Excitonic collapse in semiconducting transition-metal dichalcogenides

Semiconducting transition metal dichalcogenides (STMDC) are two-dimensional (2D) crystals characterized by electron-volt-size band gaps, spin-orbit coupling (SOC), and $d$-orbital character of its valence and conduction bands. We show that these materials carry unique exciton quasiparticles (electron-hole bound states) with energy within the gap but which can “collapse” in the strong coupling regime by merging into the band structure continuum. The exciton collapse seems to be a generic effect in these 2D crystals.

Figure 1

Real (solid) and imaginary (dashed) plots of $f(E,\overline{\omega })=8\pi \left|m_l\right|P(q,\omega )/q^2$ from Eq. (6) for $E_l=1$ (blue), $1.01$ (purple), 1.5 (yellow), and 2 (green).

Figure 2

Optical absorption energies for ${\mathrm{MoS}}_2$ ($a=3.193\AA$, $\Delta =1.66$ eV, $t=1.1$ eV, $\lambda =0.075$ eV) on SiC. Red and blue circles correspond to different spins due to SOC. The dashed lines denote the energies equal to the band gaps for both spins. As the principal quantum number $n\to \infty$, the absorption energy approaches $\Delta \pm \lambda$, depending on the spin.

Figure 3

A phase diagram obtained from the solution of Eq. (26) for a range of $S_l=\sqrt{m_l/t}$. We also show where STMDS are located on this plot if they are on vacuum, ${\epsilon }_0=1$ (filled symbols), and if the samples are placed on BN (${\epsilon }_0=2.63$, empty symbols): ${\mathrm{MoS}}_2$ (circles), ${\mathrm{WS}}_2$ (squares), ${\mathrm{MoSe}}_2$ (triangles), ${\mathrm{WSe}}_2$ (diamonds). For each material, there are two points due to the SOC. The material information is obtained from Ref. 9.