Excursions in Ill-Condensed Quantum Matter: From Amorphous Topological Insulators to Fractional Spins

Description

Impurities, disorder or amorphous systems – ill-condensed matter – are mostly considered inconveniences in the study of materials, which is otherwise heavily based on idealized perfect crystals. The Kondo effect and the scaling theory of localization are among the fundamental and early discoveries which revealed the novelty hidden in impure or disordered systems. Recent advances in condensed matter physics have emphasized the role of topology, spin-orbit coupling, and certain discrete symmetries such as time reversal in many physical phenomena. These have irreversibly transformed the essential ideas and purview of condensed matter physics, both in theoretical and experimental directions. However, many of these recent developments and their implications are limited to, or by, ideas that pertain to clean systems. This thesis deals with various aspects of these new developments, but in the case of unclean systems. The author introduces new ideas such as amorphous topological insulators, fractalized metals and fractionalized spins. Front Matter ....Pages i-xxiii Introduction (Adhip Agarwala)....Pages 1-31 Tenfold Way (Adhip Agarwala)....Pages 33-59 Topological Insulators in Amorphous Systems (Adhip Agarwala)....Pages 61-79 Seeking Topological Phases in Fractals (Adhip Agarwala)....Pages 81-92 Killing the Hofstadter Butterfly (Adhip Agarwala)....Pages 93-108 Fractional Spins and Kondo Effect (Adhip Agarwala)....Pages 109-123 Structure of Many-Body Hamiltonians in Different Symmetry Classes (Adhip Agarwala)....Pages 125-152 Epilogue (Adhip Agarwala)....Pages 153-157 Back Matter ....Pages 159-163