We demonstrate the coexistence of pseudospin- and valley-Hall-like edge states in a photonic crystal with $C_{3v}$ symmetry, which is composed of three interlacing triangular sublattices with the same lattice constants. By tuning the geometry of the sublattices, three complete photonic band gaps with nontrivial topology can be created, one of which is due to the band inversion associated with the pseudospin degree of freedom at the $Γ$ point and the other two due to the gapping out of Dirac cones associated with the valley degree of freedom at the $K, K'$ points. The system can support tri-band pseudospin- and valley-momentum locking edge states at properly designed domain-wall interfaces. Furthermore, to demonstrate the novel interplay of the two kinds of edge states in a single configuration, we design a four-channel system, where the unidirectional routing of electromagnetic waves against sharp bends between two routes can be selectively controlled by the pseudospin and valley degrees of freedom. Our work combines the pseudospin and valley degrees of freedom in a single configuration and may provide more flexibility in manipulating electromagnetic waves with promising potential for multiband and multifunctional applications.
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…
We present a symmetric double-sided pillared phononic crystals (PPnCs) that can emulate both quantum spin Hall effect (QSHE) and quantum valley Hall effect (QVHE) by solely imposing different geometric perturbations. Indeed, the Dirac cones can occur in the low (deep subwavelength) and high frequency regime by judiciously turning the parameters of the attached pillars and even a double Dirac cone can be achieved. We realize the valley-protected, the pseudospin-protected or the pseudospin-valley coupled edge states with the proposed platform. Besides, we show a variety of refraction phenomena (…
Pseudo-spin and valley degrees of freedom (DOFs) engineered in photonic analogues of topological insulators (TI) provide potential approaches to optical encoding and robust signal transport. Here we observe a ballistic edge state whose spin-valley indices are locked to the direction of propagation along the interface between a valley photonic crystal and a metacrystal emulating the quantum spin Hall effect. We demonstrate the inhibition of inter-valley scattering at a Y-junction formed at the interfaces between photonic TIs carrying different spin-valley Chern numbers. These results open up th…
Modifying the hexagonal lattices of graphene enables the repositioning and merging of the Dirac cones which proves to be a key element in the use of these materials for alternative electronic applications such as valleytronics. Here we study the nonequilibrium transport of carriers within a system containing two Dirac cones in both standard graphene and semi-Dirac graphene. In the latter, the lattice modifications cause the relativistic and parabolic dispersion bands to coexist, furnishing the Fermi surface with a rich pseudospin texture and a versatile Dirac cones separation. We construct a k…
Local energy extrema of the bands in momentum space, or valleys, can endow electrons in solids with pseudo-spin in addition to real spin. In transition metal dichalcogenides this valley pseudo-spin, like real spin, is associated with a magnetic moment which underlies the valley-dependent circular dichroism that allows optical generation of valley polarization, intervalley quantum coherence, and the valley Hall effect. However, magnetic manipulation of valley pseudospin via this magnetic moment, analogous to what is possible with real spin, has not been shown before. Here we report observation …
In graphene, the pseudospin and the valley flavor arise as new types of quantum degrees of freedom due to the honeycomb lattice comprising two sublattices (A and B) and two inequivalent Dirac points (K and K') in the Brillouin zone, respectively. Unique electronic properties of graphene result in striking phenomena such as Klein tunnelling, Veselago lens, and valley-polarized currents. Here, we investigate the roles of the pseudospin and the valley in electron scattering at graphene edges and show that they are strongly correlated with charge density modulations of short-wavelength oscillation…
Pioneering studies in transition metal dichalcogenides have demonstrated convincingly the co-existence of multiple angular momentum degrees of freedom -- of spin (1/2 $s_z = \pm 1/2$), valley ($τ= K, K'$ or $\pm 1$), and atomic orbital ($l_z = \pm 2$) origins -- in the valence band with strong interlocking among them, which results in noise-resilient pseudospin states ideal for spintronic type applications. With field modulation a powerful, universal means in physics studies and applications, this work develops, from bare models in the context of complicated band structure, a general effective…
Valleytronics is a rising topic to explore the emergent degree of freedom for charge carriers in energy band edges and has attracted a great interest due to many intriguing quantum phenomena and potential application in information processing industry. Creation of permanent valley polarization, i.e. unbalanced occupation at different valleys, is a chief challenge and also urgent question to be solved in valleytronics. Here we predict that the spin-orbit coupling and magnetic ordering allow spontaneous valley Zeeman-type splitting in pristine monolayer of VAgP2Se6 by using first-principles calc…
Zeeman effect induced by the magnetic field introduces a splitting between the two valleys at K$^+$ and K$^-$ points of the Brillouin zone in monolayer semiconducting transition metal dichalcogenides. In consequence, the photoluminescence signal exhibits a field dependent degree of circular polarization. We present a comprehensive study of this effect in the case of a trion in monolayer MoTe$_2$, showing that although time integrated data allows us to deduce a g-factor of the trion state, such an analysis cannot be substantiated by the timescales revealed in the time-resolved experiments.
