Electrons in Fractal Geometries

Project Information

FRACTAL

Grant agreement ID: 865570

DOI

10.3030/865570

Project closed

EC signature date 12 December 2019

Start date 1 September 2020

End date 28 February 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 2 718 750,00

EU contribution

€ 2 718 750,00

Coordinated by

UNIVERSITEIT UTRECHT
Netherlands

Periodic Reporting for period 3 - FRACTAL (Electrons in Fractal Geometries)

Reporting period: 2023-09-01 to 2025-02-28

Summary of the context and overall objectives of the project

The development of two-dimensional materials has enabled the discovery of new physical phenomena and led to the development of devices that are of crucial importance to our society. For example, we now base the definition of electrical resistance on the quantum Hall effect, a phenomenon exclusive to two dimensions. Similarly, the transistor that underpins every electronic device in use today relies on the manipulation of a two-dimensional electron gas. The realization that a material can have very different properties in two-dimensions compared to three-dimensions was a huge conceptual leap. In this project, a similar leap is taken: from integer (0,1,2,3) to non-integer, or fractional, dimensions. Specifically, we study (1) the properties of electrons in geometric fractals with dimension between 2 and 1. Fractals are objects that are self-similar on different length scales with two unique properties (i) a non-integer dimension and (ii) expansion symmetry but no periodicity. In addition, we aim to realize and experimentally characterize quasiparticles with fractional charge.

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

To engineer geometric fractals, and lattices with quasiparticles with fractional charge, the tip of a scanning tunneling microscope is used to position adsorbates with atomic scale precision. First, we developed a new platform to create artificial lattices, based on Cs atoms on InAs(111)A. This material system provides an energy resolution that is much superior that that of CO/Cu(111). We studied the manipulation mechanism in detail and built the first artificial lattices. Furthermore, in collaboration with the group of Prof. Allan (Leiden University and LMU Munich), we developed, tested, and implemented a new generation high-frequency preamplifier that can be used to measure shot-noise in a scanning tunneling microscope. Measuring shot-noise can provide direct access to the charge of (quasi)particles.

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)

Our new amplifier significantly outperforms previous generations and enables experiments that were previously impossible. We will use this amplifier to study a variety of systems, ranging from superconductors to artificial lattices that host quasiparticles with fractional charge.