Development of quantum Hall - based platforms to realize high order
non-Abelian excitations
We introduce a new platform based on spin transitions in the integer and fractional quantum Hall effect regime where Majorana fermions and parafermions - higher order non-abelian excitations - can be potentially realized. Local (gate) control of spin transitions allows formation of isolated helical domain walls, which consist of counter-propagating edge states of opposite polarization. We demonstrate formation of such hDWs in magnetic semiconductor CdTe:Te in integer QHE, where spin levels anti-cross and hDWs conduction is carried by impurity states, and in the fractional QHE regime in GaAs where no anti-crossing is observed and hDWs are conducting over many (>7) microns. In the fractional QHE regime hDWs are expected to have fractionalized charge excitations. Transport properties of hDWs will be discussed, I will also present numerical studies of hDWs which elucidate their spin texture.
When superconductivity is induced into a hDWs from s-wave superconducting contacts via proximity effect in the FQHE regime, parafermions are expected to be formed at the hDWs boundaries. In a multi-gate device a re-configurable network of domain walls can be formed allowing creation, braiding, manipulation and fusion of parafermions. In respect to the quantum computing application parafermons are more computationally intense than Majoranas and are a building block for Fibonacci fermions, even high order non-Abelian particles that can perform universal gate operations within the topologically protected subspace.