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Fractional Phases and Non-Abelian Anyons in Quantum Wires

Final Report Summary - FRACWIRE (Fractional Phases and Non-Abelian Anyons in Quantum Wires)

Topological states of matter are distinguished from conventional phases, such as magnets, crystals, and superconductors, which are classified according to Landau's paradigm of symmetry breaking. Instead, topological states show measurable phenomena such as quantized Hall conductivity which is due to emergence of metallic edge states at the surfaces of these materials that are insulators at their bulk. For example, two-dimensional (2D) topological insulators have one dimensional modes at their edges. In these edges counter-propagating modes are related by time reversal and carry opposite spin, hence they are termed ``helical states". When properly subjected to proximity coupling to superconductors and ferromagnets these edges are predicted to host localized zero energy Majorana modes.

Majorana fermions are particles that are their own antiparticles, and remarkably they may emerge in condensed matter systems. These observations attracted a lot of attention recently as, in contrast to known particles, fermions or bosons, when the Majorana particles are exchanged, the state of the system is modified, making these particles non-Abelian anyons. These particles form the seed requirement for a reliable topological quantum computer.

In two-dimensions interactions between electrons may give rise to fractionalized phases, where their elementary excitations have fractional quantum numbers, e.g. a fraction of the electron charge. Furthermore, in 2D counter-propagating edge modes may occur in fractionalized phases as well. In this research program we explore new directions to create, control and probe fractionalized phases stabilized by electron-electron correlations. The main novel ingredient that we apply is the recent theoretical understanding that general topological phases can be constructed via coupling of one dimensional quantum wires. Our approach is theoretically transparent and allows for new developments towards better implementations of fractional abelian and non-abelian states in experiments.

In the first part of this project we developed a general approach establishing that generic fractionalized phases can be constructed via a collection of coupled wires. This includes fractional topological insulators and the chiral spin liquid, which is currently under intense research both in theory and experiment. Secondly, we demonstrated that such fractionalized phases which were previously believed to live only in 2D, can be constructed directly in quasi-1D structures. This includes quantum wires with strong spin-orbit coupling and yield a new state that we term "fractional helical liquid". These systems have unusual properties e.g. their electrical conductance. We have shown theoretically that in proximity to superconductors and ferromagnets the counter-propagating 1D helical modes may be gapped to host localized fractionalized Majorana modes, that are non-abelian anyons of a new type.

These achievements allowed us to reach important goals in the second part of this research including detectable signatures of fractionalization in one dimension, manipulation of fractional charges and anyons, and finding new systems carrying non-Abelian excitations, both electronic and magnetic. The final goal is to bring these ingredients closer to a physical realization of an operating quantum computer based on Majorana fermions.