Generation and evolution of spin-, valley- and layer-polarized excited carriers in inversion-symmetric WSe2
Roman Bertoni, Christopher W. Nicholson, Lutz Waldecker, Hannes Hübener, Claude Monney, Umberto De Giovannini, Michele Puppin, Moritz Hoesch, Emma Springate, Ri… 展开作者
Roman Bertoni, Christopher W. Nicholson, Lutz Waldecker, Hannes Hübener, Claude Monney, Umberto De Giovannini, Michele Puppin, Moritz Hoesch, Emma Springate, Richard T. Chapman, Cephise Cacho, Martin Wolf, Angel Rubio, Ralph Ernstorfer
Manipulation of spin and valley degrees of freedom is a key step towards realizing novel quantum technologies, for which atomically thin transition metal dichalcogenides (TMDCs) have been established as promising candidates. In monolayer TMDCs, the lack of inversion symmetry gives rise to a spin-valley correlation of the band structure allowing for valley-selective electronic excitation with circularly polarized light. Here we show that, even in centrosymmetric samples of 2H-WSe2, circularly polarized light can generate spin-, valley- and layer-polarized excited states in the conduction band. Employing time- and angle-resolved photoemission spectroscopy (trARPES) with spin-selective excitation, the dynamics of valley and layer pseudospins of the excited carriers are investigated. Complementary time-dependent density functional theory (TDDFT) calculations of the excited state populations reveal a strong circular dichroism of the spin-, valley- and layer-polarizations and a pronounced 2D character of the excited states in the K valleys. We observe scattering of carriers towards the global minimum of the conduction band on a sub-100 femtosecond timescale to states with three-dimensional character facilitating inter-layer charge transfer. Our results establish the optical control of coupled spin-, valley- and layer-polarized states in centrosymmetric materials and suggest the suitability of TMDC multilayer materials for valleytronic and spintronic device concepts.
It is quite easy to control spin polarization and spin direction of a system via magnetic fields. However, there is no such a direct and efficient way to manipulate valley pseudospin degree of freedom. Here, we demonstrate experimentally that it is possible to realize valley polarization and valley inversion in graphene by using both strain-induced pseudomagnetic fields and real magnetic fields. The pseudomagnetic fields, which are quite different from real magnetic fields, pointing in opposite directions at the two distinct valleys of graphene. Therefore, coexistence of the pseudomagnetic fie…
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…
Inversion symmetry breaking allows contrasted circular dichroism in different k-space regions, which takes the extreme form of optical selection rules for interband transitions at high symmetry points. In materials where band-edges occur at noncentral valleys, this enables valley dependent interplay of electrons with light of different circular polarizations, in analogy to spin dependent optical activities in semiconductors. This discovery is in perfect harmony with the previous finding of valley contrasted Bloch band features of orbital magnetic moment and Berry curvatures from inversion symm…
We report on nanosecond long, gate-dependent valley lifetimes of free charge carriers in monolayer WSe$_2$, unambiguously identified by the combination of time-resolved Kerr rotation and electrical transport measurements. While the valley polarization increases when tuning the Fermi level into the conduction or valence band, there is a strong decrease of the respective valley lifetime consistent with both electron-phonon and spin-orbit scattering. The longest lifetimes are seen for spin-polarized bound excitons in the band gap region. We explain our findings via two distinct, Fermi level-depen…
We show room temperature valley coherence with in MoS2, MoSe2, WS2 and WSe2 monolayers using linear polarization resolved hot photoluminescence (PL), at energies close to the excitation - demonstrating preservation of valley coherence before sufficient scattering events. The features of the co-polarized hot luminescence allow us to extract the lower bound of the binding energy of the A exciton in monolayer MoS2 as 0.42 (+/- 0.02) eV. The broadening of the PL peak is found to be dominated by Boltzmann-type hot luminescence tail, and using the slope of the exponential decay, the carrier temperat…
The two dimensional layered transition metal dichalcogenides provide new opportunities in future valley based information processing and also provide ideal platform to study excitonic effects. At the center of various device physics toward their possible electronic and optoelectronic applications is understanding the dynamical evolution of various many particle electronic states, especially exciton which dominates the optoelectronic response of TMDs, under the novel context of valley degree of freedom. Here, we provide a brief review of experimental advances in using helicity resolved ultrafas…
