Transport of indirect excitons and exciton mediated spin transport in a van der Waals heterostructure in magnetic fields

TL;DR

The study demonstrates long-range transport of indirect excitons and IX-mediated spin transport in a MoSe$_2$/WSe$_2$ van der Waals heterostructure under magnetic fields up to $8\, ext{T}$, with decay lengths $d_{1/e}$ and $d^{\rm s}_{1/e}$ reaching $\sim100\ \mu$m. Both transport channels exhibit a non-monotonic dependence on IX density, increasing and then decreasing as excitation power increases, and the spin transport length scales with the IX transport length, consistent with reduced scattering and spin-relaxation in the exciton fluid. The observed behavior aligns with Bose-Hubbard physics in a moiré superlattice, and the lack of strong magnetic-field suppression contrasts with GaAs-based systems, highlighting the distinct magnetoexciton dynamics in TMD heterostructures. These findings extend zero-field observations to finite magnetic fields and illuminate the potential for robust, long-range spin transport in two-dimensional vdW platforms. $d_{1/e}$ and $d^{\rm s}_{1/e}$ serve as key metrics for quantifying transport regimes in moiré-engineered exciton systems.

Abstract

We studied transport of indirect excitons (IXs) and IX mediated spin transport in a MoSe$_2$/WSe$_2$ van der Waals heterostructure in magnetic fields up to 8 T. We observed the long-range IX transport and the long-range IX mediated spin transport in the magnetic fields. The IX transport and spin transport are characterized by the 1/e decay distances reaching $\sim$ 100 micrometers. The decay distance of the spin transport correlates with the decay distance of IX transport. These decay distances first increase and then decrease with increasing IX density for all studied magnetic fields. The long-range IX transport and the long-range spin transport in the magnetic fields are consistent with the similar long-range transport in zero magnetic field.

Figures (5)

• Figure 1: IX transport in magnetic fields. (a,b) Normalized LE-IX luminescence profiles in magnetic field $B = 8$ T for laser excitation power $P_{\rm ex} = 500$, 100, 50, 10 $\mu$W (top to bottom) in (a) and $P_{\rm ex} = 500$, 2000, 5000 $\mu$W (top to bottom) in (b). The dashed line shows the DX luminescence profile in the MoSe$_2$ monolayer; this profile is close to the laser excitation profile for short-range DX transport. The $\sim 2~\mu$m laser spot is centered at $x = 0$. (c,d) The $1/e$ decay distance of IX transport $d_{1/e}$ vs. $P_{\rm ex}$ for magnetic field $B = 0$ (c) and 8 T (d). The $d_{1/e}$ values are obtained from least-squares fitting the LE-IX luminescence profiles to exponential decays in the region $x = 0 - 9$$\mu$m, from the excitation spot to the HS edge. The data with the fit indicating diverging $d_{1/e}$ are presented by circles on the edge.
• Figure 2: IX mediated spin transport in magnetic fields. (a,b) Normalized LE-IX spin density profiles $I_{\rm spin} = I_{\sigma^+} - I_{\sigma^-}$ in magnetic field $B = 8$ T for laser excitation power $P_{\rm ex} = 500$, 100, 50, 10 $\mu$W (top to bottom) in (a) and $P_{\rm ex} = 500$, 2000, 5000 $\mu$W (top to bottom) in (b). The dashed line shows the DX luminescence profile in the MoSe$_2$ monolayer; this profile is close to the laser excitation profile for short-range DX transport. The $\sim 2~\mu$m laser spot is centered at $x = 0$. (c,d) The $1/e$ decay distance of IX mediated spin density transport $d^{\rm s}_{1/e}$ vs. $P_{\rm ex}$ for magnetic field $B = 0$ (c) and 8 T (d). The $d^{\rm s}_{1/e}$ values are obtained from least-squares fitting the $I_{\rm spin}(x)$ profiles to exponential decays in the region $x = 0 - 9$$\mu$m, from the excitation spot to the HS edge. The data with the fit indicating diverging $d^{\rm s}_{1/e}$ are presented by circles on the edge.
• Figure 3: Excitation power and magnetic field dependence of IX transport and IX mediated spin transport. (a-b) The $1/e$ decay distance of LE-IX transport $d_{1/e}$ (a) and the $1/e$ decay distance of LE-IX mediated spin density transport $d^{\rm s}_{1/e}$ (b) vs. $P_{\rm ex}$ and $B$. The $d_{1/e}$ and $d^{\rm s}_{1/e}$ values are obtained from least-squares fitting the LE-IX luminescence profiles and $I_{\rm spin}$ profiles, respectively, to exponential decays in the region $x = 0 - 9$$\mu$m, from the excitation spot to the HS edge. The data with the fit indicating diverging $d_{1/e}$ (a) or $d^{\rm s}_{1/e}$ (b) are presented by cyan color. (c) Correlation between $d^{\rm s}_{1/e}$ and $d_{1/e}$. The values for $d_{1/e}$ and $d^{\rm s}_{1/e}$ are taken from (a) and (b). The data with the fit indicating diverging $d^{\rm s}_{1/e}$ and $d_{1/e}$ are presented by circles on the edge. The error bars represent the uncertainty in least-squares fitting the transport decays to exponential decays. The enhancement of $d^{\rm s}_{1/e}$ with $d_{1/e}$ is observed in a broad range of both excitation density and magnetic field variations, corresponding to the range of these parameters in (a, b).
• Figure 4: IX PL spectra. Co-polarized (blue) and cross-polarized (red) IX spectra for the excitation power $P_{\rm ex} = 5$ mW (a,b,c), 500 mW (d,e,f), and 5 $\mu$W (g,h,i) in magnetic field $B = - 8$ T (a,d,g), 0 (b,e,h), and 8 T (c,f,i). The lower-energy IX (LE-IX) PL is co-polarized. The higher-energy IX (HE-IX) PL is cross-polarized. The HE-IXs appear in the spectra at high $P_{\rm ex}$. PL spectra are normalized to the maximum of the co-polarized intensity. The Gaussian fits to the co-polarized (cross-polarized) LE-IX spectra and HE-IX spectra are shown by the thin green (black) lines. The sum of the Gaussians shown by the thin green (black) lines is shown by the thick green (black) line.
• Figure 5: Excitation power and magnetic field dependence of IX transport. The $1/e$ decay distance of spectrally integrated IX luminescence $d_{1/e}$ vs. $P_{\rm ex}$ and $B$. The $d_{1/e}$ values are obtained from least-squares fitting the spectrally integrated IX luminescence profiles to exponential decays in the region $x = 0 - 9~\mu$m, from the excitation spot to the HS edge. The data with the fit indicating diverging $d_{1/e}$ are presented by cyan color. Figure 5 is similar to Fig. 3a, however, Fig. 5 shows $d_{1/e}$ for the spectrally integrated IX PL including LE-IX and HE-IX, and Fig. 3a shows $d_{1/e}$ for LE-IX.