Valleys In Momentum Space Research Articles

Coherent control on the generation and annihilation of a pseudospin-induced optical vortex in a honeycomb photonic lattice.

We experimentally investigate the coherently controllable generation and annihilation of a pseudospin-induced optical vortex in an optically induced honeycomb photonic lattice in a Λ-type 85Rb atomic vapor cell. Three Gaussian coupling beams are coupled into the atomic gases to form a hexagonal interference pattern, which can induce a honeycomb photonic lattice under electromagnetically induced transparency. Then, two probe beams interfere with each other to form periodical fringes and cover one set of sublattice in the honeycomb lattice, corresponding to excite the K or K' valleys in momentum space. By properly adjusting the experimental parameters, the generation and annihilation of the induced optical vortex can be effectively controlled. The theoretical simulations based on the Dirac and Schrödinger equations are performed to explore the underlying mechanisms, which will support the observations. The demonstrated properties of such controllable optical vortex may lay the foundation for the design of vortex-based optical devices with multidimensional tunability.

Kekulé Moiré Superlattices.

In this paper, we discuss a new moiré system where the long moiré periodicity emerges from two dissimilar van der Waals layers with vastly different lattice constants. We reconstruct the first layer using a by supercell resembling the Kekulé distortion in graphene, and such reconstruction becomes nearly commensurate with the second layer. We term this construction a Kekulé moiré superlattice, which enables coupling between moiré bands from remote valleys in momentum space. Kekulé moiré superlattices can be realized in heterostructures of transition metal dichalcogenides and metal phosphorus trichalcogenides such as MoTe2/MnPSe3. By first-principles calculations, we demonstrate that the antiferromagnetic MnPSe3 strongly couples the otherwise degenerate Kramers' valleys of MoTe2, resulting in valley pseudospin textures that depend on the Néel vector direction, stacking geometry, and external fields. With one hole per moiré supercell, the system becomes a Chern insulator with highly tunable topological phases.

Controllable Valley Polarization and Strain Modulation in 2D 2H-VS2/CuInP2Se6 Heterostructures.

Two–dimensional (2D) transition metal dichalcogenides endow individually addressable valleys in momentum space at the K and K’ points in the first Brillouin zone due to the breaking of inversion symmetry and the effect of spin–orbit coupling. However, the application of 2H–VS2 monolayer in valleytronics is limited due to the valence band maximum (VBM) located at the Γ point. Here, by involving the 2D ferroelectric (FE) CuInP2Se6 (CIPSe), the ferrovalley polarization, electronic structure, and magnetic properties of 2D 2H–VS2/CIPSe heterostructures with different stacking patterns and FE polarizations have been investigated by using first–principles calculations. It is found that, for the energetically favorable AB–stacking pattern, the valley polarization is preserved when the FE polarization of CIPSe is upwards (CIPSe↑) or downwards (CIPSe↓) with the splitting energies slightly larger or smaller compared with that of the pure 2H–VS2. It is intriguing that, for the FE CIPSe↑ case, the VBM is expected to pass through the Fermi energy level, which can be eventually achieved by applying biaxial strain and thus the valleytronic nature is turned off; however, for the CIPSe↓ situation, the heterostructure basically remains semiconducting even under biaxial strains. Therefore, with the influence of proper strains, the FE polar reversal of CIPSe can be used as a switchable on/off to regulate the valley polarization in VS2. These results not only demonstrate that 2H–VS2/CIPSe heterostructures are promising potential candidates in valleytronics, but also shed some light on developing practical applications of valleytronic technology.

The Role of Odd‐Frequency Pairing in Multiband Superconductors

AbstractRecent progress in the understanding of multiband superconductivity and its relationship to odd‐frequency pairing are reviewed herein. The discussion begins by reviewing the emergence of odd‐frequency pairing in a simple two‐band model, providing a brief pedagogical overview of the formalism. Several examples of multiband superconducting systems are examined, in each case describing both the origin of the band degree of freedom and the nature of the odd‐frequency pairing. Throughout, it is attempted to convey a unified picture of how odd‐frequency pairing emerges in these materials and propose that similar mechanisms are responsible for odd‐frequency pairing in several analogous systems: layered 2D heterostructures, double quantum dots, double nanowires, Josephson junctions, and systems described by isolated valleys in momentum space. In addition, experimental probes of odd‐frequency pairing in multiband systems are reviewed, focusing on hybridization gaps in the electronic density of states, paramagnetic Meissner effect, and Kerr effect.

