Inequivalent Valleys Research Articles

The type-I, III nodal ring, type-I, III quadratic nodal point, and Dirac valley phonons in 2D kagome lattices M2C3 (M = As, Bi, Cd, Hg, P, Sb, Zn)

Topological phases in kagome systems have garnered considerable interest since the introduction of the colloidal kagome lattice. Our study employs first-principle calculations and symmetry analysis to predict the existence of ideal type-I, III nodal rings (NRs), type-I, III quadratic nodal points (QNPs), and Dirac valley phonons (DVPs) in a collection of two-dimensional (2D) kagome lattices M2C3 (M = As, Bi, Cd, Hg, P, Sb, Zn). Specifically, the Dirac valley points (DVPs) can be observed at two inequivalent valleys with Berry phases of +π and −π , connected by edge arcs along the zigzag and armchair directions. Additionally, the QNP is pinned at the Γ point, and two edge states emerge from its projections. Notably, these kagome lattices also exhibit ideal type-I and III nodal rings protected by time inversion and spatial inversion symmetries. Our work examines the various categories of nodal points and nodal ring phonons within the 2D kagome systems and presents a selection of ideal candidates for investigating topological phonons in bosonic systems.

Large valley splitting and vacancy-induced valley polarization in two-dimensional WSeNH.

The investigation and manipulation of valley pseudospin in promising two-dimensional (2D) semiconductors are essential for accelerating the development of valleytronics. Based on first-principles, we herein report that the WSeNH monolayer is a potential 2D valleytronic material. It is found that stable 2D WSeNH exhibits a semiconducting character with broken inversion symmetry, forming a pair of energy-degenerate but inequivalent valleys at the K and K' points. Arising from the strong spin-orbit coupling strength governed by the W-dxy/dx2-y2 orbitals, it exhibits a large valley splitting of 425 meV at the top of the valence band, which makes it highly plausible for generating the attractive valley Hall effect. Moreover, both valley splitting and optical transition energy can be efficiently modulated by external strain. Furthermore, we find that a considerable valley polarization of 23 meV can be readily realized in 2D WSeNH by introducing hydrogen vacancies. These findings not only broaden the family of 2D valleytronic materials but also provide alternative avenues for valley manipulation.

Dramatically Enhanced Valley-Polarized Emission by Alloying and Electrical Tuning of Monolayer WTe2 x S2(1- x ) Alloys at Room Temperature with 1T'-WTe2 -Contact.

Monolayer ternary tellurides based on alloying different transition metal dichalcogenides (TMDs) can result in new two-dimensional (2D) materials ranging from semiconductors to metals and superconductors with tunable optical and electrical properties. Semiconducting WTe2 x S2(1- x ) monolayer possesses two inequivalent valleys in the Brillouin zone, each valley coupling selectively with circularly polarized light (CPL). The degree of valley polarization (DVP) under the excitation of CPL represents the purity of valley polarized photoluminescence (PL), a critical parameter for opto-valleytronic applications. Here, new strategies to efficiently tailor the valley-polarized PL from semiconducting monolayer WTe2 x S2(1- x ) at room temperature (RT) through alloying and back-gating are presented. The DVP at RT is found to increase drastically from < 5% in WS2 to 40% in WTe0.12 S1.88 by Te-alloying to enhance the spin-orbit coupling. Further enhancement and control of the DVP from 40% up to 75% is demonstrated by electrostatically doping the monolayer WTe0.12 S1.88 via metallic 1T'-WTe2 electrodes, where the use of 1T'-WTe2 substantially lowers the Schottky barrier height (SBH) and weakens the Fermi-level pinning of the electrical contacts. The demonstration of drastically enhanced DVP and electrical tunability in the valley-polarized emission from 1T'-WTe2 /WTe0.12 S1.88 heterostructures paves new pathways towards harnessing valley excitons in ultrathin valleytronic devices for RT applications.

