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Multi-Dimensional Study of non Abelian Topological States of Matter

Final 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 due 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 include quantum zero dimensional dots and anti-dots, one-dimensional quantum wires, two-dimensional planar systems, and surfaces of three-dimensional systems.

Within the five years of the project there has been significant progress both on the theoretical and on the experimental fronts of the study of non-abelian states of matter. Our project has made, we believe, essential contributions to this progress.

In zero-dimension (quantum dots and anti-dots), we study quantum interference induced by quantum anti-dots and devised the utilization of quantum dots for four terminal measurement of thermal Hall conductance. In one dimension we considered topological superconductors, which carry Majorana zero 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 invariance 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.

In between one- and two- dimensions we proposed a way to create a topological superconductor at the normal spacing between two 2D superconductors in an SNS Josephson junction, in which the normal part is subjected to spin-orbit coupling and Zeeman magnetic field. Experimental realizations of this proposal have already been reported.

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. We took part in experimental studies of thermal quantum Hall effect, showing the nu=5/2 state to be non-abelian, and explained the discrepancy between the observations and numerical calculations. Side by side, we studied manifestations of the same properties that give rise to the thermal Hall conductance in bulk quantities. 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. These states included the hard-to-grasp orbifold Quantum Hall States, and several realizations of parafermionic states. 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. These constructions included a fractionalized Weyl semi-metals and gapped states that emerge from it.

Over all, we published sixty-five works in leading scientific journals.