Multi-functional photonic spin Hall effect sensor controlled by phase transition

Photonic spin Hall effect(PSHE), as a novel physical effect in light–matter interaction, provides an effective metrological method for characterizing the tiny variation in refractive index(RI). In this work, we propose a multi-functional PSHE sensor based on VO_(2), a material that can reveal the phase transition behavior. By applying thermal control, the mutual transformation into different phase states of VO_(2) can be realized, which contributes to the flexible switching between multiple RI sensing tasks. When VO_(2) is insulating, the ultrasensitive detection of glucose concentrations in human blood is achieved. When VO_(2) is in a mixed phase, the structure can be designed to distinguish between the normal cells and cancer cells through no-label and real-time monitoring. When VO_(2) is metallic, the proposed PSHE sensor can act as an RI indicator for gas analytes. Compared with other multi-functional sensing devices with the complex structures, our design consists of only one analyte and two VO_(2) layers, which is very simple and elegant. Therefore, the proposed VO_(2)-based PSHE sensor has outstanding advantages such as small size, high sensitivity, no-label, and real-time detection, providing a new approach for investigating tunable multi-functional sensors.

Surface phonon resonance:A new mechanism for enhancing photonic spin Hall effect and refractive index sensor

Metal-based surface plasmon resonance(SPR)plays an important role in enhancing the photonic spin Hall effect(SHE)and developing sensitive optical sensors.However,the very large negative permittivities of metals limit their applications beyond the near-infrared regime.In this work,we theoretically present a new mechanism to enhance the photonic SHE by taking advantage of SiC-supported surface phonon resonance(SPhR)in the mid-infrared regime.The transverse displacement of photonic SHE is very sensitive to the wavelength of incident light and the thickness of SiC layer.Under the optimal parameter setup,the calculated largest transverse displacement of SiC-based SPhR structure reaches up to 163.8 ym,which is much larger than the condition of SPR.Moreover,an NO_(2) gas sensor based on the SPhR-enhanced photonic SHE is theoretically proposed with the superior sensing performance.Both the intensity and angle sensitivity of this sensor can be effectively manipulated by varying the damping rate of SiC.The results may provide a promising paradigm to enhance the photonic SHE in the mid-infrared region and open up new opportunity of highly sensitive refractive index sensors.

Engineered photonic spin Hall effect of Gaussian beam in antisymmetric parity-time metamaterials

A model of the photonic spin Hall effect(PSHE)in antisymmetric parity-time(APT)metamaterials with incidence of Gaussian beams is proposed here.We derive the displacement expression of the PSHE in APT metamaterials based on the transport properties of Gaussian beams in positive and negative refractive index materials.Furthermore,detailed discussions are provided on the APT scattering matrix,eigenstate ratio,and response near exceptional points in the case of loss or gain.In contrast to the unidirectional non-reflection in parity-time(PT)symmetric systems,the transverse shift that arises from both sides of the APT structure is consistent.By effectively adjusting the parameters of APT materials,we achieve giant displacements of the transverse shift.Finally,we present a multi-layer APT structure consisting of alternating left-handed and right-handed materials.By increasing the number of layers,Bragg oscillations can be generated,leading to an increase in resonant peaks in transverse shift.This study presents a new approach to achieving giant transverse shifts in the APT structure.This lays a theoretical foundation for the fabrication of related nano-optical devices.

Coexistence of giant Rashba spin splitting and quantum spin Hall effect in H–Pb–F

Rashba spin splitting(RSS)and quantum spin Hall effect(QSHE)have attracted enormous interest due to their great significance in the application of spintronics.In this work,we theoretically proposed a new two-dimensional(2D)material H–Pb–F with coexistence of giant RSS and quantum spin Hall effec by using the ab initio calculations.Our results show that H–Pb–F possesses giant RSS(1.21 eV·A)and the RSS can be tuned up to 4.16 e V·A by in-plane biaxial strain,which is a huge value among 2D materials.Furthermore,we also noticed that H–Pb–F is a 2D topological insulator(TI)duo to the strong spin–orbit coupling(SOC)interaction,and the large topological gap is up to 1.35 e V,which is large enough for for the observation of topological edge states at room temperature.The coexistence of giant RSS and quantum spin Hall effect greatly broadens the potential application of H–Pb–F in the field of spintronic devices.

Photonic spin Hall effect:fundamentals and emergent applications

The photonic spin Hall effect(SHE)refers to the transverse spin separation of photons with opposite spin angular momentum,after the beam passes through an optical interface or inhomogeneous medium,manifested as the spin-dependent splitting.It can be considered as an analogue of the SHE in electronic systems:the light’s right-circularly polarized and left-circularly polarized components play the role of the spin-up and spin-down electrons,and the refractive index gradient replaces the electronic potential gradient.Remarkably,the photonic SHE originates from the spin-orbit interaction of the photons and is mainly attributed to two different geometric phases,i.e.,the spin-redirection Rytov-Vlasimirskii-Berry in momentum space and the Pancharatnam-Berry phase in Stokes parameter space.The unique properties of the photonic SHE and its powerful ability to manipulate the photon spin,gradually,make it a useful tool in precision metrology,analog optical computing and quantum imaging,etc.In this review,we provide a brief framework to describe the fundamentals and advances of photonic SHE,and give an overview on the emergent applications of this phenomenon in different scenes.

