Three-dimensional electron-hole superfluidity in a superlattice close to room temperature

Although there is strong theoretical and experimental evidence for electron-hole superfluidity in separated sheets of electrons and holes at low $T$, extending superfluidity to high $T$ is limited by strong two-dimensional fluctuations and Kosterlitz-Thouless effects. We show this limitation can be overcome using a superlattice of alternating electron- and hole-doped semiconductor monolayers. The superfluid transition in a three-dimensional superlattice is not topological, and for strong electron-hole pair coupling, the transition temperature $T_c$ can be at room temperature. As a quantitative illustration, we show $T_c$ can reach $270\mathrm{K}$ for a superfluid in a realistic superlattice of transition metal dichalcogenide monolayers.

Figure 1

(a) Schematic illustration of the $\mathrm{WS}{}_2/\mathrm{W}\mathrm{Se}{}_2$ heterostructure superlattice of periodicity $2d$, of alternating monolayers of the two different TMDs, one type $n$ doped (green lines) and the other $p$ doped (black lines). (b) Lowest conduction band and highest valence band of the superlattice as a function of $k_z$, expressed relative to the center of the $K$ valley. Blue and red bands are spin-up and spin-down bands, respectively. For the $K^{\prime }$ valley, the spins are reversed. (c) Bands predominantly associated with $\mathrm{WS}{}_2$ as a function of ${\mathit{k}}_{\parallel }$. Inset shows a close-up of the two spin-split $\mathrm{WS}{}_2$ conduction bands, separated by $2{\lambda }_c=27$ meV. (d) Bands predominantly associated with $\mathrm{W}\mathrm{Se}{}_2$ as a function of ${\mathit{k}}_{\parallel }$.

Figure 2

(a) Maximum superfluid gap ${\mathrm{\Delta }}^{\max }$ as a function of equal electron and hole densities $n$. Top axis shows effective 2D density $n_{2\text{D}}$. (b) Condensate fraction $\mathcal{C}$.

Figure 3

Superfluid transition temperature $T_c$ as a function of $n$, the equal electron and hole density in the superlattice. Red line: $T_c$ determined in the BCS and BCS-BEC crossover regimes using Eqs. (5) and (6) generalized to finite temperatures. Blue line: $T_c$ determined in the deep BEC regime using Eq. (S12) of the Supplemental Material [20]. Green line: interpolation.