Colliding quasiparticles to reconstruct their effective Hamiltonians

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Non-technical abstract: Our national competitiveness relies on our ability to make information technology faster, more energy efficient, more compact, and more affordable. Such innovation requires the discovery and implementation of new methods to characterize and then optimize the responses of materials to electricity and light. To fully understand how electrical charges move in the extremely strong and rapidly-varying electric fields that pervade modern electronics and optics, one needs to know quantities called Bloch wavefunctions, which were derived mathematically more than 90 years ago but have resisted experimental determination. The PI and his team have recently developed a robust method to reconstruct Bloch wavefunctions from experimental data which was demonstrated on a crystalline solid. The project supports reconstruction of Bloch wavefunctions in a several semiconductors that are of current scientific and technological importance. The graduate student researchers supported by this project receive broad and deep training in experimental condensed matter physics, and in turn mentor undergraduate researchers, inspire K-12 students by giving them hands-on experience with simple electrical circuits and, upon graduation are positioned for leadership in technical fields crucial to national competitiveness. Technical abstract: For many problems in modern condensed matter physics, it is important to know both the energy eigenvalues of a quasiparticle effective Hamiltonian, as well as its Bloch wavefunctions, from which the Berry curvature can be calculated. By integrating the Berry curvature over the Brillouin zone, materials can be classified topologically. Angle-Resolved Photoemission Spectroscopy enables one to measure the band structure of many materials. However, the Bloch wavefunctions and Berry curvature, which are defined at each point in quasi-momentum space, are extremely difficult to measure. This project exploits a unique opportunity to reconstruct the effective Hamiltonian of quasiparticles in semiconductors that is enabled by the phenomenon of high-order sideband generation (HSG). HSG can be thought of as a three-step process in which (1) a weak probe laser creates electron-hole pairs, (2) a strong terahertz-frequency laser adiabatically accelerates the electrons and holes first away from and then back towards each other, and (3) the electrons and holes collide and recombine, emitting sidebands that carry off the kinetic energy associated with the collision, and on whose polarization is imprinted the Berry curvature of the bands through which the electrons and holes have been accelerated. In this project, the parameters of the effective Hamiltonian that governs quasiparticle dynamics in GaAs (including the effects of strain), GeS (a layered semiconductor), and other semiconductors will be reconstructed by comparing the calculated and measured matrices that relate the polarization of sidebands to the polarization of the probe laser that excited them.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.