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number Cs for energy-bands of trilayer graphene having the essence of intrinsic spin-orbit coupling is analytically calculated. We find that for each valley and spin, Cs is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states, consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin-orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin-orbit （RSO） interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin-orbit coupling, while the other two layers have zero intrinsic spin-orbit coupling. Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.

Modulation and enhancement of photonic spin Hall effect with graphene in broadband regions

The photonic spin Hall effect(SHE)holds great potential applications in manipulating spin-polarized photons.However,the SHE is generally very weak,and previous studies of amplifying photonic SHE were limited to the incident light in a specific wavelength range.In this paper,we propose a four-layered nanostructure of prism-graphene-air-substrate,and the enhanced photonic SHE of reflected light in broadband range of 0 THz–500 THz is investigated theoretically.The spin shift can be dynamically modulated by adjusting the thickness of air gap,Fermi energy of graphene,and also the incident angle.By optimizing the structural parameter of this structure,the giant spin shift(almost equal to its upper limit,half of the incident beam waist)in broadband range is achieved,covering the terahertz,infrared,and visible range.The difference is that in the terahertz region,the Brewster angle corresponding to the giant spin shift is larger than that of infrared range and visible range.These findings provide us with a convenient and effective way to tune the photonic SHE,and may offer an opportunity for developing new tunable photonic devices in broadband range.

Enhancing terahertz photonic spin Hall effect via optical Tamm state and the sensing application

The photonic spin Hall effect(PSHE),characterized by two splitting beams with opposite spins,has great potential applications in nano-photonic devices,optical sensing fields,and precision metrology.We present the significant enhancement of terahertz(THz)PSHE by taking advantage of the optical Tamm state(OTS)in In Sb-distributed Bragg reflector(DBR)structure.The spin shift of reflected light can be dynamically tuned by the structural parameters(e.g.the thickness)of the InSb-DBR structure as well as the temperature,and the maximum spin shift for a horizontally polarized incident beam at 1.1 THz can reach up to 11.15 mm.Moreover,we propose a THz gas sensing device based on the enhanced PSHE via the strong excitation of OTS for the InSb-DBR structure with a superior intensity sensitivity of 5.873×10^(4)mm/RIU and good stability.This sensor exhibits two orders of magnitude improvement compared with the similar PSHE sensor based on In Sb-supported THz long-range surface plasmon resonance.These findings may provide an alternative way for the enhanced PSHE and offer the opportunity for developing new optical sensing devices.

Asymmetrical photonic spin Hall effect based on dielectric metasurfaces

The photonic spin Hall effect has attracted considerable research interest due to its potential applications in spincontrolled nanophotonic devices.However,realization of the asymmetrical photonic spin Hall effect with a single optical element is still a challenge due to the conjugation of the Pancharatnam-Berry phase,which reduces the flexibility in various applications.Here,we demonstrate an asymmetrical spin-dependent beam splitter based on a single-layer dielectric metasurface exhibiting strong and controllable optical response.The metasurface consists of an array of dielectric nanofins,where both varying rotation angles and feature sizes of the unit cells are utilized to create high-efficiency dielectric metasurfaces,which enables to break the conjugated characteristic of phase gradient.Thanks to the superiority of the phase modulation ability,when the fabricated metasurface is under normal incidence with a wavelength of 1550 nm,the lefthanded circular polarization(LCP)light exhibits an anomalous refraction angle of 28.9°,while the right-handed circular polarization(RCP)light transmits directly.The method we proposed can be used for the flexible manipulation of spin photons and has potentials in high efficiency metasurfaces with versatile functionalities,especially with metasurfaces in a compact space.

Spin Chern numbers and time-reversal-symmetry-broken quantum spin Hall effect

The quantum spin Hall （QSH） effect is considered to be unstable to perturbations violating the time-reversal （TR） symmetry. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. As a useful tool to characterize topological phases without the TR symmetry, the spin-Chern number theory is introduced.