In monolayers of semiconducting transition metal dichalcogenides, the light helicity ($σ^+$ or $σ^-$) is locked to the valley degree of freedom, leading to the possibility of optical initialization of distinct valley populations. However, an extremely rapid valley pseudospin relaxation (at the time scale of picoseconds) occurring for optically bright (electric-dipole active) excitons imposes some limitations on the development of opto-valleytronics. Here we show that inter-valley scattering of excitons can be significantly suppressed in a $\mathrm{WSe}_2$ monolayer, a direct-gap two-dimensiona…
We study spin-valley and lattice-pseudo spin currents in a dual ferromagnetic-gated silicene-based junction. Silicene has buckled atomic structure which allows us to take sublattice-dependent ferromagnetism into account in the investigation. One of the study results show that transmission at the junctions exhibits anisotropic property only in anti-parallel cases. Interestingly, the studied junctions can be switched from a pure spin-polarizer to a pure valley-polarizer by reversing directions of exchange fields in the parallel junctions. The perfect control of spin-valley currents can be done o…
Valley pseudospin, the quantum degree of freedom characterizing the degenerate valleys in energy bands, is a distinct feature of two-dimensional Dirac materials. Similar to spin, the valley pseudospin is spanned by a time reversal pair of states, though the two valley pseudospin states transform to each other under spatial inversion. The breaking of inversion symmetry induces various valley-contrasted physical properties; for instance, valley-dependent topological transport is of both scientific and technological interests. Bilayer graphene (BLG) is a unique system whose intrinsic inversion sy…
Topologically protected gapless edge states are phases of quantum matter which behave as massless Dirac fermions, immunizing against disorders and continuous perturbations. Recently, a new class of topological insulators (TIs) with topological corner states have been theoretically predicted in electric systems, and experimentally realized in two-dimensional (2D) mechanical and electromagnetic systems, electrical circuits, optical and sonic crystals, and elastic phononic plates. Here, we demonstrate a pseudospin-valley-coupled phononic TI, which simultaneously exhibits gapped edge states and to…
Interlayer valley excitons in bilayer MoS2 feature concurrently large oscillator strength and long lifetime, and hence represent an advantageous scenario for valleytronic applications. However, control of valley pseudospin of interlayer excitons in pristine bilayer MoS2, which lies at the heart of valleytronics, has remained elusive. Here we report the observation of highly circularly polarized photoluminescence from interlayer excitons of bilayer MoS2 with both optical and magnetic addressability. Under excitation of circularly polarized light near exciton resonance, interlayer excitons of bi…
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 mi…
Preserving a high degree of valley polarization of excitons in photo-excited transition-metal dichalcogenide monolayers (TMD-MLs) is desirable for the valley-based photonic applications, but widely recognized as a hard task hindered by the intrinsic electron-hole exchange interaction. In this study, we present a comprehensive investigation of valley-polarized finite-momentum excitons in WSe$_2$-MLs over the entire Brillouin zone by solving the density-functional-theory(DFT)-based Bethe-Salpeter equation (BSE) under the guidance of symmetry analysis. We reveal that finite-momentum excitons are …
Two-dimensional transition metal dichalcogenide (TMD) semiconductors provide a unique possibility to access the electronic valley degree of freedom using polarized light, opening the way to valley information transfer between distant systems. Excitons with a well-defined valley index (or valley pseudospin) as well as superpositions of the exciton valley states can be created with light having circular and linear polarization, respectively. However, the generated excitons have short lifetimes (ps) and are also subject to the electron-hole exchange interaction leading to fast relaxation of the v…
