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MUNATOP Report Summary

Project ID: 340210
Funded under: FP7-IDEAS-ERC
Country: Israel

Mid-Term Report Summary - MUNATOP (Multi-Dimensional Study of non Abelian Topological States of Matter)

Non-abelian topological states of matter are of great interest in condensed matter physics, both due to their extraordinary fundamental properties and to their possible use for quantum computation. The insensitivity of their topological characteristics to disorder, noise, and interaction with the environment may lead to realization of quantum computers with very long coherence times. The realization of a quantum computer ranks among the foremost outstanding problems in physics, particularly in light of the revolutionary rewards the achievement of this goal promises. We have proposed a theoretical multi-dimensional study. On the methodological side the multi-dimensionality is in the breadth of the studies we discuss, ranging all the way from phenomenology to mathematical physics. On the concrete side, the multi-dimensionality is literal.

The systems we considered so far include quantum dots and anti-dots, one dimensional quantum wires, two dimensional planar systems, and surfaces of three dimensional systems. In one dimension we considered topological superconductors, which carry Majorna end modes. We proposed several novel experimental techniques to identify these modes. We analyzed their properties in situations where they occur in pairs, due to symmetry to time reversal. Further in one dimension we searched for situations under which quantum wires may show precursors of the exotic topological order that exists in two dimensions in fractionalized systems.

We studied several measurable transport properties occurring on the one dimensional edges of two dimensional topological states of matter, such as fractional quantum Hall states. In a similar context we studied the possible coexistence of edge states and gap-less bulk in topological states. On the more theoretical side, we elaborated on ways to describe fractionalized topological states of matter in high dimensions in terms of coupled wires. We have proposed theoretically a way to construct a universal topological quantum computer by combining superconductors and fractional quantum Hall systems [20].

In 3D systems we studied experimentally-relevant issues such as the excitation spectrum and charge distribution of a thin 3D topological insulator and the non-local transport properties of Weyl semi-metals. On the more theoretical side we studied anomalous quasi-particles symmetries on gapped surfaces of weak topological insulators and mathematically constructed three dimensional fractional topological states form a set of coupled wires.

Over all, we published twenty-two works in leading scientific journals.

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