Twist Angle-Dependent Interlayer Exciton Lifetimes in van der Waals Heterostructures

In van der Waals (vdW) heterostructures formed by stacking two monolayers of transition metal dichalcogenides, multiple exciton resonances with highly tunable properties are formed and subject to both vertical and lateral confinement. We investigate how a unique control knob, the twist angle between the two monolayers, can be used to control the exciton dynamics. We observe that the interlayer exciton lifetimes in ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ twisted bilayers (TBLs) change by one order of magnitude when the twist angle is varied from 1° to 3.5°. Using a low-energy continuum model, we theoretically separate two leading mechanisms that influence interlayer exciton radiative lifetimes. The shift to indirect transitions in the momentum space with an increasing twist angle and the energy modulation from the moiré potential both have a significant impact on interlayer exciton lifetimes. We further predict distinct temperature dependence of interlayer exciton lifetimes in TBLs with different twist angles, which is partially validated by experiments. While many recent studies have highlighted how the twist angle in a vdW TBL can be used to engineer the ground states and quantum phases due to many-body interaction, our studies explore its role in controlling the dynamics of optically excited states, thus, expanding the conceptual applications of “twistronics”.

Figure 1

Conceptual description of IXs in a TBL. (a) Schematic of type-II band alignment with band offsets (${\mathrm{\Delta }}_c$ and ${\mathrm{\Delta }}_v$) and interlayer charge transfer lead to the formation of IXs. (b) Real-space representation of the moiré superlattice for twist angles of 1° and 3° with a moiré supercell marked in white. (c) Schematic of the Brillouin zone of ${\mathrm{MoSe}}_2$ ML (blue) and ${\mathrm{WSe}}_2$ ML (orange) twisted in the momentum space (left panel). $Q_{\mathrm{IX}}=K_c-K_v$ denotes a finite momentum mismatch between the two layers and corresponds to the center of mass momentum of IXs. This twist leads to an indirect transition (right panel). (d) Thermal distribution of IXs with a near-zero (left) and a finite (right) twist angle plotted in the exciton’s reference frame. Blue (red) curve illustrates the thermal distribution of IXs at a low (high) temperature. Yellow shaded region illustrates the light cone.

Figure 2

(a) Low-temperature PL spectrum from a ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ TBL with $\mathrm{\Theta }=1.0\pm 0.3°$ twist angle, featuring both intralayer excitons (neutral exciton: $X^0$, trion: $X^{-}$) and IXs. Inset shows the optical image of the hBN-encapsulated TBL. ${\mathrm{MoSe}}_2$ and ${\mathrm{WSe}}_2\mathrm{ML}$ regions are indicated inside the blue and orange dashed lines, respectively. Scale bar: $20\mu \mathrm{m}$ (b) Gaussian fitting to multiple IXs. Black solid line is measured data.

Figure 3

Twist angle dependent lifetimes of all IX resonances measured from (a) $\mathrm{\Theta }=1.0\pm 0.3°$, (b) $2.2\pm 0.3°$, and (c) $3.5\pm 0.3°$ TBLs, respectively. Inset shows the energy dependence of the fast (${\tau }_1$) and slow (${\tau }_2$) decay components of IX lifetimes. Solid and black dotted lines represent fitting with a biexponential decay and instrumental response functions, respectively. (d) Twist angle dependence of IX lifetimes measured near 1345–1355 meV in the TBLs. Inset summarizes the extracted fast and slow decay components in the three TBLs.

Figure 4

Temperature and twist angle dependence of calculated IX radiative lifetimes in the absence and presence of a moiré potential and measured temperature dependent IX dynamics. Calculated twist angle dependence of the IX lifetimes shown for various temperatures in the (a) absence and (b) presence of a moiré potential. Panels (c) and (d) show the IX band structure in the absence of a moiré potential at twist angles of $\mathrm{\Theta }=1°$ and $\mathrm{\Theta }=3°$, respectively. Moiré exciton states are classified by momenta from the first MBZ shown in inset of (f). The light cone (orange shaded area) occupies a larger fraction of the MBZ for a TBL with a smaller twist angle. Panels (e) and (f) show the moiré exciton band structure, thermal distribution, and density-of-states contribution for different twist angles at low-temperature. Scale of the symbol size is the same for panels (c),(d) and (e),(f). Note that at small twist angle the IX bands become flat due to the moiré potential. (g),(h) Measured temperature dependent fast and slow decay components of lifetimes near 1350 meV in the TBLs with $\mathrm{\Theta }=1.0\pm 0.3°$ ($3.5\pm 0.3°$) from 5 to 50 K (13 to 50 K). Error bars are smaller than the symbols for some data points.