Using time-resolved Kerr rotation, we measure the spin/valley dynamics of resident electrons and holes in single charge-tunable monolayers of the archetypal transition-metal dichalcogenide (TMD) semiconductor WSe2. In the n-type regime, we observe long (70 ns) polarization relaxation of electrons that is sensitive to in-plane magnetic fields $B_y$, indicating spin relaxation. In marked contrast, extraordinarily long (2 microsecond) polarization relaxation of holes is revealed in the p-type regime, that is unaffected by $B_y$, directly confirming long-standing expectations of strong spin-valley…
We report magneto-absorption spectroscopy of gated WSe$_2$ monolayers in high magnetic fields up to 60~T. When doped with a 2D Fermi sea of mobile holes, well-resolved sequences of optical transitions are observed in both $σ^\pm$ circular polarizations, which unambiguously and separately indicate the number of filled Landau levels (LLs) in both $K$ and $K'$ valleys. This reveals the interaction-enhanced valley Zeeman energy, which is found to be highly tunable with hole density $p$. We exploit this tunability to align the LLs in $K$ and $K'$, and find that the 2D hole gas becomes unstable agai…
Monolayer transition metal dichalcogenids (TMDs) feature valley degree of freedom, giant spin-orbit coupling and spin-valley locking. These exotic natures stimulate efforts of exploring the potential applications in conceptual spintronics, valleytronics and quantum computing. Among all the exotic directions, a long lifetime of spin and/or valley polarization is critical. The present valley dynamics studies concentrate on the band edge excitons which predominates the optical response due to the enhanced Coulomb interaction in two dimensions. The valley lifetime of free carriers remains in ambig…
In this Letter, a tunable valley polarization is investigated for honeycomb systems with broken inversion symmetry such as transition-metal dichalcogenide MX2 (M = Mo, W; X = S, Se) monolayers through elliptical pumping. As compared to circular pumping, elliptical pumping is more universal and effective method to create coherent valley polarization. When two valleys of MX2 monolayers are doped or polarized, a novel anomalous valley orbital magnetic moment Hall effect driven by opposite Berry curvatures at different valleys is predicted and can generate orbital magnetic moment current without t…
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…
Atomistic sp3d5s* tight-binding theory of PbSe and PbS nanocrystals is developed. It is demonstrated, that the valley splittings of confined electrons and holes strongly and peculiarly depend on the geometry of a nanocrystal. When the nanocrystal lacks a microscopic center of inversion and has T_d symmetry, the splitting is strongly suppressed as compared to the more symmetric nanocrystals with O_h symmetry, having an inversion center.
Electronic and spintronic devices rely on the fact that free charge carriers in solids carry electric charge and spin, respectively. There are, however, other properties of charge carriers that might be exploited in new families of devices. In particular, if there are two or more conduction (or valence) band extrema in momentum space, then confining charge carriers in one of these valleys allows the possibility of valleytronic devices. Such valley polarization has been demonstrated by using strain and magnetic fields, but neither of these approaches allow for dynamic control. Recently, optical…
In a multilayer comprising ferromagnet and heavy metal, in-plane carrier spin is induced by applied electric current owing to Rashba spin-orbit coupling, while the out-of-plane component is absent. We propose the out-of-plane carrier spin can emerge in ferromagnetic transition-metal dichalcogenides monolayer, by symmetry arguments and first-principles calculations. An intrinsic spin-orbit coupling in the monolayer provides valley-contrasting Zeeman-type spin splitting for generating the vertical induced spin. The current direction can be exploited to tune the induced spin, accompanied with val…
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…
We report the finding of the analogous valley Hall effect in phononic systems arising from mirror symmetry breaking, in addition to spatial inversion symmetry breaking. We study topological phases of plates and spring-mass models in Kagome and modified Kagome arrangements. By breaking the inversion symmetry it is well known that a defined valley Chern number arises. We also show that effectively, breaking the mirror symmetry leads to the same topological invariant. Based on the bulk-edge correspondence principle, protected edge states appear at interfaces between two lattices of different vall…
We study topological states of honeycomb photonic crystals in absence of inversion symmetry using plane wave expansion and finite element methods. The breaking of inversion symmetry in honeycomb lattice leads to contrasting topological valley indices, i.e., the valley-dependent Chern numbers in momentum space. We find that the topological corner states appear for 60$^\circ$ degree corners, but absent for other corners, which can be understood as the sign flip of valley Chern number at the corner. Our results provide an experimentally feasible platform for exploring valley-dependent higher-orde…
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…
