In monolayer hexagonal lattices, two inequivalent valleys appear in the Brillouin zone. With inversion symmetry breaking, we find chiral phonons with valley contrasting circular polarization and ionic magnetic moment. At valley centers, there is a three-fold rotational symmetry endowing phonons with a quantized pseudo angular momentum, which includes spin and orbital parts. From conservation of the pseudo angular momentum, crystal momentum and energy, selection rules in intervalley scattering of electrons by phonons are obtained. The chiral valley phonons are verified and the selection rules are predicted in monolayer Molybdenum disulfide. Due to valley contrasting phonon Berry curvature, one can also detect a valley phonon Hall effect. The valley-contrasting chiral phonon, together with phonon circular polarization, ionic magnetic moment, phonon pseudo angular momentum, valley phonon Hall effect, will form the basis for valley-based electronics and phononics applications in the future.
We investigate physical properties that can be used to distinguish the valley degree of freedom in systems where inversion symmetry is broken, using graphene systems as examples. We show that the pseudospin associated with the valley index of carriers has an intrinsic magnetic moment, in close analogy with the Bohr magneton for the electron spin. There is also a valley dependent Berry phase effect that can result in a valley contrasting Hall transport, with carriers in different valleys turning into opposite directions transverse to an in-plane electric field. These effects can be used to gene…
The valley-contrasting orbital magnetic moment of Bloch electrons allows the lifting of valley degeneracy by an out-of-plane magnetic field. We demonstrate that this leads to negative magnetoresistance, utilizing a gapped two-dimensional multi-valley model as an example. An intuitive physical picture in terms of the increased carrier density from a magnetic gating effect is proposed for this negative magnetoresistance. In particular, giant negative magnetoresistance is achieved after one of the two valleys is depleted by the magnetic field. This new mechanism of negative magnetoresistance is a…
We examine the full static non-linear optical response of uniaxially strained transition metal dichalcogenide monolayers doped with a finite carrier density in the conduction band, in the presence of disorder. We find that the customary shift current is suppressed, yet we identify a strong, valley-dependent non-reciprocal response, which we term a \textit{unidirectional valley-contrasting photo-current} (UVCP). This DC current originates from the combined effect of strain and Kramers symmetry breaking by trigonal warping, while the contributions due to individual valleys can be separated by in…
The topological quantum states in two-dimensional (2D) materials are fascinating subjects of research, which usually highlight electron-related systems. In this work, we present a recipe that leads to Dirac phonon states with quantized valley Berry phase in 2D hexagonal lattices by first-principles calculations. We show that candidates possessing the three-fold rotational symmetry at the corners of the hexagonal Brillouin zone host valley Dirac phonons, which are guaranteed to remain intact with respect to perturbations. We identify that such special topological features populated by Dirac pho…
The valley dependent optical selection rules in recently discovered monolayer group-VI transition metal dichalcogenides (TMDs) make possible optical control of valley polarization, a crucial step towards valleytronic applications. However, in presence of Landaul level(LL) quantization such selection rules are taken over by selection rules between the LLs, which are not necessarily valley contrasting. Using MoS$_{2}$ as an example we show that the spatial inversion-symmetry breaking results in unusual valley dependent inter-LL selection rules, which directly locks polarization to valley. We fin…
Valley, as a degree of freedom, has been exploited to realize valley-selective Hall transport and circular dichroism in two-dimensional layered materials. On the other hand, orbital angular momentum of light with helical phase distribution has attracted great attention for its unprecedented opportunity to optical communicagtions, atom trapping, and even nontrivial topology engineering. Here, we reveal valley-contrasting orbital angular momentum in all-dielectric photonic valley crystals. Selective excitation of valley chiral bulk states is realized by sources carrying orbital angular momentum …
We study spin-orbit torques in two dimensional hexagonal crystals such as graphene, silicene, germanene and stanene. The torque possesses two components, a field-like term due to inverse spin galvanic effect and an antidamping torque originating from Berry curvature in mixed spin-$k$ space. In the presence of staggered potential and exchange field, the valley degeneracy can be lifted and we obtain a valley-dependent Berry curvature, leading to a tunable antidamping torque by controlling the valley degree of freedom. The valley imbalance can be as high as 100\% by tuning the bias voltage or mag…
Contrasting $Γ$- and K-Valley Moiré Physics in Twisted Monolayer/Bilayer WSe$_2$
University of California, Los Angeles（加州大学洛杉矶分校）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；National Institute for Materials Science（国立材料研究所）
