Essay : Where Can Quantum Geometry Lead Us

Loading...
Thumbnail Image

Access rights

openAccess

URL

Journal Title

Journal ISSN

Volume Title

A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Date

2023-12-15

Major/Subject

Mcode

Degree programme

Language

en

Pages

7
1-7

Series

Physical Review Letters, Volume 131, issue 24

Abstract

Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry, including the amplitude distance characterized by the quantum metric, has started to receive attention in the last few years. Various quantum transport and interaction phenomena have been found to be critically influenced by quantum geometry. For example, quantum geometry allows counterintuitive flow of supercurrent in a flat band where single electrons are immobile. In this Essay, I will discuss my view of the important open problems and future applications of this research topic and will try to inspire the reader to come up with further ideas. At its best, quantum geometry can open a new chapter in band theory and lead to breakthroughs as transformative as room-temperature superconductivity. However, first, more experiments directly showing the effect of quantum geometry are needed. We also have to integrate quantum geometry analysis in our most advanced numerical methods. Further, the ramifications of quantum geometry should be studied in a wider range, including electric and electromagnetic responses and interaction phenomena in free- and correlated-electron materials, bosonic systems, optics, and other fields.Part of a series of Essays which concisely present author visions for the future of their field.

Description

Funding Information: P. T. would like to acknowledge discussions with Milan Allan, Andrei Bernevig, Dmitri Efetov, Ion Errea, Pertti Hakonen, Kristjan Haule, Tero Heikkilä, Kukka-Emilia Huhtinen, Miguel Marques, Andrew Millis, and Sebastiano Peotta, and funding from the Academy of Finland under Project No. 349313, as well as funding from the SuperC Collaboration through the Jane & Aatos Erkko Foundation, Keele Foundation, and Magnus Ehrnrooth Foundation. Publisher Copyright: © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Keywords

Other note

Citation

Törmä, P 2023, ' Essay : Where Can Quantum Geometry Lead Us ', Physical Review Letters, vol. 131, no. 24, 240001, pp. 1-7 . https://doi.org/10.1103/PhysRevLett.131.240001