The interplay of massive electrons with spin-orbit coupling in bulk graphene results in a spin-valley dependent gap. Thus, a barrier with such properties can act as a filter, transmitting only opposite spins from opposite valleys. In this Letter we show that strain induced pseudomagnetic field in such a barrier will enforce opposite cyclotron trajectories for the filtered valleys, leading to their spatial separation. Since spin is coupled to the valley in the filtered states, this also leads to spin separation, demonstrating a spin-valley filtering effect. The filtering behavior is found to be…
2D materials with valley-related multiple Hall effect are both fundamentally intriguing and practically appealing to explore novel phenomena and applications, but have been largely overlooked up to date. Here, using first-principles calculations, we present that valley related multiple Hall effect can exist in single-layer VSi2P4. We identify single-layer VSi2P4 as a ferromagnetic semiconductor with out-of-plane magnetization and valley physics. Arising from the joint effect of inversion symmetry breaking and time reversal symmetry breaking, the exotic spontaneous valley polarization occurs in…
We address the ballistic transmission of charge carriers across ordered line defects in monolayer transition metal dichalcogenides. Our study reveals the presence of a transport gap driven by spin-orbit interactions, spin and valley filtering, both stemming from a simple picture of spin and momentum conservation, as well as the electron-hole asymmetry of charge-carrier transmission. Electronic transport properties of experimentally observed ordered line defects in monolayer MoS$_2$, in particular, the vacancy lines and inversion domain boundaries, are further investigated using first-principle…
We report novel manifestation of the valley splitting for the two valley electron system in (100) Si-inversion layers at low carrier density. We found that valley splitting causes almost 100% modulation of the Shubnikov de Haas oscillations in very low magnetic fields, almost on the bound of the quantum interference peak of the negative magnetoresistance. From the interference pattern of oscillations we determined the valley splitting in the B=0 limit which appears to vary only within a factor of 1.3 over the density range (3-7)x10^{11}/cm^2. We found also that level broadenings in both electr…
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…
Valley filters are crucial to any device exploiting the valley degree of freedom. By using an atomistic model, we analyze the mechanism leading to the valley filtering produced by a line-defect in graphene and show how it can be inverted by external means. Thanks to a mode decomposition applied to a tight-binding model we can resolve the different transport channels in k-space while keeping a simple but accurate description of the band structure, both close and further away from the Dirac point. This allows the understanding of a destructive interference effect (Fano resonance or antiresonance…
In single-layer WSe$_2$, a paradigmatic semiconducting transition metal dichalcogenide, a circularly polarized laser field can selectively excite electronic transitions in one of the inequivalent $K^{\pm}$ valleys. Such selective valley population corresponds to a pseudospin polarization. This can be used as a degree of freedom in a valleytronic device provided that the time scale for its depolarization is sufficiently large. Yet, the mechanism behind the valley depolarization still remains heavily debated. Recent time-dependent Kerr experiments have provided an accurate way to visualize the v…
Valley currents and non-local resistances of graphene nanostructures with broken inversion symmetry are considered theoretically in the linear response regime. Scattering state wave functions of electrons entering the nanostructure from the contacts represented by groups of ideal leads are calculated by solving the Lippmann- Schwinger equation and are projected onto the valley state subspaces to obtain the valley velocity fields and total valley currents in the nanostructures. In the tunneling regime when the Fermi energy is in the spectral gap around the Dirac point energy, inversion symmetry…
The semiconducting single-layer transition metal dichalcogenides have been identified as ideal materials for accessing and manipulating spin- and valley-quantum numbers due to a set of favorable optical selection rules in these materials. Here, we apply time- and angle-resolved photoemission spectroscopy to directly probe optically excited free carriers in the electronic band structure of a high quality single layer of WS$_2$. We observe that the optically generated free hole density in a single valley can be increased by a factor of 2 using a circularly polarized optical excitation. Moreover,…
Valley polarization in graphene breaks inversion symmetry and therefore leads to second-harmonic generation. We present a complete theory of this effect within a single-particle approximation. It is shown that this may be a sensitive tool to measure the valley polarization created, e.g., by polarized light and, thus, can be used for a development of ultrafast valleytronics in graphene.
