Controlling Quantum Materials: Exotic Orders and Light-Induced Dynamics

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What principles governs the collective quantum behaviour of electrons in a crystalline solid? Can one tune quantum phases of electrons by controlling dimensionality? Can light be used to control and switch between many-body quantum states of electrons? Exploring these important issues is crucial to gain a fundamental understanding of quantum condensed matter systems, and it holds the key to creating and controlling quantum materials which can lay the foundation for the next generation of quantum technologies. The equilibrium and dynamical properties of electrons in crystals are governed by the laws of quantum mechanics, together with quantum statistics as encoded in the Pauli exclusion principle. Examples of such crystals, which include silicon, the workhorse of the semiconductor industry, are extremely well-understood within the framework of band theory and Fermi liquid theory. However, when strong electron interactions become important in a crystal, the electrons can organize into remarkable new states leading to superconductivity, colossal magnetoresistance, or electronic liquid crystals. Transition metal oxides provide a canonical example of such ``emergent'' behavior, exhibiting a plethora of new collective phases, with a slew of applications such as solid state drives, catalysts, and photovoltaics. In recent years, it has been recognized that relativistic spin-orbit coupling can impart new topological character to electronic bands in solids with the potential for novel devices and the promise of new directions in the field of quantum computing. The five-year research programme outlined in this proposal focuses on two intertwined threads of research. The first thread aims to explore and understand the optical properties of exotic orders which appear in quantum materials such as heavy transition metal oxides, halides, and chalcogenides. These are quantum materials which exhibit strong atomic spin-orbit coupling, which leads to the emergence of topological phases, unconventional superconducting and magnetic orders, both in bulk crystals as well in two-dimensional thin films and interfaces. The second intertwined thread of the research deals with how one might control and manipulate such quantum materials and their electronic phases using light. The proposed research will focus on optical properties such as THz conductivity and Kerr effects, ultrafast pump-probe dynamics, and switching between electronic states of matter using optically driving of phonon modes. The proposed research will utilize numerical tools including Gutzwiller projected wavefunction techniques, high frequency expansions, strong coupling expansions, and novel methods to treat the dynamics of correlated electrons.