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Theory of Non-Linear 2D Spectroscopy for Topological Quantum Matter
[Technical Report, Final Report]
Pohang University of Science and Technology
Pagination or Media Count:
During the project, we have focused on diagnosing the nature of exotic many-electron topological states in theory and experiment and exploring novel experimental setups of realizing them, which have potential uses in quantum technology. For the detection of the states in theory, guided by the linearnon-linear responses of topological states, we have developed novel many-body topological invariants for Chern insulator, chiral hinge insulators, and also several 2D higher-order topological insulators, which are calculable in numerical simulations. Furthermore, we have designed the detection scheme for the useful quantum states in experiments, i.e. non-Fermi liquids and topological Weyl semimetals from the linear response, crystalline topological band insulators from their resonant inelastic x-ray scattering intensity. These all provide valuable contributions to the detection of the exotic quantum states which receive a huge attention from the community. Not only this, our team also explored the new experimental setups, which may be helpful in realizing interesting quantum states. For instance, we have demonstrated the realization of the steady Floquet states in low-dimensional Andreev qubit setups, which opens up a new route to explore the non-equilibrium many-body quantum states. This may be very useful in controlling the qubits via the microwaves. Another interesting setup was the twisted Josephson junctions between the two high-Tc superconductors, which was speculated to realize the time-reversal invariant topological superconductors. However, we have disproved this claim and shown that it is actually a regular d-wave superconductor. In the submitted drafts, we have investigated high temperature excitonic condensate in the quantum Hall setups of large-angle twisted bilayer graphene, and non-linear optical response to diagnose the Dirac fermion in graphene.
[A, Approved For Public Release]