Investigation of topological valley kink states along zigzag and armchair domain wall in a two-dimensional photonic crystal

This paper provides a numerical analysis of the topological valley kink states along both zigzag and armchair domain walls of a dielectric two-dimensional photonic crystal (PC), considering the photonic energy band folding mechanism. By engineering the side length of triangular holes in a honeycomb PC, we created inequivalent valleys in the momentum space. We utilized two adjacent valley PCs with inverted structures to induce a topological transition of the TE mode energy band as it crossed the interface. Further research into the projected energy bands along both zigzag and armchair directions revealed that topologically protected valley kink states can be supported by both configurations. The zigzag interface enabled valley waveguides to transport chiral optical fields at the 0°, 60°, and 120° bending angles, while maintaining their backscattering immune properties. The armchair interface, on the other hand, supported the straight propagation. By combining both armchair and zigzag interfaces, the valley waveguide can facilitate bending propagation at 90° and 180°, while also enabling the equal splitting of chiral fields at the intersection between these two interfaces. Our analyzation can be helpful to improve the applications of valley waveguides in integrated photonics.

Optical spectrum of ferrovalley materials: A case study of Janus H-VSSe

As opposed to the prototypical MoS2 with centroasymmetry, Janus ferrovalley materials such as H-VSSe are less symmetric with the mirror symmetry and time reversal symmetry broken, and hence possess spontaneous valley polarization and strong ferroelasticity. The optical transition is an important means to excite the valley carriers. We investigate the optical spectrum of H-VSSe by using the many-body perturbation-based GW approach and solving the Bethe–Salpeter equation (BSE) to include the electron–hole interactions. It is found that after the GW correction, the band gaps of the quasiparticle bands are much larger than those obtained by the normal density functional theory. The system is ferromagnetic and the valley gaps become non-degenerate due to spin–orbit coupling (SOC). The position of the lowest BSE peak is much lower than the quasiparticle band gap, indicating that the excitonic effect is large. The peak is split into two peaks by the SOC. The binding energy difference between these two BSE peaks is about the same as the difference between the inequivalent valley gaps. Our results show that in Janus H-VSSe the two lowest exciton peaks are from the two inequivalent valleys with different gaps, in contrast to the A and B exciton peaks of MoS2 which are from the same valley.

Valley polarization in transition metal dichalcogenide layered semiconductors: Generation, relaxation, manipulation and transport

In recent years, valleytronics researches based on 2D semiconducting transition metal dichalcogenides have attracted considerable attention. On the one hand, strong spin–orbit interaction allows the presence of spin–valley coupling in this system, which provides spin addressable valley degrees of freedom for information storage and processing. On the other hand, large exciton binding energy up to hundreds of meV enables excitons to be stable carriers of valley information. Valley polarization, marked by an imbalanced exciton population in two inequivalent valleys (+K and −K), is the core of valleytronics as it can be utilized to store binary information. Motivated by the potential applications, we present a thorough overview of the recent advancements in the generation, relaxation, manipulation, and transport of the valley polarization in nonmagnetic transition metal dichalcogenide layered semiconductors. We also discuss the development of valleytronic devices and future challenges in this field.

Ultrafast Dynamics of Valley-Polarized Excitons in WSe2 Monolayer Studied by Few-Cycle Laser Pulses.

We report on the experimental investigation of the ultrafast dynamics of valley-polarized excitons in monolayer WSe2 using transient reflection spectroscopy with few-cycle laser pulses with 7 fs duration. We observe that at room temperature, the anisotropic valley population of excitons decays on two different timescales. The shorter decay time of approximately 120 fs is related to the initial hot exciton relaxation related to the fast direct recombination of excitons from the radiative zone, while the slower picosecond dynamics corresponds to valley depolarization induced by Coloumb exchange-driven transitions of excitons between two inequivalent valleys.

Electron-Induced Chirality-Selective Routing of Valley Photons via Metallic Nanostructure.

