
Mapping the geometry of quantum worlds: measuring the quantum geometric tensor in solids.
Quantum states are like complex shapes in a hidden world, and understanding their geometry is key to unlocking the mysteries of modern physics. One of the most important tools for studying this geometry is the quantum geometric tensor (QGT). This mathematical object reveals how quantum states “curve” and interact, shaping phenomena ranging from exotic materials to groundbreaking technologies.
The QGT has two parts, each with distinct significance:
1. The Berry curvature (the imaginary part): This governs topological phenomena, such as unusual electrical and magnetic behaviors in advanced materials.
2. The quantum metric (the real part): Recently gaining attention, this influences surprising effects like flat-band superfluidity, quantum Landau levels, and even the nonlinear Hall effect.
While the QGT is crucial for understanding these phenomena, measuring it directly has been a challenge, previously limited to simple, artificial systems.
A breakthrough now allows scientists to measure the QGT in real crystalline solids. Using an advanced technique involving polarization-, spin-, and angle-resolved photoemission spectroscopy, researchers have reconstructed the QGT in a material called CoSn, a “kagome metal” with unique quantum properties like topological flat bands. This metal forms patterns resembling a woven basket, hosting quantum effects that were previously only theorized.