Condensed Matter Theory

Abstract:

We perform the energy minimization of the paired composite fermion (CF) wave functions, proposed by Möller and Simon (MS) [Phys. Rev. B 77, 075319 (2008)] and extended by Yutushui and Mross (YM) [Phys. Rev. B 102, 195153 (2020)], where the energy is minimized by varying the CF pairing function, in the case of an approximate model of the Coulomb interaction in the second Landau level for pairing channels ℓ = −1, 3, 1, which are expected to be in the Pfaffian, anti-Pfaffian, and particle-hole symmetric (PH) Pfaffian phases, respectively. It is found that the energy of the ℓ = −1 MS wave function can be reduced substantially below that of the Moore-Read wave function at small system sizes; however, in the ℓ = 3 case the energy cannot be reduced much below that of the YM trial wave function. Nonetheless, both our optimized and unoptimized wave functions with ℓ = −1, 3 extrapolate to roughly the same energy per particle in the thermodynamic limit. For the ℓ = 1 case, the optimization makes no qualitative difference and these PH-Pfaffian wave functions are still energetically unfavorable. The effective CF pairing is analyzed in the resulting wave functions, where the effective pairing for the ℓ = −1, 3 channels is found to be well approximated by a weak-pairing BCS ansatz and the ℓ = 1 wave functions show no sign of emergent CF pairing.

Abstract:

We study the vertex model for epithelial tissue mechanics extended to include coupling between the cell shapes and tensions in cell-cell junctions. This coupling represents an active force which drives the system out of equilibrium and leads to the formation of nematic order interspersed with prominent, long-lived +1 defects. The defects in the nematic ordering are coupled to the shape of the cell tiling, affecting cell areas and coordinations. This intricate interplay between cell shape, size, and coordination provides a possible mechanism by which tissues could spontaneously develop long-range polarity through local mechanical forces without resorting to long-range chemical patterning.