# Research Areas

#### Non Abelian Topological Systems

A fascinating property of many topological phases are collective fractionalized excitations which are highly non-local in nature. These carry fractions of the quantum numbers of the underlying microscopic degrees of freedom; e.g., they can carry fractions of the electron charge. In two spatial dimensions, such emergent excitations can have exotic exchange rules, which are different from those of either bosons or fermions. Most intriguingly, certain topological systems can support “non-Abelian” excitations, whose exchange rules are described by non-commuting matrices. Read More