to transition-metal dichalcogenides for inducing strong spin–orbit coupling in graphene.

Asymmetric spin splitting of Laguerre-Gaussian beams in chiral PT-symmetric metamaterials.

We systematically study the spin Hall effect of light (SHEL) in chiral PT-symmetric metamaterials when Laguerre Gaussian beams (LG beams) are incident and discover that cross-polarization (rs p, rp s) and intrinsic orbital angular momentum (IOAM) result in an asymmetric splitting of left-spin circularly polarized (LCP) light and right-spin circularly polarized (RCP) light. Additionally, there are spin Hall shift peaks near |rpp | ≪ |rss | (rs s and rp p are Fresnel reflection coefficients). Altering the topological charge number ℓ, the chiral parameter κ, the dimensionless frequency M, and the incident angle θ may also influence the asymmetric spin splitting and displacement peak. We believe that this research will provide new ways to manipulate and enhance the asymmetric spin splitting of light and provide new applications for spin photonic devices.

Off‐Axis Vortex‐Induced Asymmetric Spin‐Dependent Splitting

AbstractA simple and effective method to control the asymmetric spin splitting flexibly by introducing off‐axis vortex beams is reported here. Unlike the conventional spin Hall effect of light, both the value and the sign of the right‐ and left‐handed circularly polarized components can be manipulated individually by modulating the off‐axis vortex's position. Significantly, the in‐plane shifts occur when the vortex position x0 is non‐zero. In addition, it is found that this asymmetric splitting increases with increase in the topological charge. This flexibly adjustable asymmetric spin splitting provides the possibility to accelerate the development of nano‐photonic devices.

Band Structure Near the Dirac Point in HgTe Quantum Wells with Critical Thickness.

Mercury telluride (HgTe) thin films with a critical thickness of 6.5 nm are predicted to possess a gapless Dirac-like band structure. We report a comprehensive study on gated and optically doped samples by magnetooptical spectroscopy in the THz range. The quasi-classical analysis of the cyclotron resonance allowed the mapping of the band dispersion of Dirac charge carriers in a broad range of electron and hole doping. A smooth transition through the charge neutrality point between Dirac holes and electrons was observed. An additional peak coming from a second type of holes with an almost density-independent mass of around was detected in the hole-doping range and attributed to an asymmetric spin splitting of the Dirac cone. Spectroscopic evidence for disorder-induced band energy fluctuations could not be detected in present cyclotron resonance experiments.

Universal transparency and asymmetric spin splitting near the Dirac point in HgTe quantum wells

Spin-orbit coupling in thin HgTe quantum wells results in a relativistic-like electron band structure, making it a versatile solid state platform to observe and control nontrivial electrodynamic phenomena. Here we report an observation of universal terahertz (THz) transparency determined by fine-structure constant $\ensuremath{\alpha}\ensuremath{\approx}1/137$ in 6.5-nm-thick HgTe layer, close to the critical thickness separating phases with topologically different electronic band structure. Using THz spectroscopy in a magnetic field we obtain direct evidence of asymmetric spin splitting of the Dirac cone. This particle-hole asymmetry facilitates optical control of edge spin currents in the quantum wells.

Transformation from asymmetric spin splitting to symmetric spin splitting with phase compensation in photonic spin Hall effect.

Generally, when an arbitrary polarized light beam is reflected or refracted from an isotropic interface, the spin splitting in photonic spin Hall effect (SHE) shows asymmetry properties. In this paper, we theoretically propose a phase compensation scheme to achieve the transformation from asymmetric spin splitting to symmetric spin splitting in photonic SHE. We experimentally acquire the spin splitting after phase compensation in the case of a 45 degrees linear polarized Gaussian light beam totally internally reflected from a prism-air interface. Particularly, whether or not phase compensation, the transverse shift of total barycenter of reflected field [i.e., the Imbert-Fedorov (IF) shift] does not change. These findings can solve this problem that asymmetric spin splitting cannot be observed by weak measurements.

Symmetric spin splitting of elliptically polarized vortex beams reflected at air-gold interface via pseudo-Brewster angle.

