Trion Valley Coherence in Monolayer Semiconductors

Abstract

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 recombination lifetime, its robust valley polarization, and its coupling to residual electronic spin. Trion valley coherence has however been unexplored due to experimental challenges in accessing it spectroscopically. In this work, we employ ultrafast two-dimensional coherent spectroscopy to resonantly generate and detect trion valley coherence in monolayer MoSe₂ demonstrating that it persists for a few-hundred femtoseconds. We conclude that the underlying mechanisms limiting trion valley coherence are fundamentally different from those applicable to exciton valley coherence.

Keywords: transition-metal dichalcogenides; trions; two-dimensional coherent spectroscopy; valley coherence.

Figure 1. Trion valley coherence in monolayer MoSe₂

(a) Valley polarization and coherence are represented by a pseudospin vector on the Bloch sphere oriented along the north/south poles and in the equatorial plane, respectively. (b) Linearly polarized optical excitation can generate trion valley coherence between the lowest-energy negative trion states in MoSe₂. (c) Electron-hole recombination leads to a spin-photon entangled state due to the opposite residual electronic spins, preventing detection of the trion valley coherence in photoluminescence.

Figure 2. Resonant generation and detection of trion valley coherence

(a) Image of the MoSe₂ monolayer. The low temperature photoluminescence spectrum features trion and exciton emission at ~1620 meV and ~1650 meV, respectively. (b) Three pulses with variable delays and polarizations interact with the sample to generate a nonlinear four-wave mixing signal. (c) Cross-circularly polarized excitation and detection, in which the first and third (second and signal) pulses are left- (right-) circularly polarized. The quantum pathway corresponding to the generation, evolution, and detection of trion valley coherence is illustrated by the three-level energy diagram in the interaction picture.

Figure 3. Inter-valley coherence and valley polarization dynamics

(a) Optical 2DCS zero-quantum spectrum acquired using the cross-circular polarization scheme. Two peaks are present at the emission energies of the exciton (X) and trion (T), respectively. (b)–(c) The half-width at half-maximum of Lorentzian fit functions (solid lines) to the lineshapes along the zero-quantum axis ħω₂ yields the valley decoherence rate γ_ν (valley coherence time τ_ν = ħ/γ_ν), equal to ${\gamma }_{\nu }^T=2.9\text{meV}({\tau }_{\nu }^T=230\text{fs})$ and ${\gamma }_{\nu }^X=4.8\text{meV}({\tau }_{\nu }^X=140\text{fs})$ for the trion and exciton, respectively. Valley polarization dynamics for the (d) trion and (e) exciton obtained from one-quantum spectra acquired for co- and cross-circular polarization. (f) Bi-exponential fits to the amplitudes in (d) and (e) are used to determine the degree of circular polarization versus t₂.

Figure 4. Interband optical coherence dynamics

(a) Optical 2DCS one-quantum spectrum acquired using co-circular polarization. The peaks on the diagonal line correspond to excitation and emission at the exciton and trion resonances. (b) The resonance lineshapes along the cross-diagonal direction are fit with Lorentzian functions to obtain the homogeneous linewidth (coherence time) ${\gamma }^T=1.3\text{meV}(T_2^T=510\text{fs})$ and ${\gamma }^X=1.4\text{meV}(T_2^X=470\text{fs})$ for the trion and exciton, respectively.