Valleytronics in 2Dtransition metal dichalcogenides has raised a great impact in nanophotonic information processing and transport as it provides the pseudospin degree of freedom for carrier control. The imbalance of carrier occupation in inequivalent valleys can be achieved by external stimulations such as helical light and electric field. With metasurfaces, it is feasible to separate the valley exciton in real space and momentum space, which is significant for logical nanophotonic circuits. However, the control of valley-separated far-field emission by a single nanostructure is rarely reported, despite the fact that it is crucial for subwavelength research of valley-dependent directional emission. Here, it is demonstrated that the electron beam permits the chirality-selective routing of valley photons in a monolayer WS2 with Au nanostructures. The electron beam can locally excite valley excitons and regulate the coupling between excitons and nanostructures, hence controlling the interference effect of multipolar electric modes in nanostructures. Therefore, the separation degree can be modified by steering the electron beam, exhibiting the capability of subwavelength control of valley separation. This work provides a novel method to create and resolve the variation of valley emission distribution in momentum space, paving the way for the design of future nanophotonic integrated devices.

Manipulation of electromagnetic waves induced by pseudomagnetic fields in two dimensional photonic crystals

Many interesting phenomena, such as quantization of Landau levels and quantum Hall effect, can occur in an electronic system under a strong magnetic field. However, photons do not carry charge, and they do not have many properties induced by external magnetic fields, either. Recently, the pseudomagnetic field, an artificial synthetic gauge field, has attracted intense research interest in classical wave systems, in which the propagation of the wave can be manipulated like in a real magnetic field. The photonic crystal is an optical structure composed of periodic material distributions and provides a good platform for studying the control of electromagnetic waves. In this work, we construct a uniform pseudomagnetic field by introducing uniaxial linear gradient deformation of metallic rods in a two-dimensional photonic crystal. The strong pseudomagnetic field leads to the quantization of photonic Landau levels in photonic crystal. The sublattice polarization of &lt;i&gt;n&lt;/i&gt; = 0 Landau level is also demonstrated in our simulations. Unlike the real magnetic field, the pseudomagnetic fields of photonic crystal is opposite in two inequivalent energy valleys, and the time-reversal symmetry of the system is not broken. Our designed gradient photonic crystals support the transport of edge state in the gap between &lt;i&gt;n&lt;/i&gt; = 0 and &lt;i&gt;n&lt;/i&gt; = ±1 Landau levels. The edge state can propagate unidirectionally when it is excited by a chiral source. When a gaussian beam impinges on the photonic crystal, the propagating paths of two splitting beams can be controlled, which gives rise to the bend of two beams. Two photonic crystals with opposite pseudomagnetic fields are assembled together, and the interesting phenomenon of “snake-state” can be obtained. Our proposal opens the way for designing information processing devices by manipulating electromagnetic waves.

Landau levels and snake states of pseudo-spin-1 Dirac-like electrons in gapped Lieb lattices

This work reports the three-band structure associated with a Lieb lattice with arbitrary nearest and next-nearest neighbors hopping interactions. For specific configurations, the system admits a flat band located between two dispersion bands, where three inequivalent Dirac valleys are identified. Furthermore, quasi-particles are effectively described by a spin-1 Dirac-type equation. Under external homogeneous magnetic fields, the Landau levels are exactly determined as the third-order polynomial equation for the energy can be solved using Cardano’s formula. It is also shown that an external anti-symmetric field promotes the existence of current-carrying states, so-called snake states, confined at the interface where the external field changes its sign.

Realizing Valley-Polarized Energy Spectra in Bilayer Graphene Quantum Dots via Continuously Tunable Berry Phases.

