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Abstract: A fundamental probe of electrons in solids is charge transport, that is the motion of particles under the influence of external fields. For over a century, transport measurements have served as an indispensable tool for examining quantum effects in condensed matter. Among transport triumphs are superconductivity, magnetism, ferroelectricity and topological properties of materials.

Recently, theoretical and experimental efforts have been focused on understanding transport phenomena and by extension collective electronic behavior through the lens of geometry: reintroducing concepts familiar from general relativity and other areas of physics and mathematics to the study of coherent electron propagation in solids. This is now broadly termed "quantum geometry".

Here, I will review the strides made in this direction. I will show how geometric objects (such as metrics and curvatures) naturally appear in observables such as charge conductivities, electron-lattice coupling and the capacitance of insulators. I will then present recent breakthrough in understanding quantum geometry through particular emphasis on nonlinear charge current response and real-space imaging probes such as Scanning-Tunneling microscopy. I will survey new materials that have challenged our prevailing understanding of transport: topological antiferromagnetic metals and unconventional superconductors in transition-metal dichalcogenides.

Fundamentally, I will explain how optical responses and light-matter interaction are connected with the (non-trivial) metric and curvature of electronic wavefunctions in periodic systems. This allows using optical probes for sensitive examination of symmetries in correlated states of matter — such as superconductors. I will present an example in which photocurrents directly sense the order parameter of high-temperature superconductors.

As an outlook, I will show practical and conceptual advances that are enabled by quantum geometry: sliding ferroelectricity, vibrational anharmonicity in solids and optical rectification by magnets. I will conclude by demonstrating a novel notion of a metric in neural networks which has been used to predict two novel superconductors using AI.

Hosted by Professor Rufus Boyack

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https://dartmouth.zoom.us/j/93672234574?pwd=lXV2bhO5mDoPEVrBkFArmIFPbP7aC8.1

Meeting ID: 936 7223 4574
Email Physics.Department@dartmouth.edu for passcode