Voltage-controlled long-range propagation of indirect excitons in a van der Waals heterostructure

Indirect excitons (IXs), also known as interlayer excitons, can form the medium for excitonic devices whose operation is based on controlled propagation of excitons. A proof of principle for excitonic devices was demonstrated in GaAs heterostructures where the operation of excitonic devices is limited to low temperatures. IXs in van der Waals transition-metal dichalcogenide (TMD) heterostructures are characterized by high binding energies making IXs robust at room temperature and offering an opportunity to create excitonic devices operating at high temperatures suitable for applications. However, a characteristic feature of TMD heterostructures is the presence of moiré superlattice potentials, which are predicted to cause modulations of IX energy reaching tens of meV. These in-plane energy landscapes can lead to IX localization, making IX propagation fundamentally different in TMD and GaAs heterostructures and making uncertain whether long-range IX propagation, sufficiently long to allow for creating elaborate excitonic devices and circuits, can be realized in TMD heterostructures. In this work, we realize long-range IX propagation with the $1/e$ IX luminescence decay distances reaching 13 microns in a ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterostructure. We trace the IX luminescence along the IX propagation path. In the presented TMD materials, the long-range IX propagation occurs up to $\sim 50$ K. This is a step toward the room temperature operation, which can be realized in TMD heterostructures due to the high IX binding energy. We also realize control of the long-range IX propagation by voltage. The IX luminescence signal in the drain of an excitonic transistor is controlled within 40 times by gate voltage. The control of the IX propagation in the ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterostructure is governed by new mechanisms, beyond the mechanism for controlling IX transport by an energy barrier to IX propagation (or a trap for IXs) created by the gate electrode, known since the studies of GaAs heterostructures. We discuss the origin of the voltage-controlled long-range IX propagation in the ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterostructure, in particular, the electric-field control of the moiré potential.

Figure 1

Voltage-controlled IX propagation. (a) Band diagram of van der Waals ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterostructure. The ovals indicate a direct exciton (DX) and an indirect exciton (IX) composed of an electron ($-$) and a hole ($+$). (b) Microscope image showing the layer pattern of the device; scale bar is $10\mu \mathrm{m}$. The green, red, and yellow lines indicate the boundaries of the ${\mathrm{WSe}}_2$ and ${\mathrm{MoSe}}_2$ monolayers and graphene gate, respectively. (d), (e) x-y images of IX luminescence in the on (d) and off (e) state of the excitonic transistor. The white and yellow dashed lines show the boundary of the ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterostructure and graphene gate, respectively. The gate voltage $V_{\mathrm{g}}$ controls the IX propagation from the laser excitation spot at $x=0$ (the source) to the other side of the graphene gate $x\gtrsim 6\mu \mathrm{m}$ (the drain). $V_{\mathrm{g}}=10$ V (d), 0 (e). (f) Normalized IX luminescence profiles along $y=0$ for the images in (d) and (e) shown by the red and black lines, respectively. Inset shows the same IX luminescence profile in the on state on log scale. For comparison, dashed line shows exponential signal reduction with $1/e$ decay distance $13\mu \mathrm{m}$. A lower IX luminescence intensity is seen in the region covered by the graphene gate, which is centered at $x=4\mu \mathrm{m}$. (c) Total IX luminescence intensity in the drain (integrated over $x=6–13\mu \mathrm{m}$) vs $V_{\mathrm{g}}$. For all data, $P_{\mathrm{ex}}=4$ mW, $T=1.7$ K.

Figure 2

Voltage-controlled IX energy. Tracing IX luminescence along IX propagation. (a) IX luminescence spectra at $x=13\mu \mathrm{m}$ for gate voltages $V_{\mathrm{g}}=9$ and 13 V. (b) IX energy vs $V_{\mathrm{g}}$ for positions in the drain region $x=7$, 10, and $13\mu \mathrm{m}$. (c) IX spectra in on (red) and off (black) state of the excitonic transistor for positions in the drain region $x=7$, 10, and $13\mu \mathrm{m}$. $V_{\mathrm{g}}=10$ V (on), 8.5 V (off). For all data, $P_{\mathrm{ex}}=4$ mW, $T=1.7$ K.

Figure 3

Excitation power dependence of IX propagation. (a), (b) $x$-energy images of IX luminescence in the drain region for $P_{\mathrm{ex}}=2$ mW (a) and 0.05 mW (b). (c) Total IX luminescence intensity in the drain (integrated over $x=6–13\mu \mathrm{m}$) vs $P_{\mathrm{ex}}$. (d) IX energy vs position for $P_{\mathrm{ex}}=0.05$ (black), 0.5 (blue), and 2 (red) mW. For all data, $V_{\mathrm{g}}=10$ V, $T=1.7$ K.