Graphene electrons feature a pair of massless Dirac cones of opposite pseudospin chirality at two valleys. Klein tunneling refers to the intriguing capability of these chiral electrons to penetrate through high and wide potential barrier. The two valleys have been treated independently in the literature, where time reversal symmetry dictates that neither the normal incidence transmission nor the angle-averaged one can have any valley polarization. Here we show that, when intervalley scattering by barrier is accounted, graphene electrons normally incident at a superlattice barrier can experienc…
In crystals, energy band extrema in momentum space can be identified by their valley index. The internal quantum degree of freedom associated with valley pseudospin indices can act as a useful information carrier analogous to electronic charge or spin. Interest in valleytronics has been revived in recent years following the discovery of atomically thin materials such as graphene and transition metal dichalcogenides. However, the valley coherence time, a key quantity for manipulating the valley pseudospin, has never been measured in any material. In this work, we use a sequence of laser pulses …
We describe an angularly asymmetric interface-scattering mechanism which allows to spatially separate the electrons in the two low-energy valleys of bilayer graphene. The effect occurs at electrostatically defined interfaces separating regions of different pseudospin polarization, and is associated with the helical winding of the pseudospin vector across the interface, which breaks the reflection symmetry in each valley. Electrons are transmitted with a preferred direction of up to 60 degree over a large energetic range in one of the valleys, and down to -60 degree in the other. In a Y-junctio…
The chiral two-dimensional electron gas in Landau levels $\left\vert N\right\vert >0$ of a Bernal-stacked graphene bilayer has a valley-pseudospin Ising quantum Hall ferromagnetic behavior at odd filling factors $ν_{N}=1,3$ of these fourfold degenerate states. At zero interlayer electrical bias, the ground state at these fillings is spin polarized and electrons occupy one valley or the other while a finite electrical bias produces a series of valley pseudospin-flip transitions. In this work, we extend the Ising behavior to chirally-stacked multilayer graphene and discuss the hysteretic behavio…
Monolayer (1L) transition metal dichalcogenides (TMDCs) are attractive materials for several optoelectronic applications because of their strong excitonic resonances and valley-selective response. Valley excitons in 1L-TMDCs are formed at opposite points of the Brillouin zone boundary, giving rise to a valley degree of freedom that can be treated as a pseudospin and may be used as a platform for information transport and processing. However, short valley depolarization times and relatively short exciton lifetimes at room temperature prevent using valley pseudospin in on-chip integrated valley …
In monolayer transition metal dichalcogenides, tightly bound excitons have been discovered with a valley pseudospin that can be optically addressed through polarization selection rules. Here, we show that this valley pseudospin is strongly coupled to the exciton center-of-mass motion through electron-hole exchange. This coupling realizes a massless Dirac cone with chirality index I=2 for excitons inside the light cone, i.e. bright excitons. Under moderate strain, the I=2 Dirac cone splits into two degenerate I=1 Dirac cones, and saddle points with a linear Dirac spectrum emerge in the bright e…
Electrons in graphene, in addition to their spin, have two pseudospin degrees of freedom: sublattice and valley pseudospin. Valleytronics uses the valley degree of freedom as a carrier of information similar to the way spintronics uses electron spin. We show how a double barrier structure consisting of electric and vector potentials can be used to filter massive Dirac electrons based on their valley index. We study the resonant transmission through a finite number of barriers and we obtain the energy spectrum of a superlattice consisting of electric and vector potentials. When a mass term is i…
The valley pseudospin in monolayer transition metal dichalcogenides (TMDs) has been proposed as a new way to manipulate information in various optoelectronic devices. This relies on a large valley polarization that remains stable over long timescales (hundreds of ns). However, time resolved measurements report valley lifetimes of only a few ps. This has been attributed to mechanisms such as phonon-mediated inter-valley scattering and a precession of the valley psedospin through electron-hole exchange. Here we use transient spin grating to directly measure the valley depolarization lifetime in …