The exploration of topological states is of significant fundamental and practical importance in contemporary condensed matter physics, for which the extension to two-dimensional (2D) organometallic systems is particularly attractive. Using first-principles calculations, we show that a 2D hexagonal triphenyl-lead lattice composed of only main group elements is susceptible to a magnetic instability, characterized by a considerably more stable antiferromagnetic (AFM) insulating state rather than the topologically nontrivial quantum spin Hall state proposed recently. Even though this AFM phase is …
In this letter, we examine the role of Coulomb interactions in the emergence of macroscopically ordered states in graphene supported on hexagonal boron nitride substrates. Due to incommensuration effects with the substrate, graphene can develop gapped low energy modes that spatially conform into a triangular superlattice of quantum rings. In the presence of these modes, we show that Coulomb interactions lead to spontaneous formation of chiral loop currents in bulk and to macroscopic spin-valley order at zero temperature. We show that this exotic state breaks time reversal symmetry and can be d…
Graphene superlattices have recently been attracting growing interest as an emergent class of quantum metamaterials. In this paper, we report the observation of nonlocal transport in bilayer graphene (BLG) superlattices encapsulated between two hexagonal boron nitride (hBN) layers, which formed hBN/BLG/hBN moiré superlattices. We then employed these superlattices to detect a long-range charge-neutral valley current using an all-electrical method. The moiré superlattice with broken inversion symmetry leads to a hot spot with Berry curvature accumulating at the charge neutral point (CNP), and it…
Diffusion currents are theoretically examined in two-dimensional Dirac materials, such as those of the transition metal dichalcogenides (TMD) family. The transversal effects are analogues of the valley Hall (VHE) and photogalvanic (PGE) transport phenomena in case when the electron driving force is not an electric field but a gradient of electron density distribution in the sample. The latter can be created by a finite-sized laser spot or by the injection of electrons from other materials. We develop the theory of diffusive VHE effect assuming the anisotropic electron-short-range-impurity skew…
We report on the experimental observation of topologically protected edge waves in a two-dimensional elastic hexagonal lattice. The lattice is designed to feature K point Dirac cones that are well separated from the other numerous elastic wave modes characterizing this continuous structure. We exploit the arrangement of localized masses at the nodes to break mirror symmetry at the unit cell level, which opens a frequency bandgap. This produces a non-trivial band structure that supports topologically protected edge states along the interface between two realizations of the lattice obtained thro…
We perform both lattice dynamics analysis and molecular dynamics simulations to demonstrate the existence of topologically protected phonon modes in a two-dimensional, monolayer hexagonal boron nitride sheet. The topological phonon modes are found to be localized at an in-plane interface that divides the system into two regions of distinct valley Chern numbers. The dispersion of this topological phonon mode crosses over the frequency gap [1123, 1278] cm^{-1}, which is opened through analogy with the quantum valley Hall effect by breaking inversion symmetry of the boron and nitride atoms in the…
We show that inversion symmetry breaking together with spin-orbit coupling leads to coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides, making possible controls of spin and valley in these 2D materials. The spin-valley coupling at the valence band edges suppresses spin and valley relaxation, as flip of each index alone is forbidden by the valley contrasting spin splitting. Valley Hall and spin Hall effects coexist in both electron-doped and hole-doped systems. Optical interband transitions have frequency-dependent polarization selection rules which allow s…
We investigate van der Waals (vdW) heterostructures made of germanene, stanene or silicene with hexagonal Boron Nitride (h-BN). The intriguing topological properties of these buckled honeycomb materials can be maintained and further engineered in the heterostructures, where the competition between the substrate effect and external electric fields can be used to control the tunable topological phase transitions. Using such heterostructures as building blocks, various vdW topological domain walls (DW) are designed, along which there exist valley polarized quantum spin Hall edge states or valley-…
The concept of ferrovalley materials has been proposed very recently. The existence of spontaneous valley polarization, resulting from ferromagnetism, in such hexagonal two-dimensional 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 va…
So far, selective excitation of a desired valley in the Brillouin zone of a hexagonal two-dimensional material has relied on using circularly polarized fields. We theoretically demonstrate a way to induce, control, and read valley polarization in hexagonal 2D materials on a few-femtosecond timescale using a few-cycle, linearly polarized pulse with controlled carrier-envelope phase. The valley pseudospin is encoded in the helicity of the emitted high harmonics of the driving pulse, allowing one to avoid additional probe pulses and permitting one to induce, manipulate and read the valley pseudos…