Figure 4

Temperature dependence. (a) IX luminescence spectra in the drain at $x=13\mu \mathrm{m}$ at temperatures $T=1.7$, 20, 40, and 50 K in on (red) and off (black) state of the excitonic transistor. $V_{\mathrm{g}}=15$ V (on) and 0 (off). (b) Total IX luminescence intensity in the drain (integrated over $x=6–13\mu \mathrm{m}$) vs temperature in on ($V_{\mathrm{g}}=15$ V) and off ($V_{\mathrm{g}}=0$) state. (c) Total IX luminescence intensity in the drain (integrated over $x=6–13\mu \mathrm{m}$) vs $V_{\mathrm{g}}$ for temperatures $T=1.7$, 20, 40, and 50 K. For all data, $P_{\mathrm{ex}}=4$ mW.

Figure 5

Voltage-controlled IX propagation. (a)–(c) The white and yellow dashed lines show the boundaries of ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterostructure and graphene gate, respectively. The laser excitation spot [red circle in (a)–(c)] is positioned at the source [(a), (d), (g)], gate [(b), (e), (h)], and drain [(c), (f), (i)] region of the device. The gate voltage $V_{\mathrm{g}}$ controls the IX propagation from the laser excitation spot. (d)–(f) Normalized IX luminescence profiles along $y=0$ for $V_{\mathrm{g}}=10$ V (red lines) and 0 (black lines). (g)–(i) Same IX luminescence profiles on log scale. For comparison with the IX luminescence profiles at $V_{\mathrm{g}}=10$ V, dashed lines show exponential signal reduction with $1/e$ decay distance $d_{1/e}=14$, 11, and $12\mu \mathrm{m}$, respectively. A lower IX luminescence intensity is seen in the region covered by the graphene gate, which is centered at $x=4\mu \mathrm{m}$. For all data, $P_{\mathrm{ex}}=4$ mW, $T=1.7$ K.

Figure 6

IX luminescence decay. (a), (b) Decay of IX luminescence measured at the IX line energies 1.24–1.38 eV at short (a) and long (b) delay times vs voltage. This energy range corresponds to the IX state showing the long-range propagation (Fig. 2). For the data in (a), the laser excitation pulse duration ${\tau }_{\mathrm{pulse}}=14$ ns, period ${\tau }_{\mathrm{period}}=60$ ns, and edge sharpness $\sim 0.5$ ns and the signal integration window ${\tau }_{\mathrm{w}}=6$ ns. For the data in (b), to access the long delay times ${\tau }_{\mathrm{pulse}}$, ${\tau }_{\mathrm{period}}$, and ${\tau }_{\mathrm{w}}$ are increased to 400, 1600, and 200 ns, respectively. (c) IX luminescence decay times at short (points) and long (triangles) delay times derived from the data (a) and (b), respectively. The IX luminescence is integrated over the entire heterostructure to increase the signal. For all data, $P_{\mathrm{ex}}=4$ mW, $T=1.7$ K.

Figure 7

The layer pattern. Microscope image showing the layer pattern of the device on an area larger than in Fig. 1. Scale bar is $10\mu \mathrm{m}$. The green, red, yellow, cyan, and orange lines indicate the boundaries of ${\mathrm{WSe}}_2$ and ${\mathrm{MoSe}}_2$ monolayers, graphene gate, and bottom and top hBN layers, respectively.

Figure 8

Luminescence spectra for an extended spectral range. Luminescence spectra for an extended spectral range including the DX luminescence for excitation in the source [(a)–(c)], gate [(d)–(f)], and drain [(g)–(i)] at $x=1,4$, and $9\mu \mathrm{m}$, respectively, measured in the source [(a), (d), (g)], gate [(b), (e), (h)], and drain [(c), (f), (i)] at $x=0,4$, and $9\mu \mathrm{m}$, respectively, for gate voltages $V_{\mathrm{g}}=0$ and 10 V corresponding to the off (black) and on (red) state of the excitonic transistor. $P_{\mathrm{ex}}=0.05$ mW, $T=1.7$ K.

Figure 9

Excitation power dependence. Luminescence spectra of propagating IXs at $x=10\mu \mathrm{m}$ for $P_{\mathrm{ex}}=0.05$, 0.25, and 4 mW. Excitation spot is at $x=0$, $V_{\mathrm{g}}=10$ V, $T=1.7$ K.

Figure 10

Temperature dependence. Normalized profiles of luminescence of propagating IXs along $y=0$ at $T=1.7,20,40$, and 50 K. Dot-dashed line, which shows a normalized profile of DX luminescence in ${\mathrm{MoSe}}_2$ at 50 K, presents the limit for the excitation spot extent. Dashed lines show exponential signal reduction with $1/e$ decay distance $d_{1/e}=8$, 9, and $5\mu \mathrm{m}$. $V_{\mathrm{g}}=10$ V, $P_{\mathrm{ex}}=4$ mW.