Valley-selective Circular Dichroism Research Articles

Floquet-engineered valley topotronics in Kekulé-Y bond textured graphene superlattice

The exquisite distortion in a Kekulé -Y (Kek-Y) superlattice merges the two inequivalent Dirac cones (from the K- and the K′- points) into the highest symmetric Γ-point in the hexagonal Brillouin zone. Here, we report that UV circularly polarized light not only opens up a topological gap at the Γ-point, but also lifts the valley degeneracy at that point. Endowed with Floquet dynamics and by devising a scheme of high-frequency approximation, we propose that the left/right-handedness in polarized light offers the possibility to realize valley-selective circular dichroism in a Kek-Y-shaped graphene superlattice. In addition, the non-vanishing Berry curvature and enumeration of the valley-resolved Chern number CK/CK′=+1/−1 enable us to assign two pseudospin flavors (up/down) with the two valleys. Thereby, the above observations confirm the topological transition, suggesting the ease of realizing the valley quantum anomalous Hall state within the photon-dressed Kek-Y. These findings further manifest a non-zero optical valley polarization that is maximal at the Γ-point. Our paper thus proposes an optically switchable topological valley filter, which is desired in the evolving landscape of valleytronics.

Anomalous valley Hall effect induced by mirror symmetry breaking in transition metal dichalcogenides

The control of the valley degree of freedom in Bloch electrons has opened up new avenues for information processing. The synthesis of ferrovalley materials, however, has been limited due to the stringent requirements for breaking both time and space inversion symmetries. To address this challenge, we propose a Janus method for inducing valley polarization in nonmagnetic transition metal dichalcogenides. Our study shows that the magnetic moment in monolayer TiTeI arises from the breaking of mirror symmetry and the presence of unpaired electrons. The Stoner criterion ${I}_{ex}N({E}_{F})>1$ confirms that the band splitting originates from the $d$ orbital of titanium. Moreover, the exchange interaction combined with spin-orbit coupling opens up the valley splitting. The anomalous valley Hall effect (AVHE) can be realized by applying an in-plane electric field, as a result of the valley-contrasting Berry curvature. The modulation of valley-selective circular dichroism and AVHE by optical, electronic, and magnetic fields make TiTeI a promising material for future studies and applications in valleytronics.

Tunable valley-selective circular polarization in vdW multilayers consisting of inversion-symmetric monolayers

Valley manipulation via valley selective circular dichroism is beneficial for information encoding and processing.

Spontaneous Valley Polarization in a Ferromagnetic Fe(OH)2 Monolayer

At present, creating sizable spontaneous valley polarization is at the center of the study of valleytronics, which, however, is still a huge challenge. In this work, we determined that the ferromagnetic Fe(OH)2 monolayer of the hexagonal lattice is a highly appealing candidate for valleytronics by using first-principles calculations in conjunction with tight-binding model analysis. In light of the simultaneous inversion symmetry breaking and time-reversal symmetry breaking, we illustrated that the strong spin-orbit coupling and robust ferromagnetic exchange interaction cause a spontaneous valley polarization as large as 67 meV for Fe(OH)2, indicative of room-temperature application. In addition, the physics of valley-selective circular dichroism, spin/valley Hall effects, and topological phase transition were also discussed.

Tunable magnetocrystalline anisotropy and valley polarization in an intrinsic ferromagnetic Janus 2H -VTeSe monolayer

Two-dimensional Janus monolayers with specular asymmetry exhibit excellent physicochemical properties and are a good candidate for optoelectronic, valley electronic, and nanoelectronics devices. Based on the density functional theory, the Janus $2H$-VTeSe monolayer is an intrinsic ferromagnetic semiconductor with an indirect band gap of 0.324 eV and exhibits a good thermodynamic and kinetic stability, in-plane magnetocrystal anisotropy, large spontaneous valley polarization of 155 meV, and high Curie temperature (${T}_{c}$) of 380 K. The biaxial strain ($\ensuremath{-}6%<\ensuremath{\varepsilon}<6%$) can effectively tune the Janus $2H$-VTeSe monolayer from the bipolar magnetic semiconductor phase to half-semiconductor, spin gapless semiconductor, and half-metallic phases. Moreover, the magnetocrystal anisotropy energy (MAE) is modulated by the strain from 0.54 meV ($\ensuremath{\varepsilon}=\ensuremath{-}6%$) to 1.32 meV ($\ensuremath{\varepsilon}=\ensuremath{-}2%$), and the easy [100] and hard [001] magnetic axes could be switched from each other by charge carrier doping. The calculated valley optical response of the Janus $2H$-VTeSe monolayer exhibits a valley-selective circular dichroism. Due to the broken inversion and time-reversal symmetry, the valley polarization and Berry curvature can be continuously tuned by applying biaxial strains (modulation range 24.2%), external electric field (modulation range 2%), and varying the magnetization angle (0 to 180 degrees). The Janus $2H$-VTeSe monolayer possesses intrinsic ferromagnetic ordering, large spontaneous valley polarization, high ${T}_{c}$ of 380 K, and considerable MAE of 1.15 meV, giving it a potential application in the two-dimensional spintronic devices.