The recent observation [R. V. Gorbachev et al., Science {\bf 346}, 448 (2014)] of nonlocal resistance $R_\mathrm{NL}$ near the Dirac point (DP) of multiterminal graphene on aligned hexagonal boron nitride (G/hBN) has been interpreted as the consequence of topological valley Hall currents carried by the Fermi sea states just beneath the bulk gap $E_g$ induced by the inversion symmetry breaking. However, the valley Hall conductivity $σ^v_{xy}$, quantized inside $E_g$, is not directly measurable. Conversely, the Landauer-Büttiker formula, as numerically exact approach to observable nonlocal trans…
We report on the design and experimental validation of a two-dimensional phononic elastic waveguide exhibiting topological Valley-Hall edge states. The lattice structure of the waveguide is inspired by the diatomic graphene and it is imprinted in an initially flat plate by means of geometric indentations. The indentations are distributed according to a hexagonal lattice structure which guarantees the existence of Dirac dispersion at the boundary of the Brillouin zone. Starting from this basic material, domain walls capable of supporting edge states can be obtained by contrasting waveguides hav…
This is a numerical study of the conductance of an Aharonov-Bohm interferometer in a tight-binding model of graphene. Two single-mode ballistic point contacts with zigzag edges are connected by two arms of a hexagonal ring enclosing a magnetic flux $Φ$. The point contacts function as valley filters, transmitting electrons from one valley of the band structure and reflecting electrons from the other valley. We find, in the wider rings, that the magnetoconductance oscillations with the fundamental periodicity $ΔΦ=h/e$ are suppressed when the two valley filters have opposite polarity, while the s…
We investigate the anomalous effects due to the Berry correction and the considerable perturbations in the silicene-like hexagonal lattice system. The Berry curvature in periodic Bloch band system which related to the electromagnetic field is explored, the induced transverse anomalous velocity gives rise to the intrinsic Hall conductivity (without the vertex correction) expecially in the quantum anomalous Hall phase. The quantum anomalous Hall effect which related to the anomalous velocity term is detected, including the band avoided corssing effect and the generated special band gap. %{Enlarg…
Rhombohedral $N = 3$ trilayer graphene on hexagonal boron nitride (TLG/BN) hosts gate-tunable, valley-contrasting, nearly flat topological bands that can trigger spontaneous quantum Hall phases under appropriate conditions of the valley and spin polarization. Recent experiments have shown signatures of C = 2 valley Chern bands at 1/4 hole filling, in contrast to the predicted value of C = 3. We discuss the low-energy model for rhombohedral N-layer graphene (N = 1, 2, 3) aligned with hexagonal boron nitride (hBN) subject to off-diagonal moire vector potential terms that can alter the valley Che…
Effects of antidot lattices on electronic structures of graphene and hexagonal BN (h-BN) are investigated using the first principles method based on density functional theory. For graphene, we find that when the antidot lattice is along the zigzag direction, the band gap opening can be related to the inter-valley scattering, and does not follow the simple scaling rule previously proposed in literature for the antidot lattice along the armchair direction. For h-BN, our calculations show that the antidot lattice results in reducing of band gaps. Coupled with doping of carbon atoms, the band gap …
We investigate with polarized microphotoluminescence the optical pumping of the valley degree of freedom in charge-tunable MoS2 monolayers encapsulated with hexagonal boron nitride at cryogenic temperatures. We report a large steady state valley polarization of the different excitonic complexes following circularly-polarized laser excitation 25 meV above the neutral exciton transition. For the first time in this material we reveal efficient valley pumping of positively-charged trions, which were so far elusive in non-encapsulated monolayers due to defect and laser-induced large electron doping…
We report experimental observation of 2s exciton radiative emission from monolayer tungsten diselenide, enabled by hexagonal boron nitride protected high-quality samples. The 2s luminescence is highly robust and persists up to 150K, offering a new quantum entity for manipulating the valley degree of freedom. Remarkably, the 2s exciton displays superior valley polarization and coherence than 1s under similar experimental conditions. This observation provides evidence that the Coulomb-exchange-interaction-driven valley-depolarization process, the Maialle-Silva-Sham mechanism, plays an important …
The coupling between spin, charge, and lattice degrees of freedom plays an important role in a wide range of fundamental phenomena. Monolayer semiconducting transitional metal dichalcogenides have emerged as an outstanding platform for studying these coupling effects because they possess unique spin-valley locking physics for hosting rich excitonic species and the reduced screening for strong Coulomb interactions. Here, we report the observation of multiple valley phonons, phonons with momentum vectors pointing to the corners of the hexagonal Brillouin zone, and the resulting exciton complexes…
Using time-resolved optical Kerr rotation, we measure the low temperature valley dynamics of resident electrons and holes in exfoliated WSe$_2$ monolayers as a systematic function of carrier density. In an effort to reconcile the many disparate timescales of carrier valley dynamics in monolayer semiconductors reported to date, we directly compare the doping-dependent valley relaxation in two electrostatically-gated WSe$_2$ monolayers having different dielectric environments. In a fully-encapsulated structure (hBN/WSe$_2$/hBN, where hBN is hexagonal boron nitride), valley relaxation is found to…