Electroluminescence from multi-particle exciton complexes in transition metal dichalcogenide semiconductors

Light emission from higher-order correlated excitonic states has been recently reported in hBN-encapsulated monolayer WSe2 and WS2 upon optical excitation. These exciton complexes are found to be bound states of excitons residing in opposite valleys in momentum space, a promising feature that could be employed in valleytronics or other novel optoelectronic devices. However, electrically-driven light emission from such exciton species is still lacking. Here we report electroluminescence from bright and dark excitons, negatively charged trions and neutral and negatively charged biexcitons, generated by a pulsed gate voltage, in hexagonal boron nitride encapsulated monolayer WSe2 and WS2 with graphene as electrode. By tailoring the pulse parameters we are able to tune the emission intensity of the different exciton species in both materials. We find the electroluminescence from charged biexcitons and dark excitons to be as narrow as 2.8 meV.

Efficient generation of neutral and charged biexcitons in encapsulated WSe2 monolayers

Higher-order correlated excitonic states arise from the mutual interactions of excitons, which generally requires a significant exciton density and therefore high excitation levels. Here, we report the emergence of two biexcitons species, one neutral and one charged, in monolayer tungsten diselenide under moderate continuous-wave excitation. The efficient formation of biexcitons is facilitated by the long lifetime of the dark exciton state associated with a spin-forbidden transition, as well as improved sample quality from encapsulation between hexagonal boron nitride layers. From studies of the polarization and magnetic field dependence of the neutral biexciton, we conclude that this species is composed of a bright and a dark excitons residing in opposite valleys in momentum space. Our observations demonstrate that the distinctive features associated with biexciton states can be accessed at low light intensities and excitation densities.

Valleytronics: Opportunities, Challenges, and Paths Forward.

A lack of inversion symmetry coupled with the presence of time-reversal symmetry endows 2D transition metal dichalcogenides with individually addressable valleys in momentum space at the K and K' points in the first Brillouin zone. This valley addressability opens up the possibility of using the momentum state of electrons, holes, or excitons as a completely new paradigm in information processing. The opportunities and challenges associated with manipulation of the valley degree of freedom for practical quantum and classical information processing applications were analyzed during the 2017 Workshop on Valleytronic Materials, Architectures, and Devices; this Review presents the major findings of the workshop.

Optical control of room-temperature valley polaritons

Valley-polarized light–matter quasiparticles in two-dimensional semiconductor microcavities are demonstrated. Access to spin–valley physics may be useful for photonic quantum technologies. The formation of half-light half-matter quasiparticles under strong coupling results in properties unique from those of the constituent components. Fingerprints of both light and matter are imprinted on the new quasiparticles, called polaritons. In the context of two-dimensional (2D) materials, this opens up the possibility of exploiting the intriguing spin–valley physics of a bare semiconductor combined with the light mass of the photonic component for possible quantum technologies. Specifically, the valley degree of freedom1,2, which remained largely unexplored until the advent of these materials, is highly attractive in this context as it provides an optically accessible route for the control and manipulation of electron spin. Here, we report the observation of room-temperature strongly coupled light–matter quasiparticles that are valley polarized because of the coupling of photons with specific helicity to excitons that occupy quantum mechanically distinct valleys in momentum space. The realization of valley polaritons in 2D semiconductor microcavities presents the first step towards engineering valley-polaritonic devices.

