Anomalously robust valley polarization and valley coherence in bilayer WS ₂

Abstract

We report the observation of anomalously robust valley polarization and valley coherence in bilayer WS 2 . The polarization of the photoluminescence from bilayer WS 2 follows that of the excitation source with both circular and linear polarization, and remains even at room temperature. The near-unity circular polarization of the luminescence reveals the coupling of spin, layer, and valley degree of freedom in bilayer system, and the linearly polarized photoluminescence manifests quantum coherence between the two inequivalent band extrema in momentum space, namely, the valley quantum coherence in atomically thin bilayer WS 2 . This observation provides insight into quantum manipulation in atomically thin semiconductors.valleytronics | spin-valley coupling | valley quantum control T ungsten sulfide WS 2 , part of the family of group VI transition metal dichalcogenides (TMDCs), is a layered compound with buckled hexagonal lattice. As WS 2 thins to atomically thin layers, WS 2 films undergo a transition from indirect gap in bulk form to direct gap at monolayer level with the band edge located at energy-degenerate valleys (K, K′) at the corners of the Brillouin zone (1-3). Like the case of its sister compound, monolayer MoS 2 , the valley degree of freedom of monolayer WS 2 could be presumably addressed through nonzero but contrasting Berry curvatures and orbital magnetic moments that arise from the lack of spatial inversion symmetry at monolayers (3, 4). The valley polarization could be realized by the control of the polarization of optical field through valley-selective interband optical selection rules at K and K′ valleys as illustrated in Fig. 1A (4-6). In monolayer WS 2 , both the top of the valence bands and the bottom of the conduction bands are constructed primarily by the d orbits of tungsten atoms, which are remarkably shaped by spin-orbit coupling (SOC). The giant spin-orbit coupling splits the valence bands around the K (K′) valley by 0.4 eV, and the conduction band is nearly spin degenerated (7). As a result of time-reversal symmetry, the spin splitting has opposite signs at the K and K′ valleys. Namely, the Kramer's doublet jK↑i and jK′↓i is separated from the other doublet jK′↑i and jK↓i by the SOC splitting of 0.4 eV. The spin and valley are strongly coupled at K (K′) valleys, and this coupling significantly suppresses spin and valley relaxations as both spin and valley indices have to be changed simultaneously.In addition to the spin and valley degrees of freedom, in bilayer WS 2 there exists an extra index: layer polarization that indicates the carriers' location, either up-layer or down-layer. Bilayer WS 2 follows the Bernal packing order and the spatial inversion symmetry is recovered: each layer is 180°in plane rotation of the other with the tungsten atoms of a given layer sitting exactly on top of the S atoms of the other layer. The layer rotation symmetry switches K and K′ valleys, but leaves the spin unchanged, which results in a sign change for the spin-valley coupling from layer to layer (Fi...

Excitons in atomically thin transition-metal dichalcogenides

“…(Cao et al, 2012;Xiao et al, 2012), optical valley initialization is based on chiral selection rules for interband transitions: σ + polarized excitation results in the inter-band transitions in the K + valley, and, correspondingly, σ − polarized excitation results in transitions in the K − valley. Initial experimental confirmation of this effect was reported in steady-state PL measurements in MoS 2 monolayers (Cao et al, 2012;Mak et al, 2012;Sallen et al, 2012;Zeng et al, 2012), as well as in WSe 2 and WS 2 systems Kim et al, 2014;Mai et al, 2014b;Sie et al, 2015b;Wang et al, 2014;Zhu et al, 2014a). The overall degree of polarization has been shown to reach almost unity.…”

Manipulating spin-polarized photocurrents in 2D transition metal dichalcogenides

“…Given that the effective bias added on the channel is on the order of V ds − ðE g + E exciton binding Þ ∼ 2.5 eV where we assume the band bending at both contacts is roughly of the electronic band gap at most and the mobility of 0.1-1 cm 2 · v=s of the devices (SI Appendix), the spin-free path indicates the estimated spin-valley lifetime around 10 1 ∼10 2 ns. This estimate is orders of magnitude larger than the valley lifetime estimated from polarization-resolved photoluminescence and pump-probe spectroscopy in which the exciton effect predominates the optical properties and consequently the valley lifetime of excitons instead of free carriers is probed (37,38). Note that the electron-hole exchange interaction provides the major channel for excitons' spinvalley depolarization (39), whereas the exchange interactions are greatly suppressed in oppositely drifting free carriers in a nearly intrinsic state, and consequently the free carriers presumably show significantly longer spin-valley lifetime.…”

Interlayer coupling in commensurate and incommensurate bilayer structures of transition-metal dichalcogenides

“…The resulted spin-layer locking could lead to various magnetoelectric effects allowing for their quantum manipulations. [6][7][8][9][10][11] On the other hand, the interlayer couplings in the valence band Γ and conduction band Q valleys are significantly larger, which strongly shifts their energy positions compared to those of the monolayers and results in a transition from direct to indirect band gap.…”