A simple expression of the transverse spatial spin splitting of light-carrying intrinsic orbital angular momentum (IOAM) is theoretically derived for reflections at strong absorbing media surfaces. By introducing an asymmetric spin splitting (ASS) factor, the transverse spatial symmetric spin splitting (SSS) and ASS of an arbitrary polarized vortex beam can be distinguished. Here, the transverse spatial SSS of an elliptically polarized vortex beam with a phase difference of 90° is predicted when the incident angle is close to the pseudo-Brewster angle. Remarkably, the larger transverse spatial SSS reaches 1100 nm for the incident circularly polarized LG beam with l=3. It is noteworthy that the transverse spatial SSS can be flexibly manipulated by changing the polarized angle, meaning it is theoretically possible to realize fully polarization-controllable transverse spatial SSS for elliptically polarized incident vortex beams. These results could potentially be applied to precision polarization metrology and edge-enhanced imaging.

Actively manipulating asymmetric photonic spin Hall effect with graphene

The photonic spin Hall effect (SHE), manifesting itself as spin-dependent splitting of light, holds potential applications in precise metrology and spin-based nanophotonic devices. Thus, it’s highly desirable to control this effect at will. However, there lacks an active way for manipulating asymmetric spin splitting, i.e., the asymmetric splitting properties are fixed and cannot be dynamically modulated when the material is fabricated. In this work, we propose a simple and active method for manipulating the asymmetric in-plane spatial and angular shifts by considering a light beam reflected at the glass-air interface embedding with monolayer graphene. We theoretically establish the relationship between the in-plane spin shifts and the conductivity of graphene. We reveal that the in-plane spatial and angular shifts can be significantly adjusted and show obvious asymmetric features by changing the Fermi energy in graphene when the light beam is reflected near the Brewster and critical angles. Interesting, when the incident light is horizontally polarized, the optical shifts are more sensitive to the changes of Fermi energy near the Brewster angle than that near the critical angle. Finally, we propose a potential method that using spin angular shifts to directly detect the tiny variation of Fermi energy.

Tunable asymmetric spin splitting by black phosphorus sandwiched epsilon-near-zero-metamaterial in the terahertz region.

In-plane photonic spin splitting effect is investigated in tunneling terahertz waves through an epsilon-near-zero metamaterial sandwiched between monolayer black phosphorus (BP). The strong in-plane anisotropy of BP layers will induce in-plane asymmetric spin splitting. The asymmetric spin splitting can be flexibly tuned by the angles between the incident plane and the armchair crystalline directions of the top and bottom BP layers, i.e., ϕ1 and ϕ2. Based on this, an angle-resolved barcode-encryption scheme is discussed. For the special case of ϕ1 = ϕ2 = 0 or 90°, the transmitted beam undergoes Goos-Hänchen shift, which varies with the carrier density of BP. We believe these findings can facilitate the development of novel optoelectronic devices in the Terahertz region.

Entropy production by thermodynamic currents in ambipolar conductors with identical spin dynamics characteristics between holes and electrons

We have evaluated the role of spin current in the energy dissipation mechanism in ambipolar conductors with identical spin-related characteristics between holes and electrons. Application of the Gibbs–Duhem relation to ambipolar conductors establishes a thermodynamic relation between the spin-dependent chemical potentials of holes and electrons, inducing an asymmetric spin splitting between the hole and electron chemical potentials. This yields two types of spin relaxation so as to allow the antiparallel spin current, where hole and electron spins flow in the opposite direction, to have a large spin diffusion length, but to retain that of the parallel spin current at a standard value.

Photonic spin Hall effect of monolayer black phosphorus in the Terahertz region

Abstract As a two-dimensional (2D) material, black phosphorus (BP) has attracted significant attention owing to exotic physical properties such as low-energy band gap, high carrier mobility, and strong in-plane anisotropy. The striking in-plane anisotropy is a promising candidate for novel light-matter interaction. Here, we investigate the photonic spin Hall effect (PSHE) on a monolayer of BP. Due to the in-plane anisotropic property of BP, the PSHE is accompanied with Goos-Hänchen and Imbert-Fedorov effects, resulting in an asymmetric spin splitting. The asymmetric spin splitting can be flexibly tuned by the angle between the incident plane and the armchair crystalline direction of BP and by the carrier density via a bias voltage. The centroid displacements of two opposite spin components of the reflected beam along directions parallel and perpendicular to the incident plane can be considered as four independent channels for information processing. The potential application in barcode-encryption is proposed and discussed. These findings provide a deeper insight into the spin-orbit interaction in 2D material and thereby facilitate the development of optoelectronic devices in the Terahertz region.

