In this paper, we report on the study of Abelian and non-Abelian statistics through Fabry-Perot interferometry of fractional quantum Hall (FQH) systems. Our detection of phase slips in quantum interference experiments demonstrates a powerful, new way
of detecting braiding of anyons. We confirm the Abelian anyonic braiding statistics in the $ u = 7/3$ FQH state through detection of the predicted statistical phase angle of $2pi/3$, consistent with a change of the anyonic particle number by one. The $ u = 5/2$ FQH state is theoretically believed to harbor non-Abelian anyons which are Majorana, meaning that each pair of quasiparticles contain a neutral fermion orbital which can be occupied or unoccupied and hence can act as a qubit. In this case our observed statistical phase slips agree with a theoretical model where the Majoranas are strongly coupled to each other, and strongly coupled to the edge modes of the interferometer. In particular, an observed phase slip of approximately $pi$ is interpreted as a sudden flip of a qubit, or entry of a neutral fermion into the interferometer. Our results provide compelling support for the existence of non-Abelian anyons.
We study the ultrafast phonon response of mixed-valence perovskite Cs$_2$Au$_2$I$_6$ using pump-probe spectroscopy under high-pressure in a diamond anvil cell. We observed a remarkable softening and broadening of the Au - I stretching phonon mode wit
h both applied pressure and photoexcitation. Using a double-pump scheme we measured a lifetime of the charge transfer excitation into single valence Au$^{2+}$ of less than 4 ps, which is an indication of the local character of the Au$^{2+}$ excitation. Furthermore, the strong similarity between the pressure and fluence dependence of the phonon softening shows that the inter-valence charge transfer plays an important role in the structural transition.
We have measured the microwave conductance of mechanically exfoliated graphene at frequencies up to 8.5 GHz. The conductance at 4.2 K exhibits quantum oscillations, and is independent of the frequency.
We report the observation of a resonance in the microwave spectra of the real diagonal conductivities of a two-dimensional electron system within a range of ~ +- .0.015 $ from filling factor $ u=1/3$. The resonance is remarkably similar to resonances
previously observed near integer $ u$, and is interpreted as the collective pinning mode of a disorder-pinned Wigner solid phase of $e/3$-charged carriers .
Experimental study of quantum Hall corrals reveals Aharonov-Bohm-Like (ABL) oscillations. Unlike the Aharonov-Bohm effect which has a period of one flux quantum, $Phi_{0}$, the ABL oscillations possess a flux period of $Phi_{0}/f$, where $f$ is the i
nteger number of fully filled Landau levels in the constrictions. Detection of the ABL oscillations is limited to the low magnetic field side of the $ u_{c}$ = 1, 2, 4, 6... integer quantum Hall plateaus. These oscillations can be understood within the Coulomb blockade model of quantum Hall interferometers as forward tunneling and backscattering, respectively, through the center island of the corral from the bulk and the edge states. The evidence for quantum interference is weak and circumstantial.