Optical manipulation of valley pseudospin

The coherent manipulation of spin and pseudospin underlies existing and emerging quantum technologies, including NMR, quantum communication, and quantum computation. Valley polarization, associated with the occupancy of degenerate, but quantum mechanically distinct valleys in momentum space, closely resembles spin polarization and has been proposed as a pseudospin carrier for the future quantum electronics. Valley exciton polarization has been created in the transition metal dichalcogenide (TMDC) monolayers using excitation by circularly polarized light and has been detected both optically and electrically. In addition, the existence of coherence in the valley pseudospin has been identified experimentally. The manipulation of such valley coherence has, however, remained out of reach. Here we demonstrate an all-optical control of the valley coherence by means of the pseudomagnetic field associated with the optical Stark effect. Using below-bandgap circularly polarized light, we experimentally rotate the valley exciton pseudospin in monolayer WSe2 on the femtosecond time scale. Both the direction and speed of the rotation can be optically manipulated by tuning the dynamic phase of excitons in opposite valleys. This study completes the generation-manipulation-detection paradigm for valley pseudospin, enabling the platform of excitons in 2D materials for the control of this novel degree of freedom in solids.

Polarization and valley switching in monolayer group-IV monochalcogenides

Group-IV monochalcogenides are a family of two-dimensional puckered materials with an orthorhombic structure that is comprised of polar layers. In this article, we use first principles calculations to show the multistability of monolayer SnS and GeSe, two prototype materials where the direction of the puckering can be switched by application of tensile stress or electric field. Furthermore, the two inequivalent valleys in momentum space, which are dictated by the puckering orientation, can be excited selectively using linearly polarized light, and this provides an additional tool to identify the polarization direction. Our findings suggest that SnS and GeSe monolayers may have observable ferroelectricity and multistability, with potential applications in information storage.

Evolution of the Valley Position in Bulk Transition-Metal Chalcogenides and Their Monolayer Limit.

Layered transition metal chalcogenides with large spin orbit coupling have recently sparked much interest due to their potential applications for electronic, optoelectronic, spintronics, and valleytronics. However, most current understanding of the electronic structure near band valleys in momentum space is based on either theoretical investigations or optical measurements, leaving the detailed band structure elusive. For example, the exact position of the conduction band valley of bulk MoS2 remains controversial. Here, using angle-resolved photoemission spectroscopy with submicron spatial resolution (micro-ARPES), we systematically imaged the conduction/valence band structure evolution across representative chalcogenides MoS2, WS2, and WSe2, as well as the thickness dependent electronic structure from bulk to the monolayer limit. These results establish a solid basis to understand the underlying valley physics of these materials, and also provide a link between chalcogenide electronic band structure and their physical properties for potential valleytronics applications.

Nonlinear optical selection rule based on valley-exciton locking in monolayer ws2

Optical selection rule fundamentally determines the optical transition between energy states in a variety of physical systems from hydrogen atoms to bulk crystals such as GaAs. It is important for optoelectronic applications such as lasers, energy-dispersive X-ray spectroscopy and quantum computation. Recently, single layer transition metal dichalcogenide (TMDC) exhibits valleys in momentum space with nontrivial Berry curvature and excitons with large binding energy. However, it is unclear how the unique valley degree of freedom combined with the strong excitonic effect influences the optical excitation. Here we discover a new set of optical selection rules in monolayer WS2,imposed by valley and exciton angular momentum. We experimentally demonstrated such a principle for second harmonic generation (SHG) and two-photon luminescence (TPL). Moreover, the two-photon induced valley populations yield net circular polarized photoluminescence after a sub-ps interexciton relaxation (2p->1s) and last for 8 ps. The discovery of this new optical selection rule in valleytronic 2D system not only largely extend information degrees but sets a foundation in control of optical transitions that is crucial to valley optoeletronic device applications such as 2D valley-polarized light emitting diodes (LED), optical switches and coherent control for quantum computing.