The Berry phase plays an important role in determining many physical properties of quantum systems. However, tuning the energy spectrum of a quantum system via Berry phase is comparatively rare because the Berry phase is usually a fixed constant. Here, we report the realization of an unusual valley-polarized energy spectra via continuously tunable Berry phases in Bernal-stacked bilayer graphene quantum dots. In our experiment, the Berry phase of electron orbital states is continuously tuned from about π to 2π by perpendicular magnetic fields. When the Berry phase equals π or 2π, the electron states in the two inequivalent valleys are energetically degenerate. By altering the Berry phase to noninteger multiples of π, large and continuously tunable valley-polarized energy spectra are realized. Our result reveals the Berry phase's essential role in valleytronics and the observed valley splitting, on the order of 10meV at a magnetic field of 1T, is about 100 times larger than Zeeman splitting for spin, shedding light on graphene-based valleytronics.

Spin-valley-coupled quantum spin Hall insulator with topological Rashba-splitting edge states in Janus monolayer CSb1.5Bi1.5

Achieving combination of spin and valley polarized states with topological insulating phase is pregnant to promote the fantastic integration of topological physics, spintronics and valleytronics. In this work, a spin-valley-coupled quantum spin Hall insulator (svc-QSHI) is predicted in Janus monolayer CSb1.5Bi1.5 with dynamic, mechanical and thermal stabilities. Calculated results show that the CSb1.5Bi1.5 is a direct band gap semiconductor with and without spin–orbit coupling, and the conduction-band minimum and valence-band maximum are at valley point. The inequivalent valleys have opposite Berry curvature and spin moment, which can produce a spin-valley Hall effect. In the center of Brillouin zone, a Rashba-type spin splitting can be observed due to missing horizontal mirror symmetry. The topological characteristic of CSb1.5Bi1.5 is confirmed by the Z 2 invariant and topological protected conducting helical edge states. Moreover, the CSb1.5Bi1.5 shows unique Rashba-splitting edge states. Both energy band gap and spin-splitting at the valley point are larger than the thermal energy of room temperature (25 meV) with generalized gradient approximation level, which is very important at room temperature for device applications. It is proved that the spin-valley-coupling and nontrivial quantum spin Hall state are robust again biaxial strain. Our work may provide a new platform to achieve integration of topological physics, spintronics and valleytronics.

Phononic linear and quadratic nodal points in monolayer XH (X=Si, Ge, Sn)

Topological phases in two-dimensional (2D) systems have been attracting tremendous attention since the discovery of graphene. Since the experimental probing could proceed in the whole phonon spectrum, intensive research effort has been devoted to the topological quantum phases in phononic systems. Via first-principles calculations, we predict that a family of 2D hexagonal materials, XH (X = Si, Ge, Sn), hosts ideal linear nodal points (LNPs) and quadratic phononic nodal points (QNPs). Specifically, the LNPs appear at the two inequivalent valleys, akin to the 2D Dirac point in graphene, connecting by an edge arc. The QNP is pinned at the Γ point, two edge states emerge from their projections. Remarkably, both LNPs and QNP enjoy an emergent chiral symmetry, we then show that they feature nontrivial topological charges. As a consequence, our work discusses the nodal points in the phonon spectrum of 2D materials and provides ideal candidates to study the topology for bosonic systems.

Valley Hall Effect in Symmetrically Biased Dice Lattice

The existence of two inequivalent valleys in the Brillouin zone of some two-dimensional crystals with honeycomb lattice structure provides electrons to possess an extra degree of freedom, known as pseudospin/valley in addition to their intrinsic charge and spin. A dice lattice, in which the low energy excitations are described by the Dirac-Weyl Hamiltonian with pseudospin S = 1, also has the valley degree of freedom. Here, we consider an inversion-symmetry broken low energy model of a symmetrically biased dice lattice. We find that the Berry curvature has equal magnitude with opposite signs in two valleys. This causes the electrons to acquire opposite anomalous velocities in the respective valleys. The Hall conductivity is calculated using the semi-classical formulation of electron dynamics. The dependence of the valley contrasted Hall conductivity on the chemical potential at various temperatures is shown.

Electrically Tunable and Dramatically Enhanced Valley-Polarized Emission of Monolayer WS2 at Room Temperature with Plasmonic Archimedes Spiral Nanostructures.

