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
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."
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.