Talks by Ashvin Vishwanath

Magnetism, Skyrmions and Superconductivity in Moiré Lattices

Ashvin Vishwanath Harvard University

The remarkable properties of electrons moving through crystalline lattices continue to surprise us. Recently, electrons in artificial moiré lattices have emerged as an extraordinary new platform. The simplest such moiré material consists of a pair of graphene sheets twisted relative to one another. At a  "magic" angle of about 1 degree, a variety of phenomena, including strong-coupling superconductivity, is observed. In this talk, I will review this rapidly moving field and describe our theoretical ideas that invoke the geometry of quantum states and topological textures like skyrmions.

New routes to topological order: Toric code order in Rydberg atoms and fractional Chern insulators in moire materials

Ashvin Vishwanath Harvard University

Despite decades of theoretical work, the physical realization of topological order, outside of the fractional quantum Hall effect, has proved to be an elusive goal. Even the simplest example of a time-reversal symmetric topological order, as encountered in the paradigmatic toric code, awaits experimental realization. Key challenges include the lack of physically realistic models in these phases, and of ways to probe their defining properties.

Symmetry Protected Topological Phases; from Quantum Entanglement to Interaction Effects

Ashvin Vishwanath Harvard University
I will briefly review topological phases of non interacting fermions, such as topological insulators, and discuss how ideas from quantum information, in particular the entanglement spectrum, can be used to characterize them. For topological phases protected by inversion symmetry I argue that this is the ideal tool, and discuss how it leads to a classification of 3D topological phases. Next, I will discuss topological phases that only appear in the presence of interactions, although they share essential characteristics with non-interacting topological phases.

Exotic Phases and Phase Transitions from Geometrical Frustration

Ashvin Vishwanath Harvard University
In frustrated systems, competing interactions lead to complex phase diagrams and sometimes entirely new states of matter. Frustration often arises from the lattice geometry, leaving the system delicately balanced between a variety of possible orders. A number of normally weak effects can lead to a lifting of this degeneracy. For example, I will discuss how quantum fluctuations can stabilize a supersolid phase, where the system is at once both a crystal and a superfluid.