Rashba Splitting and Electronic Valley Characteristics of Janus Sb and Bi Topological Monolayers.

Janus Sb and Bi monolayers as a new class of 2D topological insulator materials, which could be fulfilled by asymmetrical functionalizations with methyl or hydroxyl, are demonstrated by first-principles spin–orbit coupling (SOC) electronic structure calculations to conflate nontrivial topology, Rashba splitting and valley-contrast circular dichroism. Cohesive energies and phonon frequency dispersion spectra indicate that all Janus Sb and Bi monolayers possess a structural stability in energetic statics but represent virtual acoustic phonon vibrations of the hydrogen atoms passivating on monolayer surfaces. Band structures of Janus Sb and Bi monolayers and their nanoribbons demonstrate they are nontrivial topological insulators. Rashba spin splitting at G point in Brillouin zone of Janus Bi monolayers arises from the strong SOC px and py orbitals of Bi bonding atoms together with the internal out-of-plane electric field caused by asymmetrical functionalization. Janus Sb and Bi monolayers render direct and indirect giant bandgaps, respectively, which are derived from the strong SOC px and py orbitals at band-valley Brillouin points K and K′ where valley-selective circular dichroism of spin valley Hall insulators is also exhibited.

Chiral phonons entangled with multiple Hall effects and unified convention for pseudoangular momentum in two-dimensional materials

Recently, a series of two-dimensional nonmagnetic layered materials $X{\mathrm{Si}}_{2}{Y}_{4}$ ($X$=transition metals; $Y$ = pnictogens) having similar crystal structures with transition-metal dichalcogenides (TMDs) were proposed for their potential application value. Like TMDs, we propose that chiral phonon involved valley-selective optical circular dichroism can be also obtained in $X{\mathrm{Si}}_{2}{Y}_{4}$, and it can be further entangled with multiple Hall effects. However, it is difficult to compare such effect between $X{\mathrm{Si}}_{2}{Y}_{4}$ and TMDs due to the nonunified conventions for pseudoangular momentum (PAM) in the previous studies. Here we use ${\mathrm{MoSi}}_{2}{\mathrm{As}}_{4}$ and ${\mathrm{MoS}}_{2}$ as examples to establish a unified convention for both phonon PAM and electronic PAM, together with showing their similarities and differences in crystal structure, band structures, and valley-selective optical circular dichroism. In particular, we find in ${\mathrm{MoSi}}_{2}{\mathrm{As}}_{4}$, the chiral phonon emission/absorption, the spin, the valley, and the transverse Hall current, can be modulated by changing either the energy or the handedness of the incident light, which show better performance than TMDs.

Chirality of Valley Excitons in Monolayer Transition-Metal Dichalcogenides.

By enabling control of valley degrees of freedom in transition-metal dichalcogenides, valley-selective circular dichroism has become a key concept in valleytronics. Herein, we show that valley excitons, bound electron-hole pairs formed at the K or K̅ valleys upon absorption of circularly polarized light, are chiral quasiparticles characterized by a finite orbital angular momentum (OAM). We further formulate an ab initio many-body theory of valley-selective circular dichroism and valley excitons based on the Bethe-Salpeter equation. Besides governing the interaction with circularly polarized light, the OAM confers upon excitons a finite magnetization that manifests itself through an excitonic Zeeman splitting upon interaction with external magnetic fields. The good agreement between our ab initio calculations and recent experimental measurements of the exciton Zeeman shifts corroborates this picture, indicating that valley excitons can carry angular momentum even in their singlet state.

