Excitonic transport driven by repulsive dipolar interaction in a van der Waals heterostructure

Abstract

Dipolar bosonic gases are currently the focus of intensive research due to their interesting many-body physics in the quantum regime. Their experimental embodiments range from Rydberg atoms to GaAs double quantum wells and van der Waals heterostructures built from transition metal dichalcogenides. Although quantum gases are very dilute, mutual interactions between particles could lead to exotic many-body phenomena such as Bose-Einstein condensation and high-temperature superfluidity. Here, we report the effect of repulsive dipolar interactions on the dynamics of interlayer excitons in the dilute regime. By using spatial and time-resolved photoluminescence imaging, we observe the dynamics of exciton transport, enabling a direct estimation of the exciton mobility. The presence of interactions significantly modifies the diffusive transport of excitons, effectively acting as a source of drift force and enhancing the diffusion coefficient by one order of magnitude. The repulsive dipolar interactions combined with the electrical control of interlayer excitons opens up appealing new perspectives for excitonic devices.

Figure 1

a, Optical image of the device, highlighting the regions for different materials. Scale bar, 10 μm. b, Schematic of the encapsulated heterotrilayer device with the global top and bottom split gates, as well as electrical connections. c, IX PL emission intensity as a function of laser average power P_ave and energy. The sharp peak at 1.46 eV originates from the imperfect filtering of the laser line at 850 nm (Supplementary Note 3). d, PL peak intensity (red squares) and peak energy (black squares) extracted from c. The arrows point out the estimated exciton density at three different powers which will be used in the data in Figure 2. e, CCD image of the excitation laser spot. f & g, CCD images of the normalized IX PL intensity, acquired for P_ave = 50 μW and 200 μW. The yellow solid lines indicate the shape of the heterostructure.

Figure 2

a, 2D PL images $I_{norm}^{time}$ for P_ave = 200 μW acquired by the scanning APD system at different times after the excitation. The yellow solid lines indicate the shape of the heterostructure. b, Simulated exciton area as a function of time for different diffusion coefficients D. The fitting parameters are as follows. Dashed lines: U_XX = 0, τ = 3.5 ns; solid lines: U_XX = 2.6 μeVμm², n ₀= 1 × 10¹¹ cm^-2, τ = 3.5 ns. c, Exciton area as a function of time for different excitation powers. The gray line shows the area of the excitation laser spot size (see Figure S6). The solid lines are fits using equation (2) for n ₀= 1 × 10¹¹, 2 × 10¹¹ and 4 × 10¹¹ cm^-2 respectively. The fitting parameters are U_XX = 2.6 μeV·μm², τ = 3.5 ns, D = 0.15 cm²/s and T = 4.6 K. The black dashed line indicates the simulated exciton area without considering U_XX. The red dashed line indicates the slope of the area increasing for P_ave = 200 μW at t < 1 ns.

Figure 3

a, b and c, 1D normalized PL intensity along x = 0 in Figure 2a for P_ave = 100 μW, 200 μW and 350 μW. Upper panel: $I_{norm}^{time}$; lower panel: $I_{norm}^{space}$. White dashed lines enclose the region of IXs transport. Black dashed lines are guides for the eye for v_eff. d, Simulation of 1D normalized exciton distribution along x = 0 using equation (2) for n ₀ = 4 × 10¹¹ cm^-2. Upper panel: $n_{norm}^{time}$; lower panel: $n_{norm}^{space}$. e, Exciton effective velocity v_eff as a function of the spectral blue-shift δE_xx extracted from Figure 1d. The error bars of v_eff are given by the linear fits along the black dashed lines in a, b and c (see Figure S12). The red solid line is a linear fit to the data.

Figure 4

a, b, Effect of electro-static potential applied to the back-gate (V_bg) on the exciton spatial and temporal distribution. Upper panel: schematic of the energy profiles as well as the expected exciton motion; middle panel: CCD images of the normalized IX PL intensity; lower panel: 1D normalized PL intensity $I_{norm}^{time}$ along y = 0. The black dashed lines enclose the region of the local back gate. The yellow solid lines indicate the shape of heterostructure. c, 1D normalized PL intensity $I_{norm}^{time}$ along y = 0 for V_bg = -1 V. d, Simulation of 1D normalized exciton distribution $n_{norm}^{time}$ along y = 0 for $\delta E_{el}^0/\delta E_{XX}^0~0.5$. e, Schematic of the energy profile of δE_xx(t) = n(t)U_XX and δE_el. f, Exciton propagation distance L_x as a function of $\delta E_{el}^0/\delta E_{XX}^0$. Insert: schematic of the energy profile in simulations. Red: δE_el; yellow: δE_XX(t = 0).