We present a theory of superconductivity in twisted bilayer graphene in which attraction is generated between electrons on the same honeycomb sublattice when the system is close to a sublattice polarization instability. The resulting Cooper pairs are spin-polarized valley-singlets. Because the sublattice polarizability is mainly contributed by interband fluctuations, superconductivity occurs over a wide range of filling fraction. It is suppressed by i) applying a sublattice polarizing field (generated by an aligned BN substrate) or ii) changing moiré band filling to favor valley polarization. …
Strong correlation effects on electron transport through a spinless quantum dot are considered. When two single-particle levels in the quantum dot are degenerate, a conserved pseudospin degree of freedom appears for general tunneling matrix elements between the quantum dot and leads. Local fluctuations of the pseudospin in the quantum dot give rise to a pair of asymmetric conductance peaks near the center of a Coulomb valley. An exact relation to the population switching is provided.
The emerging field of valleytronics aims to exploit the valley pseudospin of electrons residing near Bloch band extrema as an information carrier. Recent experiments demonstrating optical generation and manipulation of exciton valley coherence (the superposition of electron-hole pairs at opposite valleys) in monolayer transition metal dichalcogenides (TMDs) provide a critical step towards control of this quantum degree of freedom. The charged exciton (trion) in TMDs is an intriguing alternative to the neutral exciton for control of valley pseudospin because of its long spontaneous recombinatio…
A monolayer of a transition metal dichalcogenide (TMD) such as WSe$_2$ is a two-dimensional (2D) direct band-gap valley-semiconductor having an effective Honeycomb lattice structure with broken inversion symmetry. The inequivalent valleys in the Brillouin zone could be selectively addressed using circularly-polarized light fields, suggesting the possibility for magneto-optical measurement and manipulation of the valley pseudospin degree of freedom. Here we report such experiments that demonstrate the valley Zeeman effect -- strongly anisotropic lifting of the degeneracy of the valley pseudospi…
For applications exploiting the valley pseudospin degree of freedom in transition metal dichalcogenide monolayers, efficient preparation of electrons or holes in a single valley is essential. Here, we show that a magnetic field of 7 Tesla leads to a near-complete valley polarization of electrons in MoSe2 monolayer with a density 1.6x10^{12} cm^{-2}; in the absence of exchange interactions favoring single-valley occupancy, a similar degree of valley polarization would have required a pseudospin g-factor exceeding 40. To investigate the magnetic response, we use polarization resolved photolumine…
Valley pseudospin in two-dimensional (2D) transition-metal dichalcogenides (TMDs) allows optical control of spin-valley polarization and intervalley quantum coherence. Defect states in TMDs give rise to new exciton features and theoretically exhibit spin-valley polarization; however, experimental achievement of this phenomenon remains challenges. Here, we report unambiguous valley pseudospin of defect-bound localized excitons in CVD-grown monolayer MoS2; enhanced valley Zeeman splitting with an effective g-factor of -6.2 is observed. Our results reveal that all five d-orbitals and the increase…
Chiral quasiparticles in Bernal-stacked bilayer graphene have valley-contrasting Berry phases of 2π. This nontrival topological structure, associated with the pseudospin winding along a closed Fermi surface, is responsible for various novel electronic properties, such as anti-Klein tunneling, unconventional quantum Hall effect, and valley Hall effect1-6. Here we show that the quantum interference due to intervalley scattering induced by atomic defects/impurities provides further insights into the topological nature of the bilayer graphene. The scattered chiral quasiparticles between distinct v…