The use of relative twist angle between adjacent atomic layers in a van der Waals heterostructure, has emerged as a new degree of freedom to tune electronic and optoelectronic properties of devices based on 2D materials. Using ABA-stacked trilayer (TLG) graphene as the model system, we show that, contrary to conventional wisdom, the band structures of 2D materials are systematically tunable depending on their relative alignment angle between hexagonal BN (hBN), even at very large twist angles. Moreover, addition or removal of the hBN substrate results in an inversion of the K and K' valley in …
Motivated by interesting recent experimental results, we consider theoretically charged-impurity scattering-limited 2D electronic transport in (100), (110), and (111)-Si inversion layers at low temperatures and carrier densities, where screening effects are important. We show conclusively that, given the same bare Coulomb disorder, the 2D mobility for a given system increases monotonically with increasing valley degeneracy. We also show that the temperature and the parallel magnetic field dependence of the 2D conductivity is strongly enhanced by increasing valley degeneracy. We analytically co…
The Fermi surface of elemental bismuth consists of three small rotationally equivalent electron pockets, offering a valley degree of freedom to charge carriers. A relatively small magnetic field can confine electrons to their lowest Landau level. This is the quantum limit attained in other dilute metals upon application of sufficiently strong magnetic field. Here, we report on the observation of another threshold magnetic field never encountered before in any other solid. Above this field, $B_{\rm{empty}}$, one or two valleys become totally empty. Drying up a Fermi sea by magnetic field in the…
The coupled spin and valley degrees of freedom in transition metal dichalcogenides (TMDs) are considered a promising platform for information processing. Here, we use a TMD heterostructure ${\text{MoS}_{2}-\text{MoSe}_{2}}$ to study optical pumping of spin/valley polarized carriers across the interface and to elucidate the mechanisms governing their subsequent relaxation. By applying time-resolved Kerr and reflectivity spectroscopies, we find that the photoexcited carriers conserve their spin for both tunneling directions across the interface. Following this, we measure dramatically different …
Atomically thin transition metal dichalcogenides (TMDs) possess coupling of spin and valley degrees of freedom, making them promising for spin-valleytronics. ln monolayer TMDs, the emission helicity is locked to the valleys as a consequence of spin-orbit coupling and inversion symmetry breaking, leading to a valley analog of Zeeman effect in presence of out-of-plane magnetic field. As inversion symmetry is recovered in bilayers, the emission helicity should no longer be locked to the valleys. Here we show that Zeeman splitting, however, still persists in bilayers, as a result of an additional …
A two-dimensional honeycomb lattice harbors a pair of inequivalent valleys in the k-space electronic structure, in the vicinities of the vertices of a hexagonal Brillouin zone, K}$_{\pm}$. It is particularly appealing to exploit this emergent degree of freedom of charge carriers, in what is termed "valleytronics", if charge carrier imbalance between the valleys can be achieved. The physics of valley polarization will make possible electronic devices such as valley filter and valley valve, and optoelectronic Hall devices, all very promising for next-generation electronic and optoelectronic appl…
Transconductance as a Probe of Valley Thermodynamics in Multilayer WSe$_2$
Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS)（物质·材料纳米结构研究センター（MANA），国立物質研究所（NIMS））；Department of Nanotechnology for Sustainable Energy, Kwansei Gakuin University（关西学院大学持続可能エネルギーナノテクノロジー学科）
An $\it{ab \,\, initio}$ based fully microscopic many-body approach is used to study the carrier relaxation dynamics in monolayer transition-metal dichalcogenides. Bandstructures and wavefunctions as well as phonon energies and coupling matrix elements are calculated using density functional theory. The resulting dipole and Coulomb matrix elements are implemented in the Dirac-Bloch equations to calculate carrier-carrier and carrier-phonon scatterings throughout the whole Brillouin zone. It is shown that carrier scatterings lead to a relaxation into hot quasi-Fermi distributions on a single fem…
We show that excitons and free carriers in K and K' valleys of transition metal dichalcogenide monolayers can be entangled with respect to their valley degree of freedom by absorbing linearly polarized single photons. This effect does not require any interaction between K and K' excitons in contrast to conventional mechanisms of entanglement that are mediated by coupling between quantum systems (e.g.~entanglement of photons in nonlinear optical interactions). The valley entanglement of excitons and free carriers can be verified by measuring the polarization of their photoluminescence or fluctu…
We investigated the valley depolarization and carrier relaxation process of monolayer and bilayer WS2 at 10 K by using time-resolved Kerr rotation (TRKR) and differential reflectance measurement simultaneously. Two decay processes extracted from TRKR signals were observed on both monolayer and bilayer WS2. In monolayer WS2, the initial ultrafast decay component (less than 1 ps) was interpreted as the stimulated emission or Pauli-blocking of electrons and holes in one valley by comparing with carrier decay process. The relatively slow component was around 4 ps under low excitation energy (less …
