Interplay of Rashba spin-orbit coupling and Coulomb interaction in topological spin-triplet excitonic condensates

Abstract

The cooperative effect of Rashba spin-orbit coupling (SOC) and Coulomb attraction in stabilizing topological spin-triplet excitonic condensates (ECs) in two-dimensional electron-hole systems in external magnetic field is investigated by using an unrestricted Hartree-Fock approach combined with the random-phase approximation. At weak electron-hole Coulomb interaction, the intraband Rashba SOC induces spin-momentum locking and topological semimetal behavior, while stronger interaction stabilizes spin-triplet ECs. Increasing the valence-band SOC drives a transition from a topologically trivial EC with coexisting spin-up and spin-down components to a topological spin-up EC only with quantized Chern number $C=2$. The dynamical excitonic susceptibility reveals a soft spin-up triplet mode acting as the precursor of the condensate. These results establish a microscopic mechanism for Rashba SOC-induced topological ECs and suggest realistic situations for their realization in noncentrosymmetric Janus transition-metal dichalcogenides and twisted van der Waals heterostructures.

Figures (8)

• Figure 1: Magnitude of spin-triplet EC order parameters $|\Delta_{\sigma\sigma}|$ (top and middle) and Chern number $C$ (bottom) as functions of $\lambda_f$ at different values of Coulomb interaction $U$ and $\lambda_c=0.18$.
• Figure 2: Quasiparticle energies $E^n_{\mathbf{k}}$ as eigenvalues of the diagonalized Hamiltonian along high-symmetry $k_x=k_y$ direction in the 1BZ for some values of $\lambda_f$ at $U=2$ and $\lambda_c=0.18$.
• Figure 3: Momentum distribution of the real part of the conduction-valence electron pair amplitudes $d_{\sigma\sigma'}(\mathbf{k})=\langle c^\dagger_{\mathbf{k}\sigma} f^{}_{\mathbf{k}\sigma'}\rangle$ in the whole 1BZ for some values of $\lambda_f$ at $U=2$ and $\lambda_c=0.18$.
• Figure 4: Momentum distribution of the imaginary part of the conduction-valence electron pair amplitudes $d_{\sigma\sigma'}(\mathbf{k})=\langle c^\dagger_{\mathbf{k}\sigma} f^{}_{\mathbf{k}\sigma'}\rangle$ in the whole 1BZ for some values of $\lambda_f$ at $U=2$ and $\lambda_c=0.18$.
• Figure 5: The Berry curvature in the whole 1BZ for two different values of $\lambda_f$ at $U=2$ and $\lambda_c=0.18$.