Tunable linear polarization of interface excitons at lateral heterojunctions

Abstract

We develop a theory of polarized photoluminescence of interface excitons localized at lateral heterojunctions between transition metal dichalcogenide monolayers. We show that the circular selection rules governing interband optical transitions exactly at the band extrema are modified at finite wave vectors. The corresponding wave-vector-dependent corrections to the optical matrix elements result in a net linear polarization of excitonic photoluminescence. We identify two microscopic mechanisms responsible for linear polarization$-$trigonal warping of the electron and hole dispersions and the energy dependence of the effective masses. Their interplay controls both the magnitude and the angle of the emitted light polarization, with distinct dependences on the crystallographic orientation of the interface. Using a microscopic variational approach, we demonstrate that the degree of linear polarization can reach values exceeding 10% in realistic heterostructures. Furthermore, due to the large built-in dipole moment of interface excitons, their optical response can be tuned by an external in-plane electric field, enabling control over the strength and direction of the polarization.

Figures (6)

• Figure 1: Linearly polarized luminescence of interface excitons. (a) Sketch of an interface exciton localized at a lateral heterojunction. The intensity of the emitted radiation is different for electric field along and perpendicular to the interface resulting in the linear polarization of the excitonic photoluminescence. (b) Lateral heterojunction oriented at an arbitrary angle $\theta$ with respect to the crystallographic axes $x$ and $y$. (c) Type-II band alignment of conduction and valence bands leads to the formation of a spatially indirect exciton.
• Figure 2: The scheme of polarization of optical transitions in the $K_+$ and $K_-$ valleys of bulk TMD monolayers. The transitions occur in circular polarization strictly at $\bm k = 0$, whereas at $\bm k \neq 0$ the polarization becomes elliptical, see Eq. \ref{['select_rules']}. Polarization (a) due to the trigonal warping and (b) due to the dependence of mass on energy.
• Figure 3: Linear polarization of the interface excitons as a function of the interface orientation. (a) Degree of linear polarization $P_{\rm lin}$ for different ratios between the two contributions $P_A = A \kappa_1$ and $P_\beta = \beta \kappa_2$ in Eq. \ref{['Xpol']}. The inset shows the same in the form of a polar plot. (b) Direction of linear polarization with respect to the interface. The insets depict the heterostructures corresponding to the two different zigzag ($\theta = 0,\,60^\circ$) and armchair ($\theta = 30^\circ,\,90^\circ$) interfaces.
• Figure 4: Tunable interface excitons in lateral heterostructures on a SiO$_2$ substrate (red lines) and encapsulated in h-BN (blue lines). (a) Exciton energy (solid lines) counted from the band gap as a function of the band offset. Dashed lines show the energies of "bulk" 2D excitons, black dotted line shows the $-V_0$ function. (b) Static dipole moment as a function of the band offset. The inset schematically depicts the studied structures. (c) Exciton energy as a function of electric field applied perpendicularly to the interface. The curves are calculated using $V_0 = 200$ meV for the encapsulated structure and $V_0 = 300$ meV for the structure on a substrate [shown by stars in panel (a)]. The dotted black lines show linear approximation with the slope determined by $d_{eh}$ at $F = 0$. (d) Static dipole moment as a function of electric field.
• Figure 5: Linear polarization of the interface exciton emission. Solid and dashed lines show the contributions related to the energy dependence of mass ($P_\beta$) and the trigonal warping ($P_A$), respectively. Blue and red lines correspond to encapsulated and supported structures. Dependences of $P_\beta$ and $P_A$ (a) on the band offset and (b) on the electric field are shown. The curves in (b) are plotted for the band offsets indicated by the stars in (a).