The exciton valley dynamics in van der Waals heterostructures with transition metal dichalcogenides monolayers is driven by the long-range exchange interaction between the electron and the hole in the exciton. It couples the states active in the opposite circular polarizations resulting in the longitudinal-transverse splitting of excitons propagating in the monolayer plane. Here we study theoretically the effect of the dielectric environment on the long-range exchange interaction and demonstrate how the encapsulation in the hexagonal boron nitride modifies the exciton longitudinal-transverse s…
In this paper, we study topological phases in a 2D photonic crystal with broken time ($\mathcal{T}$) and parity ($\mathcal{P}$) symmetries by performing calculations of band structures, Berry curvatures, Chern numbers, edge states and also numerical simulations of light propagation in the edge modes. Specifically, we consider a hexagonal lattice consisting of triangular gyromagnetic rods. Here the gyromagnetic material breaks $\mathcal{T}$ symmetry while the triangular rods breaks $\mathcal{P}$ symmetry. Interestingly, we find that the crystal could host quantum anomalous Hall (QAH) phases wit…
The coupled light-matter modes supported by plasmonic metasurfaces can be combined with topological principles to yield subwavelength topological valley states of light. We give a systematic presentation of the topological valley states available for lattices of metallic nanoparticles: All possible lattices with hexagonal symmetry are considered, as well as valley states emerging on a square lattice. Several unique effects which have yet to be explored in plasmonics are identified, such as robust guiding, filtering and splitting of modes, as well as dual-band effects. We demonstrate these by m…
We report on scattering induced valley polarization enhancement in monolayer molybdenum disulfide. With thermally activated and charge doping introduced scattering, our sample exhibits seven? and twelve-folds of improvements respectively. This counter-intuitive effect is attributed to disruptions to valley pseudospin precession caused by rapid modulation of exciton momentum and concomitant local exchange interaction field, at time scales much shorter than the precession period. In contrast, the valley coherence is improved by thermally activated scattering, but not by charge doping induced sca…
We explore the transport properties of a periodically modulated $α$-$\mathcal{T}_3$ lattice in the presence of a perpendicular magnetic field. The effect of the Berry phase on electrical conductivity oscillation, so-called Weiss oscillation, caused by the modulation induced non-zero drift velocity of charge carriers is investigated. Employing linear response theory within the low temperature regime, we analyze Weiss oscillation as a function of the external magnetic field for both electrically and magnetically modulated $α$-$\mathcal{T}_3$ lattice numerically as well as analytically. The Berry…
Monolayers of semiconducting transition metal dichalcogenides are two-dimensional direct-gap systems which host tightly-bound excitons with an internal degree of freedom corresponding to the valley of the constituting carriers. Strong spin-orbit interaction and the resulting ordering of the spin-split subbands in the valence and conduction bands makes the lowest-lying excitons in WX$_2$ (X~being S or Se) spin-forbidden and optically dark. With polarization-resolved photoluminescence experiments performed on a WSe$_2$ monolayer encapsulated in a hexagonal boron nitride, we show how the intrinsi…
Embedding a WS$_2$ monolayer in flakes of hexagonal boron nitride allowed us to resolve and study the photoluminescence response due to both singlet and triplet states of negatively charged excitons (trions) in this atomically thin semiconductor. The energy separation between the singlet and triplet states has been found to be relatively small reflecting rather weak effects of the electron-electron exchange interaction for the trion triplet in a WS$_2$ monolayer, which involves two electrons with the same spin but from different valleys. Polarization-resolved experiments demonstrate that the h…
Exotic correlated insulating phases emerge in the ABC-stacked trilayer graphene-boron nitride Moire super-lattice at both quarter and half-filling. A single-band minimal model with valley contrasting staggered-flux is proposed to capture the relevant band structure, where the conspiracy of perfect Fermi-surface nesting and van Hove singularity strongly enhance the valley fluctuation, leading to inter-valley spiral (IVS) order at half filling. In this paper, we consider a strong coupling U(1)$_{v}\times $SU(2)$_{s}$ symmetric spin-valley model to obtain the correlated insulating state and the p…
The magnetically-induced valley-spin filtering in transition metal dichalcogenide monolayers ($MX_{2}$, where $M$=Mo, W and $X$=S, Se, Te) promises new paradigm in information processing. However, the detailed understanding of this effect is still limited, regarding its underlying transport processes. Herein, it is suggested that the filtering mechanism can be greately elucidated by the concept of metal-induced gap states (MIGS), appearing in the electrode-terminated $MX_{2}$ materials {\it i.e.} the referential filter setup. In particular, the gap states are predicted here to mediate valley- …
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…
