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

Topological magnetic structures like magnetic domain walls and magnetic skyrmions are promising candidates for next generation magnetic storage devices. In contrast to current technology, the basic units of information in these structures are insensitive to continuous noisy perturbations. Quantum effects are thought to be devastating for this classical topological protection because they enable topologically nontrivial configurations to tunnel to trivial ones. It is important to realize that topological schemes for classical systems and quantum systems are fundamentally different in the sense that quantum topology is concerned with complex vector bundles that are a priori unrelated to the classical magnetic real space structure. Yet, if classical topological systems are scaled down, classical and quantum topological aspects overlap. This classic-quantum crossover has so far eluded a systematic analysis. The following two interesting questions arise. First, how can the classical topology be protected against emerging devastating quantum effects such as tunneling? Second, does the classical topology systematically induce topological quantum effects? I conjecture a general principle underlying these questions, based on my recent findings in helically magnetized atomic chains. There, I have discovered archetypal topological quantum effects in helically magnetized atomic chains, like a non-Abelian Berry connection, Kramers degeneracy, and an adiabatic quasi-particle pump. Additionally, I showed that stable magnetic helices are protected even in the deep quantum regime at singular points of the parameter space. In this proposal, I aim to study the classical-quantum crossover of noncollinearly magnetized atomic spin chains. I thereby hope to reveal a fundamental principle that connects the classical topology to induced topological quantum effects and that determines protective parameters at which the classical topology is immune against quantum effects. I furthermore intend to show how the induced topological quantum effects enable spin-chain-based quantum computing with helically magnetized chains and prove a part of the Haldane conjecture. I thereby want to establish a constructive view on the role of quantum effects on classical topology. Extending the results to more complex topological magnetic structures offers a new ground for topologically protected quantum effects with possible technological applications. Ultimately, the results can pave the way for utilizing topological magnetic storage devices based on, e.g., domain walls, magnetic helices, or magnetic skyrmions, for topologically protected quantum computing. Additionally, one could immensely scale down these devices at special parameter values without affecting their classical topological protection and functionality.

• DFG Programme: Research Grants