## Topological quantum Systems

**Research **

Placing many electrons together into a solid state environment often leads to the formation of new and even surprising physical behavior. Under certain conditions, this behavior is aptly described in terms of the underlying topology of the system, most notably in the case of the topological insulators. These relatively new states of electronic matter are characterized by the presence of an energy bandgap within the bulk of the material, while the material’s edge or surface hosts topologically protected gapless modes. In the fractional quantum Hall effect, the nontrivial topology gives rise to fractionally charged elementary excitations which in some cases may even possess non-Abelian braiding statistics. More recently, the discovery of the quantum spin Hall effect has provided another route toward these exotic non-Abelian particles, called Majorana fermions, via superconductivity injected into helical edge states. Our group is currently attempting to find Majorana fermions using transport techniques in quantum wells formed by HgTe/HgCdTe heterostructures, as well as in InAs quantum wells.

The differential resistance of a Josephson junction with aluminum leads oscillates due to Josephson interference as the perpendicular field varies. Increasing the parallel field modulates the strength of induced superconductivity. The superconductivity briefly dies out at around 1 T of parallel field before reemerging. For more information on this project, see:S. Hart et al. Nature Physics Sept 2016

A map of differential resistance across a Josephson junction shows a sinusoidal interference pattern, suggesting that the supercurrent density is clearly dominated by the contribution from the junction edges, see:S. Hart et al. Nature Physics Aug. 2014