Probing topological excitations with a scanning tunneling microscope: from Yu-Shiba-Rusinov states to fractional quantum Hall states

Abstract

Interacting electrons in quantum materials behave differently than a single electron: the interaction induces topology and correlation in the collective excitations and gives rise to many completely new properties such as unusual statistics of the quasi-particles. A scanning tunneling microscope (STM) probes the tunneling event for an electron between the tip and the local electronic environment of the sample, thus can serve as a tool to probe the topological excitations in the sample. In the first part of this dissertation, we use the STM tip to study various magnetic atomic structures on a superconducting surface and measure their Yu-Shiba-Rusinov (YSR) states. We are able to tune both the spin ground states and YSR band topology with atomic manipulation experiments, which gives us parameter space where Majorana quasi-particles can potentially emerge in a longer chain. In the second part of the dissertation, we study the integer (IQH) and fractional quantum Hall (FQH) effect of a bilayer graphene device in a perpendicular magnetic field. We identify the broken symmetry states in the lowest Landau level (LL) by imaging the wavefunction. In the N=0 LL orbital state, we observe the Jain sequence of FQH states with a large thermodynamic gap size. We also measure the tunneling gap of FQH states which reflects the anyonic excitations in the composite fermion LL. In the N=1 orbital state we observe even-denominator states and their Levin-Halperin daughter states, which identify the even-denominator states to be the Moore-Read Pfaffian states. The thermodynamic gap of the Pfaffian states measured by STM is about 30 K. These experiments serve as important steps for STM to study anyons and their topological excitations.