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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 3 - QUANTMATT (Dynamics and transport of quantum matter --- exploring the interplay of topology, interactions and localization)

Teaser

Summary

Any technology is based and dependent on the existence and understanding of the relevant functional materials, as is often reflected in their name: the semiconductor industry, silicon valley, and so on.
A quantum technology is reliant on a fundamental understanding of quantum matter. In quantum matter the quantum nature of the matter constituents is of paramount interest. Quantum particles, such as the electron, have a wave-like character and therefore have an associated phase. Particles moving from A to B simultaneously take all possible paths connecting the two points, with their different phase factors interfering in the process. This makes quantum particles fundamentally different from their classical counterparts, those that we encounter in daily life and know always just take one path at a time in getting between places. In a newly discovered family of materials, which we refer to as topological quantum matter, the phase factor of the electrons winds in a topologically nontrivial way---in some sense it is tied into a knot. This results in some unique electronic properties: topological insulator are bulk insulators with a stable metallic surface shell; topological semimetals (or Weyl semimetals) have unusual response to electromagnetic fields, and topological superconductors host exotic particles, called Majorana fermions, that may potentially be used in quantum computing. In another class of material, interactions between different particles results in strong correlations and entanglement. Entanglement is a unique quantum phenomena in which the state of one particle can instantaneously affect the state of another distant particle; it is also the resource needed for performing quantum computations.

The major objective of this project is to develop a fundamental understanding of the inner working of such quantum materials, and to find ways of uncovering their deep quantum nature in an experimental setup. This includes developing new computational ways of simulating quantum materials, and designing and modeling devices that allow for experimental verification of their theoretical description. Studies like this build the fundamental foundation on which the rapidly emergent quantum technology will rest.

Work performed

The project is concerned with three main classes of materials: topological insulator nanowires, Weyl semimetals and many-body localized insulators. Up till now we have published 18 research articles on these topics, including 8 on topological insulators, 4 on Weyl semimetals, 4 on many-body localized insulators. The work on topological insulators nanowires included two papers analyzing thermal transport in such wires, with one of the main results being that under certain conditions, one can obtain a current that flows from a cold reservoir to a hot reservoir, contrary to intuition. A couple of papers discussed how one can observe characteristic features of these materials in conductance noise and in other transport properties, and one more resolved an outstanding confusion about what is called the bulk-boundary-correspondence in one-dimensional topological systems. This correspondence says that depending on the properties of the bulk (or inside) properties of topological materials the surface (outside) will have certain properties; it had been observed that this correspondence sometimes fails, and we clarified why and when it does fail.

The work on Weyl semimetals first discussed the possibility of realizing what one can call a fractional Weyl semimetal, and showed that it would respond to electromagnetic fields as if the constituents of the material had a fraction of the elementary charge of an electron. We then analyzed how the resistance of a Weyl semimetal in a magnetic field can have an extremely strong dependence on the direction in which the magnetic field is pointing and discussed how this could be important for analyzing conductance measurements. We have also discussed how to construct even more exotic material, so called nodal-line Weyl semimetals, from heterostructures of Weyl semimetals. Finally we have demonstrated how certain types of Weyl material may have interesting thermal properties.

Our work on the many-body localized insulator, which is an insulator of many interacting correlated electrons, revealed how one can obtain information about the properties of the system by looking at certain one-particle properties. This allows for a clear way of obtaining information in simulations, but may also be useful for experimentally exploring these materials.

Final results

We have and are developing simulation schemes that allow us to extend our studies of quantum materials to larger system sizes and longer times of time evolution, as well as being able to study their transport properties. This is important in order to understand the underlying physics of these systems. In particular we have implemented a effective way of studying the time evolution of many-body localized insulators that are driven by an external field, for example a laser, of certain types, and are working on obtaining the quantum states of the same systems in the absence of driving. This we expect to allow us to study details of phase transitions in these systems. For Weyl semimetals, we are implementing a simulation technique that will allow us to simulate the transport properties of Weyl semimetal nanowires, in the presence of external magnetic field, that can be used to tune their properties. This will be especially important to analyze and understand recent and upcoming experiment in Weyl semimetal nanowires.