Long valley lifetime of dark excitons in single-layer WSe2

Abstract

Single-layer transition metal dichalcogenides provide a promising material system to explore the electron's valley degree of freedom as a quantum information carrier. The valley degree of freedom can be directly accessed by means of optical excitation. However, rapid valley relaxation of optically excited electron-hole pairs (excitons) through the exchange interaction has been a major roadblock. Theoretically such valley relaxation is suppressed in dark excitons, suggesting a potential route for long valley lifetimes. Here we develop a waveguide-based method to detect time-resolved and energy-resolved dark exciton emission in single-layer WSe₂, which involves spin-forbidden optical transitions with an out-of-plane dipole moment. The valley degree of freedom of dark excitons is accessed through the valley-dependent Zeeman effect under an out-of-plane magnetic field. We find a short valley lifetime for the dark neutral exciton, likely due to the short-range electron-hole exchange, but long valley lifetimes exceeding several nanoseconds for the dark charged excitons.

Fig. 1

Dark excitons in WSe₂ and experimental geometry. a, b Electronic configuration of a dark electron trion (a) and dark hole trion (b) in single-layer WSe₂. Blue and orange curves represent electronic bands with electron spin up and spin down, respectively. The hole spin is opposite to what’s shown for the electron spin. Dashed ellipses indicate the electron-hole pairs involved in the recombination. c Schematic side view of a dual-gated WSe₂ device on a GaSe waveguide. WSe₂ is excited by a focused light beam (red lightning symbol) and the resultant PL guided by the waveguide (red arrowed line) is detected. The IP and OP emission dipoles are selected by a half-wave plate (WP) and a polarizer (pol). WSe₂ is grounded. TG and BG are the top and bottom gate voltages, respectively. d Optical reflection and PL images (overlaid) of a typical device. Inner and outer white dashed lines show the boundary of WSe₂ and GaSe, respectively. The dotted white line, which is perpendicular to the edge, is referred to as the focal-edge line. The color bar represents the PL intensity.

Fig. 2

Resolving IP and OP dipoles by polarization. a Contour plot of the edge PL spectrum as a function of polarization direction for a hole-doped WSe₂ sample (both gates at −2.2 V). Dashed lines indicate the polarization corresponding to the OP and IP channels. b Comparison of the PL spectrum from the edge OP (black line) and IP (red line) channels and from the focal point (blue dotted line). The latter is rescaled to match the edge IP channel spectrum. c, d Contour plot of the edge PL spectrum as a function of gate voltage for the IP (c) and OP (d) channels. The IP channel is rescaled by a factor of 0.22 so that the PL intensity of the bright electron trion X^−,B in two channels have a comparable intensity. The two gates are set to the same voltage, which varies only the doping density in WSe₂ with symmetric top (TG) and bottom (BG) gates. The color bar represents the PL intensity in a, c, d. X^0,B, X^+,B, X^0,D, X^+,D and X^−,D denote the bright exciton, bright hole trion, dark exciton, dark hole trion and dark electron trion, respectively. The energy splitting between the bright and dark exciton (41 meV) in b agrees with the literature value^,.

Fig. 3

Resolving the valley degree of freedom of dark excitons by the Zeeman shift. a, b Contour plot of the PL spectrum of the OP channel as a function of magnetic field for a hole doped WSe₂ sample (both gates at −2.2 V). a is for the LCP excitation and b for the RCP excitation. The color bar represents the PL intensity. c–e PL spectra of the OP channel under RCP (black line) and LCP (red line) excitation. The out-of-plane field is about 8 T. The gate voltages −2.2 V (c), −0.5 V (d), and −1.75 V (e) correspond to a hole-doped, electron-doped, and neutral sample, respectively.

Fig. 4

Dark exciton valley dynamics. Time-resolved PL of the dark hole trion in a hole doped WSe₂ sample (both gates at −2.2 V) under a magnetic field of 8 T for the RCP (a) and LCP (b) excitation. Black and red symbols represent the PL of the Zeeman-split dark hole trion associated with the K′ and K valleys, respectively. The solid blue curves are the valley contrast $\mid \rho \left(t\right)\mid$ as defined in the main text. The dotted blue curves are a single-exponential fit, revealing a decay time constant of 32 ± 4 ns and 4.1 ± 0.2 ns, respectively, for the RCP and LCP excitation