The valley degeneracy of electron states in graphene stimulates intensive research of valley-related optical and transport phenomena. While many proposals on how to manipulate valley states have been put forward, experimental access to the valley polarization in graphene is still a challenge. Here, we develop a theory of the second optical harmonic generation in graphene and show that this effect can be used to measure the degree and sign of the valley polarization. We show that, at the normal incidence of radiation, the second harmonic generation stems from imbalance of carrier populations in…
This paper presents a mathematical and numerical analysis of the flatband wavefunctions occurring in the chiral model of twisted bilayer graphene at the "magic" twist angles. We show that the chiral model possesses an exact intra-valley inversion symmetry. Writing the flatband wavefunction as a product of a lowest Landau level quantum Hall state and a spinor, we show that the components of the spinor are anti-quantum Hall wavefunctions related by the inversion symmetry operation introduced here. We then show numerically that as one moves from the lowest to higher magic angles, the spinor compo…
Graphene on hBN (G/hBN) has a long period moiré superstructure owing to the lattice mismatch between two materials. Long periodic potential caused by the moiré superstructure induces modulation of electronic properties of the system. In this paper, we numerically calculate optical conductivity of G/hBN under circularly polarized light irradiation. The lack of spatial inversion symmetry in G/hBN induces the valley polarization. In further, the valley polarization becomes most pronounced in the infrared and terahertz regions if the twist angle between two materials is close to zero for non-dopin…
Valley-selective optical selection rules and a spin-valley locking in transition-metal dichalcogenide (TMDC) monolayers are at the heart of "valleytronic physics", which exploits the valley degree of freedom and has been a major research topic in recent years. In contrast, valleytronic properties of TMDC bilayers have not been in the focus so much by now. Here, we report on the valleytronic properties and optical characterization of bilayers of WS2 as a representative TMDC material. In particular, we study the influence of the relative layer alignment in TMDC homo-bilayer samples on their pola…
An analogue of the Datta-Das spin FET is investigated, which is all-graphene and based on the valley degree of freedom of electrons / holes. The "valley FET" envisioned consists of a quantum wire of gapped graphene (channel) sandwiched between two armchair graphene nanoribbons (source and drain), with the following correspondence to the spin FET: valley (K and K') \leftrightarrow spin (up and down), armchair graphene nanoribbons \leftrightarrow ferromagnetic electrodes, graphene quantum wire \leftrightarrow semiconductor quantum wire, valley-orbit interaction \leftrightarrow Rashba spin-orbit …
Although single-layer transition-metal dichalcogenides with novel valley functionalities are promising candidate to realize valleytronic devices, the essential understanding of valley depolarization mechanisms is still incomplete. Based on pump-probe experiments performed for MoSe2 and WSe2 monolayers and corroborating analysis from density functional calculations, we demonstrate that coherent phonons at the K-point of the Brillouin zone can effectively mediate the valley transfer of electron carriers. In the MoSe2 monolayer case, we identify this mode as the flexural acoustic ZA(K) mode, whic…
We study a Josephson junction involving an inversion-asymmetric Weyl semimetal in presence of time-reversal symmetric (TRS) or time-reversal symmetry broken tilt in the Weyl spectra. We reveal that both types of tilts in the Weyl nodes lead to a Josephson $0$-$π$ transition and a zero bias valley/chiral supercurrent. Strikingly, the TRS tilt gives rise to a pure valley Josephson current (VJC) and TRS broken tilt induces a pure chirality Josephson current (CJC) in this system. The VJC and CJC are the manifestation of valley symmetry broken and $\mathbb{Z}_2$ symmetry broken by the respective ti…
We theoretically study transport signatures associated with a spontaneous 2-valley to 1-valley quantum phase transition in a two-dimensional electron gas (2DEG) tuned by decreasing the 2D carrier density, as claimed in a recent experiment [Phys. Rev. Lett. 127, 116601 (2021)]. The key issue we focus on is whether the experimentally measured 2D resistivity as a function of carrier density is consistent (or not) with an underlying spontaneous valley-polarization transition as assumed uncritically in the experimental report. Our theoretical analysis is particularly germane since the experiment do…
By means of density functional theory calculations, we predict that several two dimensional AB binary monolayers, where A and B atoms belong to group IV or III-V, are ferroelectric. Dipoles arise from the buckled structure, where the A and B ions are located on the sites of a bipartite corrugated honeycomb lattice with trigonal symmetry. We discuss the emerging valley-dependent properties and the coupling of spin and valley physics, which arise from the loss of inversion symmetry, and explore the interplay between ferroelectricity and Rashba spin-spitting phenomena. We show that valley-related…
