It is one of the main goals of condensed matter physics to understand and classify phases of matter both because of its fundamental interest and because
useful technological advance, key to a developing society, generally relies on such a basic knowledge.
In electronic systems, like metals or insulators, different phases of matter emerge from collective behaviour of their constituent electrons.
The last decade of research has provided strong evidence that a novel class of phenomena, topological phases of matter, are important examples of these collective electronic phases.
These states are understood and classified with tools borrowed from the mathematical field of topology, unlike more familiar phases (e.g. crystals or magnets), that are classified in terms of the breaking of a continuous symmetry (e.g. space translations or spin rotations).
Topological phases cannot be destroyed by local perturbations (e.g. impurities), making them one of the most robust states of matter.
Such topological stability is thought to hold the key to important technological applications including spintronics and fault-tolerant quantum computation.
Framed in this context the Marie Curie project FRACTIONAL attempted to address three pressing issues in this field
• how and where to realize the less common topological phases from the far more common topologically trivial matter,
• formulating the general paradigm that incorporates the unique response of topological matter (both insulating and metallic) driven by external time dependent perturbations and
• foster the discovery and probing of new topological metallic phases.
Inspired by these questions this project explores how interaction, dynamical and out of equilibrium effects can i) enhance and catalyse the emergence of both known and novel topological phases and ii) drive distinct physical responses and phenomena rooted in the interplay of topology interactions and dynamics.
Implementing this project successfully relies on three important aspects: 1) the development and combination of analytical and state-of-the-art numerical tools and methods that can also provide useful input for existing and future experiments in the field,
2) a leading theoretical and experimental surrounding expertise and 3) a strong background in the field and the ability to adapt to novel emergent questions.
Period 'Nov 2015 to Nov 2017'
Part of the main goals of the project was to establish a route for the physical realization of fractionalized states of matter and establish and generalize our understanding of topological semimetals.
One of the main conclusions of this part is that it is possible to detect fractional topological insulating phases
in current experimental systems through dynamical signatures. Arrays of cold atoms are the most promising platform to implement our results.
Secondly, in this reporting period we understood topological semimetal phases, a subject that is not only driving the field but also presents formidable challenges relating to objective.
We have reported how electronic properties in these materials can be manipulated by light and strain, leading to striking predictions like an enhancement of conductivity via strain or quantization of non-linear responses.
We have also shown that via the wire construction a fractional analogue of the Weyl semimetal phase can be conceived, pushing the paradigm of topological metallic phases further.
Period 'Nov 2017 to Nov 2018'
For this period we have understood how quantised non-linear responses can occur in metals, in particular RhSi.
Also we have shown that TaAs is a material with a large second-harmonic generation.
