Weyl excitonic condensation

Abstract

We consider a half-filled two-dimensional Su-Schrieffer-Heeger lattice and examine the role of the long-range Coulomb electron-hole attractive interaction. We demonstrate that, under specific conditions, a rare interplay of topological and excitonic-collective behavior emerges as a novel state of matter. A unique Bose-Einstein condensate of excitons forms, exhibiting co-presence of pseudo-spin chiral texture. The emerging complex order-parameter, a particle-hole pairing-gap, has non-zero real and imaginary parts throughout the Brillouin zone (BZ) but vanish separately on two different nodal lines, which intersect at two Weyl points. The Weyl nodes possess opposite pseudo-spin chiralities, which act as source and drain of a Berry-flux associated with the particle-hole pairing-wavefunction, and are the cause of Bogoliubov-deGennes Fermi-arc edge-states. We self-consistently calculate the full momentum-dependence of the particle-hole pairing gap throughout the entire BZ. Near the Weyl points, the pairing gap exhibits the unconventional time-reversal-symmetry breaking $p_x+ip_y$ character. Finally, we discuss general potential experimental realizations of this novel state of matter.

Figures (9)

• Figure 1: Illustration of the SSH lattice. The conventional unit cell is shown as the black rectangular with sides $a$ and $b$. The reason for requiring two identical atoms in the unit cell is the inversion symmetry breaking because of the two different hopping matrix elements $t$ and $t^{\prime}$ caused by the dimerization. This leads to the two sublattice ($A$ (garnet) and $B$ (gold)) breakup.
• Figure 2: (Left) The non-interacting bands of the Hamiltonian given by Eq. \ref{['SSH']} for $t=0.6$$t^{\prime} = 1.2$ and $t_d =1.1$ and $t'_d=1.3$. Note the display of the two Dirac-Weyl opposite chirality nodes along the $k_y$ axis. (Right) The bands when we choose $t=0.6$$t^{\prime} = 1.2$ and $t_d =1.0$ and $t'_d=1.4$.
• Figure 3: The non-interacting bands of the Hamiltonian given by Eq. \ref{['SSH']} for $t=0.6$$t^{\prime} = 1.2$ and $t_d =1.1$ and $t'_d=1.3$ and $t^{y}=0.5$.
• Figure 4: The states of a ribbon. The purple dispersionless bands represent two Fermi-arc states which are localized on the opposite ribbon edges.
• Figure 5: Real (panel (a)) and imaginary part (panel (b)) of the gap $\Delta(k_x,k_y)$ obtained by solving Eq. \ref{['eq:gap']} iteratively until self-consistency was achieved.