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Novel phases of matter emerging from topology, interactions, and symmetries

Periodic Reporting for period 3 - TopInSy (Novel phases of matter emerging from topology, interactions, and symmetries)

Reporting period: 2019-04-01 to 2020-09-30

"The discovery of how the interplay of topology and symmetry can govern quantum mechanical behaviour has reshaped our understanding of the forms matter can take. We have learned that topological insulators exist whose electrical insulation in the bulk protects a highly conducting ""skin"". Topological superconductors have been discovered where a superconducting bulk implies the emergence of novel exotic particles, so-called Majorana fermions.

These early examples are mostly based on the physics of weakly interacting electrons. They have already seen a number of striking experimental demonstrations and form the basis of exciting new lines of research, including experimental programmes towards the potential use of Majorana fermions for quantum computation.

This project investigates systems displaying phenomena governed by topology and symmetry, but where interactions play an important role. Strong interactions can not only lead to qualitatively different behaviour than that of weakly interacting electrons (including new forms of protected ""skins"" and exotic particles), but can also underpin topological phenomena based on systems with qualitatively different constituents, for example topological insulators of bosons (instead of electrons) which would be impossible without interactions.

The broad objectives of the project are: to theoretically study how the interplay of topology, interactions, and symmetries can lead to new forms of matter; how they can underpin new signatures in experiments; and to link to new directions in quantum technology."
The main directions we have been studying include: the identification of simple microscopic model systems to realise new states of matter protected by topology, interactions, and symmetries; and the prediction of novel experimental signatures arising from collective phenomena linked to symmetries and topology.

In the former strand, key results pertain to fractional topological insulators (FTIs): a two-dimensional (2D) electronic state arising from interactions, topology, and time-reversal symmetry. We have shown how precursors of this state can arise in quasi-1D ladder systems, and that, building on these precursors, such ladders may be used as ingredients towards creating 2D FTIs. We have also found that, despite being quasi-1D, such ladders already display a fractionally quantised time-reversal symmetry breaking signature that one would normally expect only in 2D.

In terms of signatures, highlights include novel transport results on interacting devices supporting Majorana fermions. Such devices are leading candidates for demonstrating fundamental features related to the potential of Majorana fermions for quantum computation. Our results include a theory of the nonequilibrium conductance, and the prediction of a series of quantised fractions of the electron charge appearing in current fluctuations. Key results on the signatures of topology, interactions, and symmetries have also been obtained for certain 1D fermion systems by utilising a new link between the physics near the boundaries of these and a recently introduced interaction-only model for the holographic principle. We have shown that this model has symmetry classification with structure organised around new multiparticle cousins of Majorana fermions. These, in turn, furnish novel signatures indicative of the topological character of the respective fermion chains.
Our fractional topological insulator findings provide the first microscopically informed results on this state of matter that go beyond systems of a few particles. They introduce a paradigm of how the theoretical control over microscopic ladder models may allow developing routes to creating interacting, higher dimensional, topological states protected by symmetries, and how breaking these symmetries may be used to furnish new signatures already in the quasi-1D limit. Our work on interacting Majorana fermion devices introduces a novel approach based on exact solutions that makes it possible to describe such devices in nonequlibrium situations. This may be be useful in analysing future experiments for diagnosing topological qubits, the fundamental ingredients for Majorana-based quantum information processing.