Monolayer transition metal dichalcogenides (TMDs) have intrinsic valley degrees of freedom, making them appealing for exploiting valleytronic applications in information storage and processing. WS2 monolayer possesses two inequivalent valleys in the Brillouin zone, each valley coupling selectively with a circular polarization of light. The degree of valley polarization (DVP) under the excitation of circularly polarized light (CPL) is a parameter that determines the purity of valley polarized photoluminescence (PL) of monolayer WS2 . Here efficient tailoring of valley-polarized PL from monolayer WS2 at room temperature (RT) through surface plasmon-exciton interactions with plasmonic Archimedes spiral (PAS) nanostructures is reported. The DVP of WS2 at RT can be enhanced from <5% to 40% and 50% by using 2 turns (2T) and 4 turns (4T) of PAS, respectively. Further enhancement and control of excitonic valley polarization is demonstrated by electrostatically doping monolayer WS2 . For CPL on WS2 -2TPAS heterostructures, the 40% valley polarization is enhanced to 70% by modulating the carrier doping via a backgate, which may be attributed to the screening of momentum-dependent long-range electron-hole exchange interactions. The manifestation of electrically tunable valley-polarized emission from WS2 -PAS heterostructures presents a new strategy toward harnessing valley excitons for application in ultrathin valleytronic devices.

Valley polarization in biased bilayer graphene using circularly polarized light

Achieving a population imbalance between the two inequivalent valleys is a critical first step for any valleytronic device. A valley polarization can be induced in biased bilayer graphene using circularly polarized light. In this paper, we present a detailed theoretical study of valley polarization in biased bilayer graphene. We show that a nearly perfect valley polarization can be achieved with the proper choices of external bias and pulse frequency. We find that the optimal pulse frequency $\ensuremath{\omega}$ is given by $\ensuremath{\hbar}\ensuremath{\omega}=2a,$ where $2a$ is the potential energy difference between the graphene layers. We also find that the valley polarization originates not from the Dirac points themselves, but rather from a ring of states surrounding each. Intervalley scattering is found to greatly reduce the valley polarization for high-frequency pulses. Thermal populations are found to significantly reduce the valley polarization for small biases. This work provides insight into the origin of valley polarization in bilayer graphene and will aid experimentalists seeking to study valley polarization in the laboratory.

Microscopic theory of cavity-confined monolayer semiconductors: Polariton-induced valley relaxation and the prospect of enhancing and controlling valley pseudospin by chiral strong coupling

We apply a microscopic theory of exciton-polaritons in cavity-confined monolayer transition-metal dichalcogenides including both optical polarizations in the monolayer plane, allowing to describe how chiral cavity photons interact with the valley degrees of freedom of the active material. Upon polariton formation, the degenerate excitons inhabiting the two inequivalent valleys are shown to assume bonding and antibonding superpositions as a result of cavity-mediated intravalley interactions combined with intervalley Coulomb interactions. This is representative of a polariton-induced coherent mixing of the valley polarization. In combination with disorder, this mixing is prone to open a new valley relaxation channel which attains significance with increasing cavity coupling. Importantly, we show that optical cavities with an asymmetric reflectance of left- and right-handed circularly-polarized photons offer a considerably more robust platform to realize a conserved valley polarization, as the valley localization of excitons is reinstated by an asymmetric Rabi splitting which lifts their degeneracy. Moreover, we show this degeneracy lifting to allow for wavelength-selective access to the valley pseudospin by means of a polariton-induced chiral Stark effect, offering interesting opportunities for valleytronic applications.

First-principles investigation of the valley and electrical properties of carbon-doped α-graphyne-like BN sheet* *Project supported by the Special Foundation for Theoretical Physics Research Program of China (Grant No. 11847065) and the Natural Science Foundation of Shanxi Province, China (Grant No. 201901D211115).

