Measurements of the quantum geometric tensor in solids

Abstract

Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is at the core of modern physics. The Quantum Geometric Tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state. The imaginary part of the QGT is the well-known Berry curvature, which plays a fundamental role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence very recently, giving rise to a new set of quantum geometric phenomena, such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts, and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. In this work, we develop a framework to measure the QGT (both quantum metric and Berry curvature) in crystalline solids using polarization-, spin-, and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in solids in the archetype kagome metal CoSn, which hosts topological flat bands. The key idea is to introduce another geometrical tensor, the quasi-QGT, whose components, the band Drude weight and orbital angular momentum, are experimentally accessible and can be used for extracting the QGT. Establishing such a momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.

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Cited by in corpus (29)

• Contrasting Light-Induced Spin Torque in Antiferromagnetic and Altermagnetic Systems
• Kagome metals
• Quantum Geometry and the Hidden Scales in Materials
• Anomalous geometric transport signatures of topological Euler class
• Quantum response theory and momentum-space gravity
• Quantum geometry and $X$-wave magnets with $X=p,d,f,g,i$
• Quantum geometry and the electric magnetochiral anisotropy in noncentrosymmetric polar media
• Structure factors and quantum geometry in multiband BCS superconductors
• Quantum geometric bounds in spinful systems with trivial band topology
• Quantum Geometric Tensor for Mixed States Based on the Covariant Derivative
• Effects of the Hubbard interaction on the quantum metric
• Scattering makes a difference in circular dichroic angle-resolved photoemission
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• Quantum geometric tensors from sub-bundle geometry
• Universal intrinsic orbital dynamics from Berry curvature in electronic two-band systems
• Semi-classical geometric tensor in multiparameter quantum information
• Quantum geometry, localization, and topological bounds of spin fluctuations
• Spin-orbital mixing in the topological ladder of the two-dimensional metal PtTe${}_2$
• Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor
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• Linear thermal noise induced by Berry curvature dipole in a four-terminal system
• Orbital magnetization reveals multiband topology
• Quantum geometric tensor in systems with fractional band dispersion
• Superconductivity and geometric superfluid weight of a tunable flat band system
• Correlation lengths of flat-band superconductivity from quantum geometry
• Evolution of quantum geometric tensor of 1D periodic systems after a quench
• Intertwined geometries in collective modes of two dimensional Dirac fermions
• Circular dichroism in the photoelectron angular distribution of achiral molecules