Measurement of Topological Order based on Metric-Curvature Correspondence

Abstract

A unified expression for topological invariants has been proposed recently to describe the topological order in Dirac models belonging to any dimension and symmetry class. We uncover a correspondence between the curvature function that integrates to this unified topological invariant and the quantum metric that measures the distance between properly defined many-body Bloch states in momentum space. Based on this metric-curvature correspondence, a time-resolved and angle-resolved photoemission spectroscopy experiment is proposed to measure the violation of spectral sum rule caused by a pulse electric field to detect the quantum metric, from which the topological properties of the system may be extracted.

arXiv comment8 pages, 2 figures

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Cited by in corpus (7)

• Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers
• Nontrivial quantum geometry of degenerate flat bands
• Universal topological marker
• Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker
• Probing Chern number by opacity and topological phase transition by a nonlocal Chern marker
• Quantum optics measurement scheme for quantum geometry and topological invariants
• Optical absorption measurement of spin Berry curvature and spin Chern marker