Finite size effects on the quantum spin Hall state in HgTe quantum wells under two different types of boundary conditions

The finite size effect in a two-dimensional topological insulator can induce an energy gap Eg in the spectrum of helical edge states for a strip of finite width. In a recent work, it has been found that when the spin--orbit coupling due to bulk-inversion asymmetry is taken into account, the energy gap Eg of the edge states features an oscillating exponential decay as a function of the strip width of the inverted HgTe quantum well. In this paper, we investigate the effects of the interface between a topological insulator and a normal insulator on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. Two different types of boundary conditions, i.e., the symmetric and asymmetric geometries, are considered. It is found that due to the existence of the interface between topological insulator and normal insulator this oscillatory pattern on the exponential decay induced by bulk-inversion asymmetry is modulated by the width of normal insulator regions. With the variation of the width of normal insulator regions, the shift of the Dirac point of the edge states in the spectrum and the energy gap Eg closing point in the oscillatory pattern can occur. Additionally, the effect of the spin-orbit coupling due to structure-inversion asymmetry on the finite size effects is also investigated.

The robustness of the quantum spin Hall effect to the thickness fluctuation in HgTe quantum wells

The quantum spin Hall effect （QSHE） was first realized in HgTe quantum wells （QWs）, which remain the only known two-dimensional topological insulator so far. In this paper, we have systematically studied the effect of the thickness fluctuation of HgTe QWs on the QSHE. We start with the case of constant mass with random distributions, and reveal that the disordered system can be well described by a virtual uniform QW with an effective mass when the number of components is small. When the number is infinite and corresponds to the real fluctuation, we find that the QSHE is not only robust, but also can be generated by relatively strong fluctuation. Our results imply that the thickness fluctuation does not cause backscattering, and the QSHE is robust to it.

Quantum spin Hall effect in a square-lattice model under a uniform magnetic field

We study a toy square-lattice model under a uniform magnetic field. Using the Landauer Biittiker fornmla, we calculate the transport properties of the system on a two-terminal, a four-terminal and a six-terminM device. W＇e find that the quantum spin Hall （QSH） effect appears ill energy ranges where the spin-up and spin-down subsystems have different filling factors. We also study the robustness of the resulting QSH effect and find that it is robust when the Fermi levels of both spin subsystems are far away from the energy plateaus but is fragile when the Fermi level of any spin subsystem is near the energy plateaus. These results provide an example of the QSH effect with a physical origin other than time-reversal （TR） preserving spin-orbit coupling （SOC）.

Discovery of Two-Dimensional Quantum Spin Hall Effect in Triangular Transition-Metal Carbides

Though the quantum spin Hall effect（QSHE） in two-dimensional（2 D） crystals has been widely explored, the experimental realization of quantum transport properties is only limited to HgTe/CdTe or InAs/GaSb quantum wells. Here we employ a tight-binding model on the basis of d（z^2）, d（xy）, and d（x^2-y^2） orbitals to propose QSHE in the triangular lattice, which are driven by a crossing of electronic bands at the Γ point. Remarkably, 2 D oxidized Mxenes W2 M2 C3 are ideal materials with nontrivial gap of 0.12 eV, facilitating room-temperature observations in experiments. We also find that the nontrivially topological properties of these materials are sensitive to the cooperative effect of the electron correlation and spin-orbit coupling. Due to the feasible exfoliation from its 3 D MAX phase, our work paves a new direction towards realizing QSHE with low dissipation.

Design of sign-reversible Berry phase effect in 2D magneto-valley material

Manipulating sign-reversible Berry phase effects is both fundamentally intriguing and practically appealing for searching for exotic topological quantum states.However,the realization of multiple Berry phases in the magneto-valley lattice is rather challenging due to the complex interactions from spin-orbit coupling(SOC),band topology,and magnetic ordering.Here,taking single-layer spin-valley RuCl_(2)as an example,we find that sign-reversible Berry phase transitions from ferrovalley(FV)to half-valley semimetal(HVS)to quantum anomalous valley Hall effect(QAVHE)can be achieved via tuning electronic correlation effect or biaxial strains.Remarkably,QAVHE phase,which combines both the features of quantum anomalous Hall and anomalous Hall valley effect,is introduced by sign-reversible Berry curvature or band inversion of d_(xy)/d_(x^(2)-y^(2))and d_(z^(2))orbitals at only one of the K/K′valleys of single-layer RuCl_(2).And the boundary of QAVHE phase is the HVS state,which can achieve 100%intrinsically valley polarization.Further,a k·p model unveiled the valleycontrollable sign-reversible Berry phase effects.These discoveries establish RuCl_(2)as a promising candidate to explore exotic quantum states at the confluence of nontrivial topology,electronic correlation,and valley degree of freedom.