Janus 2H-VSSe monolayer: two-dimensional valleytronic semiconductor with nonvolatile valley polarization

Valleytronic as a hot topic in recent years focuses on electrons’ valley degree of freedom as a quantum information carrier. Here, by combining two-band k.p model with high-throughput density functional theory (DFT) calculations, the valley states of Janus 2H-VSSe monolayer are studied which have spontaneous polarization. Nonvolatile valley polarization state is mainly arises from intrinsic ferromagnetism contributed by V-3d electronic configuration and not the spontaneous out-of-plane dipole moment of VSSe monolayer. The effective Hamiltonian model and DFT calculations both showed that the valley splitting mainly originates from the smaller spin splitting coming from the spin–orbit coupling effect rather than the spin splitting of magnetic exchange field. By using the effective Dirac Hamiltonian and Kubo formula, we further calculated the longitudinal and transversal conductivities and absorption spectra of VSSe monolayer which exhibits an anomalous valley Hall effect and clear valley-selective circular dichroism. Our calculations indicate that the modification of valley and spin splitting related to Berry curvature by applying an external strain is more noticeable than by the change of the magnetic moment orientation and electric field. We found that carriers accumulation with particular spin and valley label can be manipulated by tuning effective Hamiltonian parameters. The coexistence of robust in-plane magnetic ordering and spontaneous valley polarization of 2H-VSSe monolayer supports the possibility of applications in spintronics, valleytronics and optoelectronics devices.

Dynamical symmetry and valley-selective circularly polarized high-harmonic generation in monolayer molybdenum disulfide

Circularly polarized high harmonics (CHHs) have been observed in several solid targets under single-color circularly polarized excitation. However, experimental observations show that CHHs cannot be efficiently generated in monolayer molybdenum disulphide (${\text{MoS}}_{2}$) driving by a single-color circularly polarized laser, thus letting its unique valley-selective circular dichroism (VSCD) to remain unexploited in the high harmonic generation process. Here we demonstrate that the efficient generation of CHHs in monolayer ${\text{MoS}}_{2}$ driven by counterrotating bicircular (CRB) fields and the broken inversion symmetry of monolayer ${\text{MoS}}_{2}$ leads to the generation of forbidden $3n$ ($n\ensuremath{\in}\mathbb{N}$) harmonic orders. Interestingly, we find that the VSCD lead to a distinctive valley selection of harmonic orders, while the valley selection caused by the trefoil orientation relative to the lattice is also observed. Dynamical symmetry analyses show that the rotational symmetry of the crystals can be decoded by the combination of a linearly polarized excitation scheme and CRB excitation scheme via the lowest common multiple rule. Additionally, VSCD leaves unique fingerprints in the ellipticity of harmonics.

Valley-dependent properties of monolayer MoSi2N4, WSi2N4 , and MoSi2As4

In a recent work, new two-dimensional materials, the monolayer MoSi$_{2}$N$_{4}$ and WSi$_{2}$N$_{4}$, have been successfully synthesized in experiment, and several other monolayer materials with the similar structure, such as MoSi$_{2}$As$_{4}$, have been predicted [{\color{blue}Science 369, 670-674 (2020)}]. Here, based on first-principles calculations and theoretical analysis, we investigate the electronic and optical properties of monolayer MoSi$_{2}$N$_{4}$, WSi$_{2}$N$_{4}$ and MoSi$_{2}$As$_{4}$. We show that these materials are semiconductors, with a pair of Dirac-type valleys located at the corners of the hexagonal Brillouin zone. Due to the broken inversion symmetry and the effect of spin-orbit coupling, the valley fermions manifest spin-valley coupling, valley-contrasting Berry curvature, and valley-selective optical circular dichroism. We also construct the low-energy effective model for the valleys, calculate the spin Hall conductivity and the permittivity, and investigate the strain effect on the band structure. Our result reveals interesting valley physics in monolayer MoSi$_{2}$N$_{4}$, WSi$_{2}$N$_{4}$ and MoSi$_{2}$As$_{4}$, suggesting their great potential for valleytronics and spintronics applications.

Valley degree of freedom in ferromagnetic Janus monolayer H-VSSe and the asymmetry-based tuning of the valleytronic properties

By using density-functional theory-based GW method, we studied the valley degree of freedom of Janus monolayer VSSe. The GW corrections lead to a doubling of the band gap and change the band dispersion considerably, indicating significant many-body effects. VSSe is confirmed to be ferromagnetic, which breaks the time-reversal symmetry and the odd parity of the Berry curvature in momentum space. The dissimilar magnitudes of Berry curvatures of the inequivalent valleys give rise to appreciable anomalous Hall conductivity (AHC). The calculated valley optical response of VSSe exhibits a clear valley-selective circular dichroism. The ferromagnetism induces large valley-Zeeman splitting, making it possible to realize the selective valley excitation even by unpolarized light. The Janus VSSe is more tunable by external fields because of symmetry breaking. Due to the relief of time-reversal symmetry, the valley-Zeeman splitting can be continuously tuned by varying the magnetization direction. The loss of mirror symmetry in VSSe enables a bidirection modulation of the band gap by changing the direction of electric field. The strain can linearly tune the valley gap in a considerable range. The Berry curvature and AHC can be effectively regulated in the external fields.

