Condensed Matter Theory

Abstract:

Director field alignment in inkjet printed droplets of chiral nematic liquid crystalline materials is investigated using both experiments and numerical simulations. Experimental investigations are performed by depositing droplets of varying sizes and pitches on homeotropic alignment layers. The competition between the bulk behaviour of the chiral nematic liquid crystal and the boundary conditions imposed by the droplet surface leads to the formation of a range of possible internal director configurations. Numerical investigations are performed using a free energy minimisation approach, and the resultant simulated polarising optical microscope images are found to agree well with experimental observations.

Abstract:

Recent scanning tunneling microscopy experiments in twisted bilayer [K. P. Nuckolls et al., Nature (London) 620, 525 (2023)] and trilayer [H. Kim et al., Nature (London) 623, 942 (2023)] graphene have revealed the ubiquity of Kekulé charge-density wave order in magic-angle graphene. Most samples are moderately strained and show “incommensurate Kekulé spiral” (IKS) order involving a graphene-scale charge density distortion uniaxially modulated on the scale of the moiré superlattice, in accord with theoretical predictions. However, ultralow strain bilayer samples instead show graphene-scale Kekulé charge order that is uniform on the moiré scale. This order, especially prominent near filling factor 𝜈=−2, is unanticipated by theory which predicts a time-reversal breaking Kekulé current order at low strain. We show that including the coupling of moiré electrons to graphene-scale optical zone-corner (ZC) phonons stabilizes a uniform Kekulé charge ordered state at |𝜈|=2 with a quantized topological (spin or anomalous Hall) response. Our work clarifies how this phonon-driven selection of electronic order emerges in the strong-coupling regime of moiré graphene.