Spin and valley dynamics of excitons in transition metal dichalcogenide monolayers

Monolayers of transition metal dichalcogenides, namely, molybdenum and tungsten disulfides and diselenides demonstrate unusual optical properties related to the spin-valley locking effect. Particularly, excitation of monolayers by circularly polarized light selectively creates electron-hole pairs or excitons in non-equivalent valleys in momentum space, depending on the light helicity. This allows studying the inter-valley dynamics of charge carriers and Coulomb complexes by means of optical spectroscopy. Here we present a concise review of the neutral exciton fine structure and its spin and valley dynamics in monolayers of transition metal dichalcogenides. It is demonstrated that the long-range exchange interaction between an electron and a hole in the exciton is an efficient mechanism for rapid mixing between bright excitons made of electron-hole pairs in different valleys. We discuss the physical origin of the long-range exchange interaction and outline its derivation in both the electrodynamical and $\mathbf k \cdot \mathbf p$ approaches. We further present a model of bright exciton spin dynamics driven by an interplay between the long-range exchange interaction and scattering. Finally, we discuss the application of the model to describe recent experimental data obtained by time-resolved photoluminescence and Kerr rotation techniques.

Spatially resolving valley quantum interference of a donor in silicon

Electron and nuclear spins of donor ensembles in isotopically pure silicon experience a vacuum-like environment, giving them extraordinary coherence. However, in contrast to a real vacuum, electrons in silicon occupy quantum superpositions of valleys in momentum space. Addressable single-qubit and two-qubit operations in silicon require that qubits are placed near interfaces, modifying the valley degrees of freedom associated with these quantum superpositions and strongly influencing qubit relaxation and exchange processes. Yet to date, spectroscopic measurements have only probed wavefunctions indirectly, preventing direct experimental access to valley population, donor position and environment. Here we directly probe the probability density of single quantum states of individual subsurface donors, in real space and reciprocal space, using scanning tunnelling spectroscopy. We directly observe quantum mechanical valley interference patterns associated with linear superpositions of valleys in the donor ground state. The valley population is found to be within 5% of a bulk donor when 2.85 ± 0.45 nm from the interface, indicating that valley-perturbation-induced enhancement of spin relaxation will be negligible for depths greater than 3 nm. The observed valley interference will render two-qubit exchange gates sensitive to atomic-scale variations in positions of subsurface donors. Moreover, these results will also be of interest for emerging schemes proposing to encode information directly in valley polarization.

Robust optical emission polarization in MoS2monolayers through selective valley excitation

We report polarization resolved photoluminescence from monolayer MoS2, a two-dimensional, non-centrosymmetric crystal with direct energy gaps at two different valleys in momentum space. The inherent chiral optical selectivity allows exciting one of these valleys and close to 90% polarized emission at 4K is observed with 40% polarization remaining at 300K. The high polarization degree of the emission remains unchanged in transverse magnetic fields up to 9T indicating robust, selective valley excitation.

Dynamics and spontaneous coherence of magnons in ferromagnetic thin films

A theory of the dynamics of the Bose–Einstein condensate of magnons is presented. It is shown that, despite magnon decay processes, ongoing during the condensate formation, the system manifests spontaneous quantum coherence with a pseudo-spin degree of freedom originated from the presence of two valleys in momentum space. Finally, a real space description of the condensed state is provided, revealing the condensate state as a spin density wave. The effective dynamics of the spinor condensate wavefunction is characterized, and it is shown to display Josephson-like relations.

Electron-hole asymmetry in single-walled carbon nanotubes probed by direct observation of transverse quasidark excitons

We studied the asymmetry between valence and conduction bands in single-walled carbon nanotubes through the direct observation of spin-singlet transverse dark excitons using polarized photoluminescence excitation spectroscopy. The intrinsic electron-hole $(e\text{\ensuremath{-}}h)$ asymmetry lifts the degeneracy of the transverse exciton wave functions at two equivalent $K$ and ${K}^{\ensuremath{'}}$ valleys in momentum space, which gives finite oscillator strength to transverse dark exciton states. Chirality-dependent spectral weight transfer to transverse dark states was clearly observed, indicating that the degree of the $e\text{\ensuremath{-}}h$ asymmetry depends on the specific nanotube structure. Based on comparison between theoretical and experimental results, we evaluated the band asymmetry parameters in various carbon nanotube structures and graphene.