Discoveries of New Topological States of Matter Beyond Topological Insulators

Abstract

The discoveries of new forms of matter have been so definitive that they are used to name periods in the history of mankind, such as Stone Age, Bronze Age, and Iron Age. Although all matter is composed of component particles, particles can organize in various ways leading to different phases of matter. Finding all possible distinct phases that matter can form and understanding the physics behind each of them are fundamentally important goals in physics research and often lead to new technologies, benefiting our society. A topological phase is an unusual type of crystalline solid, characterized by a nontrivial topological number. This number is a global quantity, which depends on the crystal's bulk electronic wavefunctions. In 2007, the 3D $Z_2$ topological insulator (TI) phase was discovered in bismuth-based materials, marking the first realization of a topological phase in bulk crystals. A 3D TI features spin-polarized Dirac electronic states on its surface, which enjoys a robust protection against disorder. This discovery tremendously accelerated the field and led to a surge of interest in searching for new topological phases of matter.

In this thesis, we present the experimental discovery of several new topological phases and phenomena beyond the $Z_2$ TI, including the topological quantum phase transition in BiTl(S$_{1-\delta}$Se$_{\delta}$)$_2$, the topological crystalline insulator phase in Pb$_{1-x}$Sn$_x$Te(Se), the topological Dirac semimetal phase in Cd$_3$As$_2$ and Na$_3$Bi (featuring Fermi arc surface states), evidence for the topological Kondo insulator state in SmB$_6$, and the demonstration of superconductivity and magnetism in the surface states of the prototypic TI Bi$_2$Se$_3$. Each of these new states exhibits topological surface states with unique protected properties. They may be useful in developing future technologies such as fault-tolerant topological quantum computers and low-power spintronic devices, which will revolutionize our electronic and energy industries. The new topological states of matter presented here are currently being studied by many groups worldwide. With our discoveries, the ``topological world'' has begun to unveil itself. We believe that this is only the tip of the iceberg. Our ongoing work suggests that there are many more with yet more exciting properties awaiting discovery.