Finite size effects on helical edge states in HgTe quantum wells with the spin orbit coupling due to bulk- and structure-inversion asymmetries

There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite width, the edge states on the two sides can couple together to produce a gap in the spectrum. The phenomenon is called the finite size effect in quantum spin Hall systems. In this paper, we investigate the effects of the spin-orbit coupling due to bulk- and structure-inversion asymmetries on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. When the bulk-inversion asymmetry is taken into account, it is shown that the energy gap Eg of the edge states due to the finite size effect features an oscillating exponential decay as a function of the strip width of the HgTe quantum well. The origin of this oscillatory pattern on the exponential decay is explained. Furthermore, if the bulk- and structure-inversion asymmetries are considered simultaneously, the structure-inversion asymmetry will induce a shift of the energy gap Eg closing point. Finally, based on the roles of the bulk- and structure-inversion asymmetries on the finite size effects, a way to realize the quantum spin Hall field effect transistor is proposed.

Spin Supercurrent in Phenomena of Quantum Non-Locality (Quantum Correlations, Magnetic Vector Potential) and in Near-Field Antenna Effect

It is shown that such phenomena as quantum correlations (interaction of space-separated quantum entities), the action of magnetic vector potential on quantum entities in the absence of magnetic field, and near-field antenna effect (the existence of superluminally propagating electromagnetic fields) may be explained by action of spin supercurrents. In case of quantum correlations between quantum entities, spin supercurrent emerges between virtual particles pairs (virtual photons) created by those quantum entities. The explanation of magnetic vector potential and near-field antenna effect is based on contemporary principle of quantum mechanics: the physical vacuum is not an empty space but the ground state of the field consisting of quantum harmonic oscillators (QHOs) characterized by zero-point energy. Using the properties of the oscillators and spin supercurrent, it is proved that magnetic vector potential is proportional to the moment causing the orientation of spin of QHO along the direction of magnetic field. The near-field antenna effect is supposed to take place as a result of action of spin supercurrent causing secondary electromagnetic oscillations. In this way, the electromagnetic field may spread at the speed of spin supercurrent. As spin supercurrent is an inertia free process, its speed may be greater than that of light, which does not contradict postulates of special relativity that sets limits to the speed of inertial systems only.

Spin Polarization of Fractional Quantum Hall States with <i>ν</i><2

The spin polarization of a fractional quantum Hall state shows very interesting properties. The curve of polarization versus magnetic field has wide plateaus. The fractional quantum Hall effect is caused by the Coulomb interaction because the 2D electron system without the Coulomb interaction yields no energy gap at the fractional filling factor. Therefore, the wide plateau in the polarization curve is also caused by the Coulomb interaction. When the magnetic field is weak, some electrons have up-spins and the others down-spins. Therein the spin-exchange transition occurs between two electrons with up and down spins via the Coulomb interaction. Then the charge distribution before the transition is the same as one after the transition. So these two states have the same classical Coulomb energy. Accordingly, the partial Hamiltonian composed of the spin exchange interaction should be treated exactly. We have succeeded in diagonalizing the spin exchange interaction for the first and second nearest electron pairs. The theoretical results reproduce the wide plateaus very well. If the interval modulations between Landau orbitals are taken into the Hamiltonian, the total energy has the Peierls instability. We can diagonalize the Hamiltonian with the interval modulation. The results reproduce wide plateaus and small shoulders which are in good agreement with the experimental data.

Breakdown of effective-medium theory by a photonic spin Hall effect

Effective-medium theory pertains to the theoretical modelling of homogenization,which aims to replace an inhomogeneous structure of subwavelength-scale constituents with a homogeneous effective medium.The effective-medium theory is fundamental to various realms,including electromagnetics and material science,since it can largely decrease the complexity in the exploration of light-matter interactions by providing simple acceptable approximation.Generally,the effective-medium theory is thought to be applicable to any all-dielectric system with deep-subwavelength constituents,under the condition that the effective medium does not have a critical angle,at which the total internal reflection occurs.Here we reveal a fundamental breakdown of the effective-medium theory that can be applied in very general conditions:showing it for deep-subwavelength all-dielectric multilayers even without a critical angle.Our finding relies on an exotic photonic spin Hall effect,which is shown to be ultrasensitive to the stacking order of deep-subwavelength dielectric layers,since the spin-orbit interaction of light is dependent on slight phase accumulations during the wave propagation.Our results indicate that the photonic spin Hall effect could provide a promising and powerful tool for measuring structural defects for all-dielectric systems even in the extreme nanometer scale.

Some experimental schemes to identify quantum spin liquids

Despite the apparent ubiquity and variety of quantum spin liquids in theory,experimental confirmation of spin liquids remains to be a huge challenge.Motivated by the recent surge of evidences for spin liquids in a series of candidate materials,we highlight the experimental schemes,involving the thermal Hall transport and spectrum measurements,that can result in smoking-gun signatures of spin liquids beyond the usual ones.For clarity,we investigate the square lattice spin liquids and theoretically predict the possible phenomena that may emerge in the corresponding spin liquids candidates.The mechanisms for these signatures can be traced back to either the intrinsic characters of spin liquids or the external field-driven behaviors.Our conclusion does not depend on the geometry of lattices and can broadly apply to other relevant spin liquids.