In addition to spin, electrons in many materials possess an additional pseudo-spin degree of freedom known as 'valley'. In materials where the spin and valley degrees of freedom are weakly coupled, they can be both excited and controlled independently. In this work, we study a model describing the interplay of the spin and valley Hall effects in such two-dimensional materials. We demonstrate the emergence of an additional longitudinal neutral current that is both spin and valley polarized. The additional neutral current allows to control the spin density by tuning the magnitude of the valley H…
Monolayer transition metal dichalcogenides feature tightly bound bright excitons at the degenerate valleys, where electron-hole Coulomb exchange interaction strongly couples the valley pseudospin to the momentum of exciton. Placed on periodically structured dielectric substrate, the spatial modulation of the Coulomb interaction leads to the formation of exciton Bloch states with real-space valley pseudospin texture displayed in a mesoscopic supercell. We find this spatial valley texture in the exciton Bloch function is pattern-locked to the propagation direction, enabling nano-optical excitati…
The discovery of photonic topological insulators (PTIs) has opened the door to fundamentally new topological states of light.Current time-reversal-invariant PTIs emulate either the quantum spin Hall (QSH) effect or the quantum valley Hall (QVH) effect in condensed-matter systems, in order to achieve topological transport of photons whose propagation is predetermined by either 'photonic pseudospin' (abbreviated as 'spin') or valley. Here we demonstrate a new class of PTIs, whose topological phase is not determined solely by spin or valley, but is controlled by the competition between their indu…
A new degree of freedom, the valley pseudospin, emerges in atomically thin two-dimensional transition metal dichalcogenides (MX2) and has attracted great scientific interest. The capability to manipulate the valley pseudospin, in analogy to the control of spin in spintronics, can open up exciting opportunities in valleytronics. Here we demonstrate that an ultrafast and ultrahigh valley pseudomagnetic field can be generated using circularly polarized femtosecond pulses to selectively control the valley degree of freedom in monolayer MX2. Employing ultrafast pump-probe spectroscopy, we observed …
We calculate the dispersion of spinor exciton-polaritons in a planar microcavity with its active region containing a single Transitional Metal Dichalcogenide (TMD) monolayer, taking into account excitonic and photonic spin-orbit coupling. We consider the radial propagation of polaritons in presence of disorder. We show that the reduction of the disorder scattering induced by the formation of polariton states allows to observe an optical Valley Hall effect, namely the coherent precession of the locked valley and polarization pseudospins leading to the formation of spatial valley-polarized domai…
Despite much anticipation of valleytronics as a candidate to replace the ageing CMOS-based information processing, its progress is severely hindered by the lack of practical ways to manipulate valley polarization all-electrically in an electrostatic setting. Here we propose a class of all-electric-controlled valley filter, valve and logic gate based on the valley-contrasting transport in a merging Dirac cones system. The central mechanism of these devices lies on the pseudospin-assisted quantum tunneling which effectively quenches the transport of one valley when its pseudospin configuration m…
Bilayer graphene is susceptible to a family of unusual broken symmetry states with spin and valley dependent layer polarization. We report on a microscopic study of the domain walls in these systems, demonstrating that they have interesting microscopic structures related to order-induced topological characters. We use our results to estimate Ginzburg-Landau model parameters and transition temperatures for the ordered states of bilayer graphene.
We argue that by inducing superconductivity in graphene via the proximity effect, it is possible to observes the "quantum valley Hall effect". In the presence of magnetic field, supercurrent causes "valley pseudospin" to accumulate at the edges of the superconducting strip. This, and the structure of the superconducting vortex core, provide possibilities to experimentally observe aspects of the "deconfined quantum criticality".