Enhanced valleytronic properties in germanene by direct proximity to heavy metal layer

Germanene, though with Dirac valleys, is not deemed as a good valleytronic material due to its minute band gap, negligible spin–orbit coupling and spatial inversion symmetry. In comparison of interfacing germanene with MoS2, we proposed that forming heterostructure with Tl2S, an anti-MoS2 material with two outer heavy metal layers, could be more effective in raising spin–orbit coupling and band gap in germanene due to the direct Ge-metal contact. By carrying out first-principles calculations, we studied the valleytronic properties of germanene enhanced by monolayer Tl2S. It is found that the Ge–Tl direct interaction is strong to a proper extent so that the valleys of germanene still persist and simultaneously the valley gap is drastically increased from 23 to 370 meV. The valley spin splitting, being zero in pristine germanene, become 45 meV, which is opposite at inequivalent valleys owing to the time reversal symmetry. The inversion symmetry of germanene is broken by Tl2S, resulting in large Berry curvature near the valleys and hence laying the ground for Berry phase physics in germanene, e.g., valley spin Hall effect and valley–spin locking, as revealed in our study. The calculations found a perfect valley-selective circular dichroism, by which the valley and spin degrees of freedom can be manipulated selectively and correlatively.

Theory of coherent pump–probe spectroscopy in monolayer transition metal dichalcogenides

A valley-selective circular dichroism and a pronounced spin-valley locking in monolayer transition metal dichalcogenides (TMDCs) enable the investigation of new many-body physics revealed in the ultrafast nonlinear optical response of these atomically thin materials. While this topic is experimentally well studied in pump–probe spectroscopy, only a fragmented theoretical understanding is available due to the complexity and multitude of occurring effects. Here, a microscopic approach is presented to describe the ultrafast pump–probe response of monolayer TMDCs in the coherent limit. We focus on close to band edge excitations dominated by strongly correlated, bound electron–hole pairs, namely excitonic excitations. The approach includes Hartree–Fock and correlation effects up to two excitonic excitations known from conventional semiconductors as well as TMDC typical Coulomb mechanisms such as intra- and intervalley excitation and charge transfer. The investigated coherent limit is able to explain different signatures observed in ultrafast pump–probe spectroscopy for temporal pump–probe overlap within one consistent formalism dominated by excitons, biexcitons, and exciton-exciton scattering states.

The novel plasmonics-transition metal dichalcogenides hybrid nanostructures

Transition metal dichalcogenides (TMDs) are one of the hot research areas owing to their unique optoelectronic properties, which have been demonstrated for potential usage in light harvesting, photodetectors, phototransistors, light-emitting diodes, and nanolasers, etc. Few-layer TMDs are attractive because their band gaps are in the visible to near-infrared region, their excitons have large binding energies and high oscillator strengths, and the inversion symmetry breaking in monolayer TMDs brings in valley-selective circular dichroism. Surface plasmons supported in metallic nanostructures can confine light in the subwavelength scale. The optical properties of surface plasmons, such as the resonance position, linewidth, near-field enhancement, and far-field radiation properties can be flexibly controlled by reasonable design. The combination of the plasmonic nanostructures and TMDs will advance the frontiers of nanophotonics and promote the applications of nanophotonic devices. In this paper, we review the state of the art research advances on hybrid plasmonics-TMDs structures. We first introduce the properties of propagating surface plasmon polaritons and localized surface plasmons, emphasizing on the property of the near field enhancement, which is the physical foundation of enhancing light-matter interaction in many nano-optics systems. Then, we briefly introduce the basic theoretical background of light-matter interaction and explicate the boundary between weak and strong coupling region. The next we introduce the basic lattice structure and atom composition of TMDs materials as well as the related optical properties, including the strong excitonic effect at room temperature, valley-selective circular dichroism, and the defect-related single photon emission. Further, we introduce the recent experimental advances on plasmon-exciton coupling in the weak and strong coupling region. In the weak coupling region, the related research progress on surface-enhanced spectroscopy including surface-enhanced nonlinear effect, Raman, photoluminescence, and the enhanced photocurrent effect have been introduced in detail. In the strong coupling region, we focus on the current research hotspots including single nanoparticle strong coupling, lattice structure strong coupling and the active control strong coupling devices. Finally, we make a prospect of future opportunities based on this novel hybrid material platform.

Defect-Induced Modification of Low-Lying Excitons and Valley Selectivity in Monolayer Transition Metal Dichalcogenides.

