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Fractional Report Summary

Project ID: 653846
Funded under: H2020-EU.1.3.2.

Periodic Reporting for period 1 - Fractional (Fractionalized quantum matter: Characterization, realization and generalization)

Reporting period: 2015-11-02 to 2017-11-01

Summary of the context and overall objectives of the project

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 can emerge from collective behaviour of their constituent electrons.
The last decade of theoretical and experimental research in condensed matter has provided strong evidence that a novel class of phenomena, topological phases of matter, are a significant and 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). Just like a sphere cannot be deformed with local deformations into a torus, 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. These phases represent a novel paradigm in our understanding and way of classifying fundamental phases of matter, a cornerstone of condensed matter physics. 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 proposed to explore, through concrete innovative ideas 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.

Conclusions for the report 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.
On the one hand the project has focused on their response to external perturbations as signatures of experiment. 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, this reporting period was largely employed to understand 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.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Report period: November 2015 to November 2017

During the first two years of the project the Fellow, jointly with members the Physics department at the University of California Berkeley, have focused on addressing one of the main objectives of the project
namely formulating the general paradigm that incorporates the unique response of topological matter (both insulating and metallic) driven by external time dependent perturbations.
The forefront of research to achieve this goal concerns the study of systems known as Weyl semimetals. In these systems, electrons behave as Weyl fermions, a type of particle that was predicted as a fundamental entity that now emerges as a collective degree of freedom of electrons in these materials. Related to the FRACTIONAL there are two specific fronts we considered. The first is the effect of external perturbations to transport and optical responses, key to possible applications. We considered non-linear effects under circularly polarised light, such as the circular photo galvanic effect. We predicted to be quantised and large. Research in non-linear optics can lead to novel photo-dectors and emitters, key to modern technologies.
We have also unveiled the nature of novel transport anomalies triggered by strain effects and thermal effects. This was an unexpected spin-off of the project that resulted in two important publications, one published in Nature while the other was published in Phys. Rev. X.
Finally, we addressed another leg of the project, interacting topological systems out of equilibrium, using state-of-the art density matrix renormalisation group. We showed explicitly the dynamics of edge states in a fractional Chern insulator, which were not addressed previously.

During the two implemented within the partner institution the Physics department at the University of California Berkeley, the Fellow has produced 11 research works,
one outreach article, has attended 10 international conferences and presented his research at different institutions through formal and informal seminars (see appendix for details).

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Report period Nov 2015 to Nov 2017

The main scientific progress beyond the state of the art can be summarised as follows:

1) Prediction of a non-linear quantized effect in Weyl semimetals, driven with circularly polarised light. Prediction of the use of heating as a probe of the linear Quantum Hall effect.
2) Numerical study of the edge dynamics of a fractional quantum Hall state using density matrix renormalization group.
3) Proposal of the generation and physical effects of axial gauge fields in Weyl semimetals.
4) Theory and observation of the elusive axial-gravitational anomaly in Weyl semimetals.

Expected results:

1) A deeper understanding of the degree of protection of novel non-linear quantized effects. Study of the origin of the large magnitude of the second harmonic generation
2) Study of global quenches out of equilibrium
3) Aid to experimentally observe axial gauge fields in Weyl semimetals.
4) A deeper understanding between the connection of thermal and gravitational physics.

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