Coherent control and manipulation of quantum degrees of freedom such as spins forms the basis of emerging quantum technologies. In this context, the robust valley degree of freedom and the associated valley pseudospin found in two-dimensional transition metal dichalcogenides is a highly attractive platform. Valley polarization and coherent superposition of valley states have been observed in these systems even up to room temperature. Control of valley coherence is an important building block for the implementation of valley qubit. Large magnetic fields or high-power lasers have been used in th…
In a Bernal-stacked graphene bilayer, an electronic state in Landau level $% N=0$ is described by its guiding-center index $X$ (in the Landau gauge) and by its valley, spin, and orbital indices $ξ=\pm K,σ=\pm 1,$ and $% n=0,1.$ When Coulomb interaction is taken into account, the chiral two-dimensional electron gas (C2DEG) in this system can support a variety of quantum Hall ferromagnetic (QHF)\ ground states where the spins and/or valley pseudospins and/or orbital pseudospins collectively align in space. In this work, we give a comprehensive account of the phase diagram of the C2DEG at integer…
We systematically study the impact of various electron-acoustic-phonon coupling mechanisms on valley physics in two-dimensional materials. In the static strain limit, we find that Dirac cone tilt and deformation potential have analogous valley Hall response since they fall into the same universality class of pseudospin structure. However, such argument fails for the coupling mechanism with position-dependent Fermi velocity. For the isotropic case, a significant valley Hall effect occurs near charge neutrality similar to the bond-length change, whereas for the anisotropic case, the geometric va…
Charge carriers in two-dimensional transition metal dichalcogenides (TMDs), such as WSe$_2$, have their spin and valley-pseudospin locked into an optically-addressable index that is proposed as a basis for future information processing. The manipulation of this spin-valley index requires tuning its energy, typically through external magnetic field (B), which is cumbersome. Thus, other efficient routes like all-optical control of spin-valley index are desirable. Here, we show that many-body interactions amongst interlayer excitons in WSe$_2$/MoSe$_2$ heterobilayer induce a steady-state valley Z…
We discuss the universal spin dynamics in quasi one-dimensional systems including the real spin in narrow-gap semiconductors like InAs and InSb, the valley pseudospin in staggered single-layer graphene, and the combination of real spin and valley pseudospin characterizing single-layer transition metal dichalcogenides (TMDCs) such as MoS$_2$, WS$_2$, MoSe$_2$, and WSe$_2$. All these systems can be described by the same Dirac-like Hamiltonian. Spin-dependent observable effects in one of these systems thus have counterparts in each of the other systems. Effects discussed in more detail include eq…
At low-energy, the band structure of graphene can be approximated by two degenerate valleys $(K,K^{\prime})$ about which the electronic spectra of the valence and conduction bands have linear dispersion relations. An electronic state in this band spectrum is a linear superposition of states from the $A$ and $B$ sublattices of the honeycomb lattice of graphene. In a quantizing magnetic field, the band spectrum is split into Landau levels with level N=0 having zero weight on the $B(A)$ sublattice for the $% K(K^{\prime})$ valley. Treating the valley index as a pseudospin and assuming the real sp…
Spontaneous Breaking of the SU(3) Flavor Symmetry in a Quantum Hall Valley Nematic
ENS, Université PSL, CNRS, Sorbonne Université（巴黎高等师范学院，巴黎文理研究大学，法国国家科学研究中心，索邦大学）；Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）；Chungnam National University（忠南国立大学）；National Technical University “KhPI”（哈尔科夫国立理工大学）；Johannes Kepler Universität（约翰内斯·开普林大学）；Université Paris-Saclay, CNRS, CEA（巴黎萨克雷大学，法国国家科学研究中心，法国原子能和替代能源委员会）
One of the intriguing characteristics of honeycomb lattices is the appearance of a pseudo-magnetic field as a result of mechanical deformation. In the case of graphene, the Landau quantization resulting from this pseudo-magnetic field has been measured using scanning tunneling microscopy. Here we show that a signature of the pseudo-magnetic field is a local sublattice symmetry breaking observable as a redistribution of the local density of states. This can be interpreted as a polarization of graphene's pseudospin due to a strain induced pseudo-magnetic field, in analogy to the alignment of a r…
