SCIENTIFIC ACHIEVEMENT
Using data from the Advanced Light Source (ALS), researchers found a way to reconstruct quantum geometric tensors (QGTs)—mathematical entities that encode how an electron’s wave function is shaped by its quantum environment.
SIGNIFICANCE AND IMPACT
The mapping of QGTs enables the discovery and control of novel quantum phenomena such as superconductivity and unconventional electronic phases.
Toward a second quantum revolution
The development of quantum mechanics—featuring concepts such as quantized energy levels, wave-particle duality, and the uncertainty principle—revolutionized physics in the early 20th century. It led to the rise of the wave function as a way to describe, mathematically, the quantum state of a system (such as electrons in a crystal).
A more recent development, the quantum geometric tensor (QGT) is also a mathematical entity, this time describing how wave functions are affected by changes in a material’s quantum “landscape” (e.g., the material’s structure, its topological properties, electron-electron interactions, and spin-orbit coupling). The QGT is therefore a fundamental physical concept that helps explain a range of quantum phenomena in materials. However, despite its importance, a generic method for measuring the QGT in solids has been lacking.
In this work, researchers outline a way to measure the momentum-resolved QGT of solids using angle-resolved photoemission spectroscopy (ARPES). In addition to being fundamentally interesting, the QGT is also important for potential applications in next-generation microelectronics and advanced energy technologies. Studies involving the QGT will contribute immensely to what’s been dubbed the “second quantum revolution,” focusing on the control and harnessing of quantum nature at the device scale.
Introducing the quasi-QGT
Previously, the tools available for determining the QGT could only measure momentum-integrated phenomena, which are summed over all electron momenta. However, the QGT is, by definition, momentum resolved. To overcome this problem, a collaboration—primarily between theorists from Seoul National University and experimentalists from Massachusetts Institute of Technology (MIT)—introduced a quasi-QGT that is proportional to the QGT in two-band systems and an excellent approximation in multiband systems.
Like the QGT, the quasi-QGT is a complex quantity with real and imaginary parts. However, unlike the QGT, the real and imaginary parts of the quasi-QGT correspond to quantities measurable using ARPES: the momentum-resolved effective mass of electrons (i.e., the band Drude weight) for the real part, and the orbital angular momentum (OAM) of photoemitted electrons for the imaginary part.
Read more on ALS website
Image: The curvature of the surface where it touches the sphere depicts one aspect of an electron’s quantum landscape: the momentum-resolved effective mass of electrons in a solid. In this work, researchers established that measurements of this quantity plus the orbital angular momentum of photoemitted electrons—both accessible using angle-resolved photoemission spectroscopy (ARPES)—enable the experimental reconstruction of the QGT. The sphere is shown as a local approximation to the curvature of the surface.
Credit: Comin lab/MIT