Exciton dynamics and high-temperature excitonic superfluidity in S-doped graphyne

Abstract

S-doped graphyne (S-GY) is a recently synthesized two-dimensional graphyne-based carbon allotrope that provides a promising platform for exciton engineering and coherent many-body phases. Here, we investigate the quasiparticle electronic structure, optical response, and exciton dynamics of monolayer S-GY using the G$_0$W$_0$ approximation and the Bethe--Salpeter equation (BSE). Quasiparticle corrections increase the fundamental band gap from $0.88\,\text{eV}$ (PBE) to $1.95\,\text{eV}$, while slightly reducing the carrier effective masses. The BSE optical response reveals strongly bound excitons, with the lowest bright exciton exhibiting a binding energy of $0.72\,\text{eV}$, as well as a nearly degenerate dark exciton within the thermal energy scale. Analysis of exciton wavefunctions in reciprocal space confirms a hydrogenic Rydberg series with well-defined angular-momentum character, and radiative lifetimes in the nanosecond range at room temperature, comparable to those in transition-metal dichalcogenide monolayers. Finally, we construct the excitonic phase diagram and estimate a crossover density of $\sim6 \times10^{12}~\text{cm}^{-2}$, below which the exciton gas behaves as a dilute Bose system, and the Berezinskii--Kosterlitz--Thouless (BKT) superfluid phase becomes accessible. We estimate a maximum BKT transition temperature of $\sim 143\,\text{K}$ in the freestanding limit for the 1s exciton, indicating that monolayer S-GY may provide favorable conditions for high-temperature excitonic superfluidity in graphyne-based materials.

Figures (5)

• Figure 1: Real- and reciprocal-space representations, and electronic properties of monolayer S-doped graphyne (SGY). (a) Crystal structure, with the unit cell indicated by the parallelogram. (b) Corresponding Brillouin zone with high-symmetry $\vb{k}$ points. (c) Electronic band structure of monolayer SGY, where solid lines correspond to GW bands and dashed lines to DFT-PBE results. In both cases, the respective VBM energy is set to zero.
• Figure 2: Absorption spectra for monolayer SGY obtained with the IQP-RPA (shaded area in blue) and BSE (shaded area in red). The GW fundamental band gap is marked with a vertical dashed line. In the inset below, the orange vertical lines indicate the bright excitons, while the grey lines depict the dark excitons.
• Figure 3: (Left) Energy spectrum of bound excitons in single-layer SGY. The GW direct band gap, corresponding to the continuum edge, is indicated by the dashed line at $2.19eV$. Red (grey) lines denote bright (dark) excitons. (Right, top) Exciton probability density in reciprocal space, given by the squared modulus of the exciton coefficients $\abs{A^{S}_{vc\mathbf{k}} }^{2}$, for the first few excitonic states of the hydrogenic series in SGY monolayer. (Right, bottom) Quasiparticle GW band structure with the corresponding exciton weights in reciprocal space.
• Figure 4: Temperature dependence of the exciton radiative lifetime for excitonic states in the Rydberg series for the S-GY monolayer.
• Figure 5: Temperature--density phase diagram for coherent excitonic phases of the 1s exciton in S-GY monolayer. In the dilute regime ($n<n_d$), the system exhibits a classical exciton gas at high temperature, a quantum-degenerate exciton Bose gas (DEBG) below the quantum-degeneracy line, and a BKT superfluid phase for $T<T_\text{BKT}$. For $n>n_d$, exciton overlap leads to a regime where electron-hole liquid (EHL) or electron-hole plasma (EHP) coexists with exciton gas, and a BCS-like paired phase at low temperature. Beyond the Mott critical density $n_c$, the system crosses into an electron--hole plasma/liquid (EHP/EHL) regime.