Theoretical investigation of electron-hole complexes in anisotropic two-dimensional materials

Trions and biexcitons in anisotropic two-dimensional materials are investigated within an effective mass theory. Explicit results are obtained for phosphorene and arsenene, materials that share features such as a direct quasiparticle gap and anisotropic conduction and valence bands. Trions are predicted to have remarkably high binding energies and an elongated electron-hole structure with a preference for alignment along the armchair direction, where the effective masses are lower. We find that biexciton binding energies are also notably large, especially for monolayer phosphorene, where they are found to be twice as large as those for typical monolayer transition metal dichalcogenides.

Figure 1

(a) Binding energies of positively (red open symbols) and negatively (black full symbols) charged trions in $n$-bP (squares) and $n$-As (triangles), as calculated by DMC and by the split-operator technique (blue stars and diamonds, respectively). DMC calculations have an energy variance $\approx \pm 0.3$ meV. (b) Square root of the expectation values of $x^2$ (black) and $y^2$ (red) of the exciton (full symbols) and e-c.m. (open symbols) contributions to the total wave function, for a negatively charged trion in $n$-bP (squares) and $n$-As (triangles), as obtained by the split-operator technique.

Figure 2

(a) Correlation functions for the electron-hole ($g_{e\text{−}h}$, black) pair and electron-exciton center of mass ($g_{e\text{−}c.m.}$, red) at $x=0$ (solid) and $y=0$ (dashed) in 1-bP over a ${\mathrm{SiO}}_2$ substrate. The blue dotted line illustrates $g_{e\text{−}c.m.}$ for the isotropic mass case. The full correlation function distributions over the $(x,y)$ plane are shown for (b) $g_{e\text{−}h}(x,y)$, (c) $g_{e\text{−}c.m.}(x,y)$, and (d) $g_{e\text{−}c.m.}(x,y)$ for the isotropic case.

Figure 3

Trion binding energies of $n$-bP (lines) and $n$-As (symbols) as a function of the dielectric constant of the substrate.