Chirality induced asymmetric spin splitting of light beams reflected from an air-chiral interface

The spin Hall effect (SHE) of light beams reflected from an air-chiral interface are investigated systematically. Due to the intrinsic chiral asymmetry of the medium, a horizontally polarized incident Gaussian beam will undergo asymmetric spin splitting, i.e., both the displacements and energies of two spin components of the reflected beam are different. One spin component can undergo large displacement near points of |rpp| = |rsp| (rpp and rsp are the Fresnel reflection coefficients), where the reflected beams are almost in circular polarization states. Moreover, for an incident beam carrying orbital angular momentum (OAM), the two spin components acquire additional OAM dependent shifts, which attribute to the asymmetric spin splitting. Thus, the asymmetric spin splitting of the reflected beam will vary with the incident OAM. These findings provide a deeper insight into the SHE of light, and they may have potential application in precision metrology.

Controllable symmetric and asymmetric spin splitting of Laguerre-Gaussian beams assisted by surface plasmon resonance.

The spin splitting of light beams carrying orbital angular momentum (OAM) is investigated theoretically in attenuated internal reflection in the Kretschmann configuration. The excitation of the surface plasmon resonance (SPR) can significantly enhance the OAM-induced Imbert-Fedorov (IF) shift and the OAM-dependent spin splitting. The cooperation effect of these two shifts will result in an asymmetric spin splitting, which varies with the incident angle and polarization state. Specially, at the SPR angle, the OAM-induced IF shift vanishes, and the OAM-dependent spin splitting will cause a symmetric spin splitting. However, when the incident beam is horizontally polarized, the OAM-induced IF shift predominates. Thus the two spin components of the reflected will not be split; instead, they will be shifted together. This flexible control of the optical spin splitting can find applications in quantum information and precision metrology.

Theoretical study of energy band splitting induced by spin–orbit interaction in helically coiled carbon nanotubes

Abstract Recent theoretical and experimental works on straight carbon nanotubes (SCNTs) have revealed that the curvature could enhance the spin–orbit interaction (SOI). Motivated by this, we further explore the effective SOI with another different curvature in helically coiled carbon nanotubes (HCCNTs) using the tight-binding model and perturbation approach. Finally, we derive the effective SOI in HCCNTs, and find the electron–hole asymmetric spin splitting. Interestingly, the asymmetric splitting largely depends on coil pitch p and coil radius r, which are not known in SCNTs. These results should be valuable for spintronic applications of carbon nanotubes.

Energy spectrum and Landau levels in bilayer graphene with spin–orbit interaction

We present a theoretical study of the band structure and Landau levels in bilayer graphene at low energies in the presence of a transverse magnetic field and Rashba spin–orbit interaction in the regime of negligible trigonal distortion. Within an effective low-energy approach the (Löwdin partitioning theory), we derive an effective Hamiltonian for bilayer graphene that incorporates the influence of the Zeeman effect, the Rashba spin–orbit interaction and, inclusively, the role of the intrinsic spin–orbit interaction on the same footing. Particular attention is paid to the energy spectrum and Landau levels. Our modeling unveils the strong influence of the Rashba coupling λR in the spin splitting of the electron and hole bands. Graphene bilayers with weak Rashba spin–orbit interaction show a spin splitting linear in momentum and proportional to λR, but scaling inversely proportional to the interlayer hopping energy γ1. However, at robust spin–orbit coupling λR, the energy spectrum shows a strong warping behavior near the Dirac points. We find that the bias-induced gap in bilayer graphene decreases with increasing Rashba coupling, a behavior resembling a topological insulator transition. We further predict an unexpected asymmetric spin splitting and crossings of the Landau levels due to the interplay between the Rashba interaction and the external bias voltage. Our results are of relevance for interpreting magnetotransport and infrared cyclotron resonance measurements, including situations of comparatively weak spin–orbit coupling.

Curvature-enhanced spin-orbit coupling in a carbon nanotube

Structure of the spin-orbit coupling varies from material to material and thus finding the correct spin-orbit coupling structure is an important step towards advanced spintronic applications. We show theoretically that the curvature in a carbon nanotube generates two types of the spin-orbit coupling, one of which was not recognized before. In addition to the topological phase-related contribution of the spin-orbit coupling, which appears in the off-diagonal part of the effective Dirac Hamiltonian of carbon nanotubes, there is another contribution that appears in the diagonal part. The existence of the diagonal term can modify spin-orbit coupling effects qualitatively, an example of which is the electron-hole asymmetric spin splitting observed recently, and generate four qualitatively different behavior of energy level dependence on parallel magnetic field. It is demonstrated that the diagonal term applies to a curved graphene as well. This result should be valuable for spintronic applications of graphitic materials.