Parafermionic zero modes are non-Abelian excitations which have been predicted to emerge at the boundary of topological phases of matter. Contrary to earlier proposals, here we show that such zero modes may also exist in multi-legged star junctions o
f quantum Hall states. We demonstrate that the quantum states spanning the degenerate parafermionic Hilbert space may be detected and manipulated through protocols employing quantum anti-dots and fractional edge modes. Such star shaped setups may be the building blocks of two-dimensional parafermionic networks.
Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of quantum Hall
phases, and time-reversal invariant topological insulators. Here we study the edge of a 2D, topologically trivial insulating phase, as a function of the strength of the electronic interactions and the steepness of the confining potential. For sufficiently smooth confining potentials, alternating compressible and incompressible stripes appear at the edge. Our findings signal the emergence of gapless edge modes which may give rise to finite conductance at the edge. This would suggest a novel scenario of a non-topological metal-insulator transition in clean 2D systems. The incompressible stripes appear at commensurate fillings and may exhibit broken translational invariance along the edge in the form of charge density wave ordering. These are separated by structureless compressible stripes.
Protected edge modes are the cornerstone of topological states of matter. The simplest example is provided by the integer quantum Hall state at Landau level filling unity, which should feature a single chiral mode carrying electronic excitations. In
the presence of a smooth confining potential it was hitherto believed that this picture may only be partially modified by the appearance of additional counterpropagating integer-charge modes. Here, we demonstrate the breakdown of this paradigm: The system favors the formation of edge modes supporting fractional excitations. This accounts for previous observations, and leads to additional predictions amenable to experimental tests.
The magnetic flux periodicity of $frac{hc}{2e}$ is a well known manifestation of Cooper pairing in typical s-wave superconductors. In this paper we theoretically show that the flux periodicity of a two-dimensional second-order topological superconduc
tor, which features zero-energy Majorana modes localized at the corners of the sample, is $frac{hc}{e}$ instead. We further show that the periodicity changes back to $frac{hc}{2e}$ at the transition to a topologically trivial superconductor, where the Majorana modes hybridize with the bulk states, demonstrating that the doubling of periodicity is a manifestation of the non-trivial topology of the state.
The interface between the two insulating oxides SrTiO$_3$ and LaAlO$_3$ gives rise to a two-dimensional electron system with intriguing transport phenomena, including superconductivity, which are controllable by a gate. Previous measurements on the (
001) interface have shown that the superconducting critical temperature, the Hall density, and the frequency of quantum oscillations, vary nonmonotonically and in a correlated fashion with the gate voltage. In this paper we experimentally demonstrate that the (111) interface features a qualitatively distinct behavior, in which the frequency of Shubnikov-de Haas oscillations changes monotonically, while the variation of other properties is nonmonotonic albeit uncorrelated. We develop a theoretical model, incorporating the different symmetries of these interfaces as well as electronic-correlation-induced band competition. We show that the latter dominates at (001), leading to similar nonmonotonicity in all observables, while the former is more important at (111), giving rise to highly curved Fermi contours, and accounting for all its anomalous transport measurements.
We propose a setup for the experimental realization of unexpected and anisotropic $0$-$pi$ transitions of the Josephson current, in a junction whose link is made of irradiated Weyl semi-metal (WSM), due to the presence of chiral nodes. We show using
a Greens function technique that the Josephson current through a time-reversal symmetric WSM has anisotropic periodic oscillations as a function of $k_0L$, where $k_0$ is the (relevant) separation of the chiral nodes and $L$ is the length of the sample. This is unexpected, for time-reversal symmetric systems, although it has been shown earlier for time-reversal symmetry breaking WSMs. We then show that the effective value of $k_0$ can be tuned with precision by irradiating the sample with photons resulting in $0$-$pi$ transitions of the critical current. Finally, we discuss the robustness of our setup.
