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Novel topological phases of matter: From topological invariants to experiments

Periodic Reporting for period 1 - NovelTopo (Novel topological phases of matter: From topological invariants to experiments)

Reporting period: 2016-09-01 to 2018-08-31

When macroscopic quantum systems are cooled down to temperatures close to absolute zero, new phases of matter emerge from the collective organization of their microscopic constituents. Topological phases are among the most exotic states of quantum matter that emerge in this way. These phases of matter are distinguished from every other by the fact that their ground state wavefunction is characterized by a topological invariant that guarantees many special physical properties. While several proposed such phases have been studied since decades, the recent realization of topological insulators has kicked off a series of discoveries greatly enlarging the amount of topological phases at our disposal. These materials can be exploited for many applications, for example in spintronics, and can serve as a platform to realize even more exotic phases like topological superconductivity and Majorana fermions, the key building block of a topological quantum computer. The purpose of this project is to identify novel, robust properties of topological phases that can serve to identify them, to motivate material realizations of these phases by making predictions for realistic materials, and to collaborate with experimentalists in the discovery of such materials and their properties.

The objectives of the project are as follows. First, we aim to propose novel platforms for the realization and manipulation of Majorana fermions. A particular focus is on platforms that may realize a large number of coupled Majorana states, that can open the path to realize the holographic Sachdev-Ye-Kitaev model. Second, we will determine the unique signatures that characterize topological Weyl semimetals. Specific aims include to study how the monopole charge of a Weyl semimetal can be accessed experimentally via photocurrent effects, and to study generalizations of Weyl semimetals in chiral lattices where the effect can be observed. A general analysis of the topological structure of photovoltaic responses will be performed to identify further robust signatures of other topological phases. Finally, the third objective is to study smoking gun signatures of magnetic Weyl semimetals, such as the Anomalous Hall Effect and the dynamics of spin-waves coupled to Weyl fermions, in the magnetic material EuCd2As2.
The main results achieved in this project are:

- The prediction of a quantized photocurrent that depends only on fundamental constants for a class materials known as chiral Weyl semimetals. This represents the first prediction of a response that measures topological invariants in metals, and in non-linear response.
- A full classification of topological chiral band crossings beyond Weyl points, a proof that the photogalvanic effect remains quantized in a range of energies for any topological semimetal featuring such crossings, and predictions of new materials with such properties.
- A collaboration leading to the experimental discovery of fourfold and sixfold chiral crossings in a material with space group 198 with Angle Resolved Photoemission Spectroscopy. This is the first experiment reporting any chiral topological semimetal, and it opens the door to the observation of the quantized photogalvanic effect.
- A proposal to realize the Anomalous Hall Effect of magnetic Weyl semimetals in EuCd2As2, a model Weyl system with only two Weyl points at the Fermi level. Result include a model Hamiltonian that may be used by the community for many purposes, AHE predictions, and an experimental confirmation with ARPES and transport experiments.
- A proposal to realize the non-superconducting version of the Sachdev-Ye-Kitaev model of interacting zero modes in mesoscopic graphene under a magnetic field, which is realizable with current technology.
- A detailed account of how Majorana fermions emerge in topological insulator nanowires coated with superconductors, which corrects a previous misunderstanding in the literature and can lead to more robust devices for Majorana manipulation.
- A collaboration leading to the identification of TaSb2 as weak topological insulator with Angle Resolved Photoemission Spectroscopy.

These results have been disseminated to the academic community in peer reviewed publications in Nature Communications, Physical Review Letters and Physical Review B. All papers produced in the project have been archived in the ArXiv repository to comply with the open access policy and to ensure maximum accessibility. Additionally, the latest results are only available in the ArXiv or will be as soon as they are accepted in a journal.

These results were also disseminated in seminars and conferences. Local seminars included the Condensed Matter Seminar series in Oxford and the Atomic and Laser Physics group meeting. Conferences included: Frontiers in Condensed matter, University of Bristol, Symposium in quantum materials, University of Oxford, Meeting of the Condensed Matter Division of the Spanish Royal Physical Society, University of Valencia, and Quantum Desginer Physics conference, Donostia International Physics Center.
Progress beyond the state of the art and results until the end of the project are described in the paragraph above. This section describes the potential academic, societal and economic impact.

In the academic context, the results of this project will be of great benefit to many research groups in the European Research Area and internationally, as there is growing interest in the field of topological phases of matter. The dissemination of results in conferences and seminars ensures these results have maximum impact and enable other research groups to build on them further. By boosting the researcher’s career and enabling him to secure a tenure-track position in the ERA, the action also contributes to making Europe a leading research hub for topological phases of matter. The network of researchers developed during the fellowship, in particular connecting theory and experiment, as well as the knowledge and skills acquired, will stay in the ERA and contribute to its research excellence. In addition, the action has also increased the ERA’s training capability, as the researcher will now start a group where PhD students and postdocs can be trained in the skills and knowledge acquired during the action.

Regarding societal and economic impact, the results of this action contribute to the progress of several fields that may lead to unprecedented technological developments. In particular, one of the results of this action is a prediction for a bulk photovoltaic effect intrinsic to topological semimetals, which required delving deeply into the theory of bulk photovoltaics. While the current results did not aim at applications, in the long term this developing body of knowledge may allow researchers to identify new materials and devices that may compete current solar cell technology, perhaps even based on the current materials hosting topological phases. Several other results in this project propose new ways to manipulate Majorana quasiparticles, which can be used as a platform to realize topological qubits. In the long term, a sustained research effort in this direction may yield a viable, scalable way to use anyons to build a quantum computer, which would have tremendous impact in solving many optimization problems and in quantum simulation.
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