Based on ab initio density functional theory calculations, we demonstrate that two carbon-doped boron nitride analog of α-graphyne structures, B3C2N3 and BC6N monolayers, are two-dimensional direct wide band gap semiconductors, and there are two inequivalent valleys in the vicinities of the vertices of their hexagonal Brillouin zones. Besides, B3C2N3 and BC6N monolayers exhibit relatively high carrier mobilities, and their direct band gap feature is robust against the biaxial strain. More importantly, the energetically most favorable B3C2N3 and BC6N bilayers also have direct wide band gaps, and valley polarization could be achieved by optical helicity. Finally, we show that BC6N monolayer might have high efficiency in photo-splitting reactions of water, and a vertical van der Waals heterostructure with a type-II energy band alignment could be designed using B3C2N3 and BC6N monolayers. All the above-mentioned characteristics make B3C2N3 and BC6N monolayers, bilayers, and their heterostructures recommendable candidates for applications in valleytronic devices, metal-free photocatalysts, and photovoltaic cells.

First principles study of distributions of Si atoms and structures of siligraphene g-SiC&lt;sub&gt;7&lt;/sub&gt;

Siligraphene, as a composite of graphene and silicene, has attracted widespread attraction since it has many excellent properties that neither of graphene and silicene possesses. The properties of siligraphene are closely related to the distribution of Si atoms and its structure, but most of the current researches of siligraphene focus on the regular distribution of Si atoms and the planar structure with high symmetry. Therefore, we study in this work all possible Si atoms’ distributions with planar and nonplanar structures for siligraphene g-SiC&lt;sub&gt;7&lt;/sub&gt; based on density functional theory. At first, 365 kinds of inequivalent Si atoms’ distributions in g-SiC&lt;sub&gt;7&lt;/sub&gt; are selected out from the 35960 kinds of Si atoms’ distributions, and then for each inequivalent Si atoms’ distribution, a comparison of the stability between the planer and nonplanar structures is made. In terms of the Si distribution, the Si atoms tend to gather together to lower the energy. The more dispersed Si atoms’ distribution usually has appreciably higher energy. In terms of the planarity of the structures, it is found that there are many non-planar structures with significantly lower energy than the planar ones. For all possible Si atoms’ distributions, there are only 8 planar structures which are stable against out-of-plane perturbations. We further study the dynamic, thermodynamic and mechanical stability of the structures with the lowest energies and find that they are stable. The energy band calculation shows that two Dirac valleys still persist in the first Brillouin zone despite their appreciable structure deformation, and a considerable band gap is opened at the Dirac point. We calculate the Berry curvatures and find that the Berry curvatures at the inequivalent valleys are opposite, indicating that the system has valley degree of freedom. Our research shows that siligraphene is more likely to have a buckled structure and a more concentrated silicon atoms’ distribution, and the most stable structures have good electronic properties.

Electrostatically Enhanced Electron-Phonon Interaction in Monolayer 2H-MoSe2 Grown by Molecular Beam Epitaxy.

The enhancement of electron-phonon interaction provides a reasonable explanation for gate-tunable phonon properties in some semiconductors where multiple inequivalent valleys are simultaneously occupied upon charge doping, especially in few-layer transition metal dichalcogenides (TMDs). In this work, we report var der Waals epitaxy of 2H-MoSe2 by molecular beam epitaxy (MBE) and gate-tunable phonon properties in monolayer and bilayer MoSe2. In monolayer MoSe2, we find that out-of-plane phonon mode A1g exhibits a strong softening and shifting toward lower wavenumbers at a high electron doping level, while in-plane phonon mode E2g1 remains unchanged. The softening and shifting of the out-of-plane phonon mode could be attributed to the increase of electron-phonon interaction and the simultaneous occupation of electrons in multiple inequivalent valleys. In bilayer MoSe2, no corresponding changes of phonon modes are detected at the same doping level, which could originate from the occupation of electrons only in single valleys upon high electron doping. This study demonstrates electrostatically enhanced electron-phonon interaction in monolayer MoSe2 and clarifies the relevance between occupation of multiple valleys and phonon properties by comparing Raman spectra of monolayer and bilayer MoSe2 at different doping levels.