Non-Hermitian Boundary Modes and Topology.

We consider conditions for the existence of boundary modes in non-Hermitian systems with edges of arbitrary codimension. Through a universal formulation of formation criteria for boundary modes in terms of local Green's functions, we outline a generic perspective on the appearance of such modes and generate corresponding dispersion relations. In the process, we explain the skin effect in both topological and nontopological systems, exhaustively generalizing bulk-boundary correspondence to different types of non-Hermitian gap conditions, a prominent distinguishing feature of such systems. Indeed, we expose a direct relation between the presence of a point gap invariant and the appearance of skin modes when this gap is trivialized by an edge. This correspondence is established via a doubled Green's function, inspired by doubled Hamiltonian methods used to classify Floquet and, more recently, non-Hermitian topological phases. Our work constitutes a general tool, as well as a unifying perspective for this rapidly evolving field. Indeed, as a concrete application we find that our method can expose novel non-Hermitian topological regimes beyond the reach of previous methods.

Elastic and hydrodynamic torques on a colloidal disk within a nematic liquid crystal.

The orientationally dependent elastic energy and hydrodynamic behavior of colloidal disks with homeotropic surface anchoring suspended in the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) have been investigated. In the absence of external torques, the disks align with the normal of the disk face â parallel to the nematic director n[over ^]. When a magnetic field is applied, the disks rotate â by an angle θ so that the magnetic torque and the elastic torque caused by distortion of the nematic director field are balanced. Over a broad range of angles, the elastic torque increases linearly with θ in quantitative agreement with a theoretical prediction based on an electrostatic analogy. When the disks are rotated to angles θ>π/2, the resulting large elastic distortion makes the disk orientation unstable, and the director undergoes a topological transition in which θ→π-θ. In the transition, a defect loop is shed from the disk surface, and the disks spin so that â sweeps through π radians as the loop collapses back onto the disk. Additional measurements of the angular relaxation of disks to θ=0 following removal of the external torque show a quasi-exponential time dependence from which an effective drag viscosity for the nematic can be extracted. The scaling of the angular time dependence with disk radius and observations of disks rotating about â indicate that the disk motion affects the director field at surprisingly modest Ericksen numbers.