We study the effect of point-defect chalcogen vacancies on the optical properties of monolayer transition metal dichalcogenides using abinitio GW and Bethe-Salpeter equation calculations. We find that chalcogen vacancies introduce unoccupied in-gap states and occupied resonant defect states within the quasiparticle continuum of the valence band. These defect states give rise to a number of strongly bound defect excitons and hybridize with excitons of the pristine system, reducing the valley-selective circular dichroism. Our results suggest a pathway to tune spin-valley polarization and other optical properties through defect engineering.

Nondegenerate valleys in the half-metallic ferromagnet Fe/WS2

We present a first principles investigation of the electronic properties of monolayer WS$_2$ coated with an overlayer of Fe. Our ab initio calculations reveal that the system is a half-metallic ferromagnet with a gap of $\sim 1$ eV for the majority spin channel. Furthermore, the combined effect of time-reversal symmetry breaking due to the magnetic Fe overlayer and the large spin-orbit coupling induced by W gives rise to non-degenerate K and K$'$ valleys. This has a tremendous impact on the excited state properties induced by externally applied circularly polarized light. Our analysis demonstrates that the latter induces a singular hot spot structure of the transition probability around the K and K$'$ valleys for right and left circular polarization, respectively. We trace back the emergence of this remarkable effect to the strong momentum dependent spin-noncollinearity of the valence band involved. As a main consequence, a strong valley-selective magnetic circular dichroism is obtained, making this system a prime candidate for spintronics and photonics applications.

Valley-selective circular dichroism and high carrier mobility of graphene-like BC6N.

The two-dimensional (2D) hybrid structures of boron nitride (BN) and graphene with properties superior to the individuals are long desired. In this work, we demonstrate theoretically that this goal can be reached in a new graphene-like borocarbonitride (g-BC6N) whose domain has been synthesized in recent experiments. It has a direct band gap of 1.833 eV and a high carrier mobility comparable to that of black phosphorene. The inversion symmetry breaking in g-BC6N leads to a pair of inequivalent valleys with opposite Berry curvatures in the vicinities of the vertices (K and K') of the Brillouin zone. The coexistence of valley-selective circular dichroism and high carrier mobility in g-BNC6 is beneficial to realize the valley Hall effect. We also propose a tight-binding (TB) model to describe the intrinsic features of this type of lattice, revealing a new class of 2D valleytronic materials.

Electrically tunable polarizer based on 2D orthorhombic ferrovalley materials

The concept of ferrovalley materials has been proposed very recently. The existence of spontaneous valley polarization, resulting from ferromagnetism, in such hexagonal 2D materials makes nonvolatile valleytronic applications realizable. Here, we introduce a new member of ferrovalley family with orthorhombic lattice, i.e. monolayer group-IV monochalcogenides (GIVMs), in which the intrinsic valley polarization originates from ferroelectricity, instead of ferromagnetism. Combining the group theory analysis and first-principles calculations, we demonstrate that, different from the valley-selective circular dichroism in hexagonal lattice, linearly polarized optical selectivity for valleys exists in the new type of ferrovalley materials. On account of the distinctive property, a prototype of electrically tunable polarizer is realized. In the ferrovalley-based polarizer, a laser beam can be optionally polarized in x- or y-direction, depending on the ferrovalley state controlled by external electric fields. Such a device can be further optimized to emit circularly polarized radiation with specific chirality and to realize the tunability for operating wavelength. Therefore, we show that 2D orthorhombic ferrovalley materials are the promising candidates to provide an advantageous platform to realize the polarizer driven by electric means, which is of great importance in extending the practical applications of valleytronics.

Excellent valleytronic properties and nontrivial topological phase in germanene heterostructure

In comparison with transition metal dichalcogenides (TMDs), germanene is not an ideal valleytronic material due to its very weak spin–orbit coupling (SOC) and tiny band gap. By performing density functional calculations, we studied the heterostructures of germanene/Sb and germanene/SbF in order to augment the valleytronic properties of germanene to a level similar to that of TMDs. Although germanene/Sb has large spin splittings, the system is found to be gapless. By proximity with the fluorine-adsorbed Sb layer, germanene can acquire large SOC. Germanene/SbF has a sizable direct band gap at Dirac points and the Dirac valleys of SbF and germanene are preserved in the heterostructure. The Ge–SbF interaction breaks the inversion symmetry, leading to large spin splittings and Berry curvatures, which are valley contrasting due to time reversal symmetry. We studied the interband optical transitions and found that valley polarization is achievable via valley-selective circular dichroism. The calculated Z2 topological invariant further confirms that Ge/SbF is a topological insulator. Our studies illustrate that weak SOC materials can be converted into good valleytronic material and that nontrivial topological phase and valleytronic properties can be simultaneously realized.