Mitchell Institute for Fundamental Physics & Astronomy
College Station, Texas 77843
Quantum statistics, spin and symmetry of the wavefunction are central to the quantum mechanical understanding of the world. Up to now all known particles exhibit Abelian statistics, where exchange of two particles amounts to a multiplication by a phase factor. Emergence of non-Abelian excitations in specially designed low dimensional systems is expected to change this world view. While signatures of Majorana fermions (the simplest type of excitations with non-Abelian statistics) have been seen in recent experiments, current experiments fall short of demonstrating non-Abelian exchange statistics. Engineering exotic states of matter with non-Abelian excitations is the first step toward development of a fault-tolerant topological quantum computer, where Majorana excitations have rather limited utility. Qubits based on parafermions, higher order non-Abelions, are expected to be orders of magnitude more computationally powerful than ones based on Majorana fermions.
I will describe our effort to built a platform to realize high-order non-Abelian excitations based on helical domain walls formed in the fractional quantum Hall regime. Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Naïvely, these helical domain walls (hDWs) constitute two counter-propagating chiral states with opposite spins. Coupled to an s-wave superconductor, helical channels are expected to lead to topological superconductivity with high order non-Abelian excitations. Experimental investigation of a transport through a single hDWs in the ν=2/3 fractional QH regime is found to be substantially smaller than the prediction of the naïve model. Luttinger liquid theory of the system reveals redistribution of currents between quasiparticle charge, spin and neutral modes, and predicts the reduction of the hDW current. Inclusion of spin-non-conserving tunneling processes reconciles theory with experiment. The theory confirms emergence of spin modes required for the formation of fractional topological superconductivity.