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The classical-quantum crossover of topological protection

Applicant Dr. Thore Posske
Subject Area Theoretical Condensed Matter Physics
Term from 2019 to 2024
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 420120155
 
Final Report Year 2024

Final Report Abstract

Recently, researchers suggested to use twisted magnets for increasing the storage density of hard drives. For instance magnetic helices, where the magnetism follows a spiral, or their 2D versions, the magnetic skyrmion, are magnetic knots that cannot easily be unwound by unwanted environmental perturbations. This makes the storage robust. The concrete form of these objects is of no relevance, just their presence. They are therefore called topological excitations. They can also be tiny, of the size of nanometers. Therefore, quantum mechanics starts playing an important role for them. This project describes the transition between classical and quantum topological magnetism. The main objectives of the project were to identify robust physical effects that can be used for technological advances and develop a suitable theory. In this project, we could show that topological quantum magnetism in magnetic chains (1D) and grids (2D), is significantly more robust against environmental perturbations than topologically trivial states, e.g., ferromagnetism. Also, 2D topological excitations, i.e., the quantum skyrmion, can be prepared robustly by controlling the boundary magnetization. However, we also showed that perturbations of topological quantum magnets still unavoidably induce decay to topologically trivial states by quantum entangled states that let the local magnetization vanish. Instead, with growing system size, we identified topological sectors of, e.g., no winding, one winding, etc., that potentially make topological quantum magnetism interesting for technological applications. Theoretical progress was furthermore made in developing a general theory of product eigenstates in quantum Heisenberg models. These states have recently been discovered in ultracold atomic systems. We extend the theory of these states to Heisenberg models in any dimension and identify an exotic mid-spectrum condensate in special systems that has a large degeneracy. We also found a generalized magnetic particle pump with arbitrary periodicity in fine-tuned quantum systems. As a byproduct to the description of quantum magnetism, the project revealed several electronic states on the surface of superconductors. These include topologically nontrivial one-dimensional superconducting bands, precursors of Majorana modes, and the 50-year-ago predicted Machida-Shibata state, which describes proximity-induced superconductivity in a twolevel system. Our findings thereby how classical concepts about topological magnetism need to be adjusted when quantum effects become dominant and reveal previously unknown fundamental quantum effects and excitations.

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