Quantum geometric bounds in spinful systems with trivial band topology

• URL: http://arxiv.org/abs/2501.16428v1
• Date: Mon, 27 Jan 2025 19:00:02 GMT
• Title: Quantum geometric bounds in spinful systems with trivial band topology
• Authors: Wojciech J. Jankowski, Robert-Jan Slager, Gunnar F. Lange,
• Abstract summary: We derive quantum geometric bounds in spinful systems with spin-topology characterized by a single $mathbbZ$-index protected by a spin gap. Our bounds provide unbounded geometric conditions on the spin topology, distinct from the known quantum geometric bounds associated with Wilson loops and nontrivial band topologies.
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• Abstract: We derive quantum geometric bounds in spinful systems with spin-topology characterized by a single $\mathbb{Z}$-index protected by a spin gap. Our bounds provide geometric conditions on the spin topology, distinct from the known quantum geometric bounds associated with Wilson loops and nontrivial band topologies. As a result, we obtain stricter bounds in time-reversal symmetric systems with a nontrivial $\mathbb{Z}_2$ index and also bounds in systems with a trivial $\mathbb{Z}_2$ index, where quantum metric should be otherwise unbounded. We benchmark these findings with first-principles calculations in elemental Bismuth realizing higher even nontrivial spin-Chern numbers. Moreover, we connect these bounds to optical responses, demonstrating that spin-resolved quantum geometry can be observed experimentally. Finally, we connect spin-bounds to quantum Fisher information and Cram\'er-Rao bounds which are central to quantum metrology, showing that the elemental Bi and other spin-topological phases hold promises for topological free fermion quantum sensors.

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