TOPOLOGICAL PHASES OF MATTER IN CRYSTALS AND SUPERCONDUCTING QUANTUM CIRCUITS

Abstract

Topological states and topologically ordered phases are a cornerstone of physics, with applications ranging from quantum materials to quantum error correction. The robust quantum properties of topological materials may be harnessed for technology. On the other hand, topological order is a powerful tool for the storage and manipulation of quantum information with high fidelity. In this dissertation, I describe the experimental observation of many topological phases of matter using photoemission spectroscopy and quantum simulation. To start, I focus on magnets with a kagome crystal structure, where quantum interference generically leads to Dirac crossings and flat bands. In quasi-two dimensional TbMn$_6$Sn$_6$, a Chern gapped state is evidenced by photoemission band structure maps, a Landau fan in tunneling spectroscopy data, and in-gap edge states. Then in the three-dimensional kagome ferromagnet Co$_3$Sn$_2$S$_2$, the annihilation of Weyl points is demonstrated through careful photoemission measurements with varying temperature. Next, I explore an extension of Weyl semimetals: higher-fold chiral semimetals. These materials host fermionic excitations that cannot be described by the standard model, where bands with large Chern number give rise to long helicoid Fermi arcs. In the topological chiral crystal Ni$_x$Rh$_{1-x}$Si, I fully characterize a higher-fold fermion by imaging all relevant bulk bands and extracting the Chern number of each band gap through the bulk-boundary correspondence. Then in stoichiometric RhSi and CoSi, I demonstrate a generic behavior of Fermi arcs to generate van Hove singularities. These van Hove points may be important for generating correlated states, such as the charge order recently observed in CoSi. The large topological nontrivial energy window in these compounds is also advantageous to search for quantized optical response. Finally, I present results from a Google superconducting quantum processor demonstrating the quantum simulation of $\mathbb{Z}_2$ lattice gauge theory, which is equivalent to the toric code in the zero-field limit. The quantum dynamics in topological and trivial phases show deconfined and confined behavior, respectively. In addition, because the simulation is in two bona fide spatial dimensions, our protocol can be leveraged to visualized the dynamics of a Wegner-Wilson string. String breaking is also observed. With the field of topological quantum materials headed toward ever more correlated platforms, the need for precise many-body quantum simulation techniques is paramount. At the same time, breakthroughs in quantum materials may put forward superior platforms for quantum computing. This dissertation promotes the budding synergetic relationship between quantum matter and quantum computers.