Condensed Matter Theory

Abstract:

We investigate the full doping and strain-dependent phase diagram of the normal state of magic-angle twisted bilayer graphene (TBG). Using comprehensive Hartree-Fock calculations, we show that at temperatures where superconductivity is absent the global phase structure can be understood based on the competition and coexistence between three types of intertwined orders: a fully symmetric phase, spatially uniform flavor-symmetry-breaking states, and an incommensurate Kekulé spiral (IKS) order. For small strain, the IKS phase, recently proposed as a candidate order at all nonzero integer fillings of the moiré unit cell, is found to be ubiquitous for noninteger doping as well. We demonstrate that the corresponding electronic compressibility and Fermi surface structure are consistent with the “cascade” physics and Landau fans observed experimentally. This suggests a unified picture of the phase diagram of TBG in terms of IKS order.

Abstract:

Breaking spatial symmetry is an essential requirement for phoretic active particles to swim at low Reynolds number. This fundamental prerequisite for swimming at the micro scale is fulfilled either by chemical patterning of the surface of active particles or alternatively by exploiting geometrical asymmetries to induce chemical gradients and achieve self-propulsion. In the present paper, a far-field analytical model is employed to quantify the leading-order contribution to the induced phoretic velocity of a chemically homogeneous isotropic active colloid near a finite-sized disk of circular shape resting on an interface separating two immiscible viscous incompressible Newtonian fluids. To this aim, the solution of the phoretic problem is formulated as a mixed-boundary-value problem that is subsequently transformed into a system of dual integral equations on the inner and outer domains. Depending on the ratio of different involved viscosities and solute solubilities, the sign of phoretic mobility and chemical activity, as well as the ratio of particle–interface distance to the radius of the disk, the isotropic active particle is found to be repelled from the interface, be attracted to it, or reach a stable hovering state and remain immobile near the interface. Our results may prove useful in controlling and guiding the motion of self-propelled phoretic active particles near aqueous interfaces.