Strain-induced exciton mobility in layered WS2 from first principles

Abstract

Exciton mobility in two-dimensional semiconductors is a key ingredient in materials-based design of optoelectronic functionalities. Monolayer transition metal dichalcogenides (TMDs) set a good test case, with tightly bound excitons and designable flexibility that offer an ideal platform for realizing strain effects on exciton energy transfer. Here, we present an ab initio study to construct strain-induced exciton energy profiles and model exciton dynamics on top of these potential surfaces. We focus on inhomogeneously-strained monolayer WS$_2$, combining excitonic band structures derived from many-body perturbation theory for a large variety of strain profiles and calculate the change in mobility characteristics using a semiclassical ballistic transport model. We connect a wealth of strain patterns to exciton drift, diffusion, and confinement. Our results point to strain-induced regimes of super-ballistic propagation and an anomalous effective diffusion, governed entirely by the strain landscape. Our results provide structure-specific understanding of ballistic strain-tunable exciton behavior, offering design principles for engineering exciton dynamics in two-dimensional materials.

Figures (4)

• Figure 1: (a) First bright excitonic band centered around the $\Gamma$ center-of-mass momentum with paths utilized for line-plot marked as $e_1$ and $e_2$. (b) Close-up of the parabolic region of the band, with the region utilized for the dynamics simulations marked by a red square. (c) First bright excitonic band along the $e_1$ and $e_2$ directions, plotted for various strains. (inset) position of the band minimum for various strains. The exciton band minimum exhibits an inverse proportionality for the range of strains utilized in this study. (d) Illustration of a 2D slice of the full potential, with a concave parabolic strain profile along one direction in position space, and a path along $e_1$ and $e_2$ in momentum space, representing the (1,1) and (1,-1) directions in crystal axes.
• Figure 2: Time evolution of the exciton distributions, expressed as the contour at 50% height for multiple time-steps and the propagation of the COM as a white arrow in position space (left) and momentum space (right) for (a) a parabolic convex in X and linear ascending in Y and (b) a parabolic concave in X and linear descending in Y strain profiles. Position-space backgrounds illustrate the appropriate strain profile. Low strain values are in blue, and high values are in green. As a guide to the eye, the projections along the axes are illustrated along the appropriate axes. Momentum-space backgrounds illustrate the average excitonic band. Low energy values are in blue, and high values are in green. As a guide to the eye, the projections along the axes are illustrated along the appropriate axes.
• Figure 3: Box plot of the strain-induced mobilities as reflected in the power law power law $\vec{r}(t)\propto t^\alpha$, resulting under (a) various initial positions with solutions grouped by initial width of momentum distribution, (b) various strain profiles with solutions grouped by initial width of momentum distribution, (c) various initial positions with solutions groups by shape of strain profile, (d) various initial width of momentum distribution with solutions groups by shape of strain profile. A purely ballistic propagation should result in linear mobility. Most strain profiles yield sub-ballistic transport behavior ($\alpha < 1$), but concave parabolic profiles in particular lead to ballistic or even super-ballistic regimes ($\alpha \approx 1 - 2$). The researched strain profiles are either linear, parabolic concave, parabolic convex, or cubic with respect to a position coordinate, as per equation \ref{['eq:general_strain']}.
• Figure 4: Behavior of the time evolution of position-space width under (a) various strain profile shapes, (b) various initial positions, and (c) various initial momentum widths. Without strain, the time-evolution of the position-space width behaves as a ballistic expansion. Concave strain profiles always result in a sub-ballistic expansion, which is related to negative diffusion regimes. Convex strain profiles always result in super-ballistic expansion. Linear strain profiles can induce either sub- or super-ballistic expansions depending on initial conditions, while cubic profiles can exhibit all three expansion behaviors. Both the sub-ballistic and super-ballistic regimes correspond to anomalous diffusion regimes when interparticle interactions are considered.