Superinsulators, Bose Metals and High-tc Superconductors: The Quantum Physics of Emergent Magnetic Monopoles

Description

In 1931 Dirac showed that topologically quantized single magnetic charges, magnetic monopoles, while classically forbidden in a gauge theory, are allowed alongside electric charges in a quantum theory of electromagnetism. Such topological magnetic excitations are indeed admitted in the spectrum of most grand unified field theories of elementary interactions. Despite 40 years of dedicated search efforts, nonetheless, they have never shown up in any experiment. This, however, does not preclude the possibility of topological magnetic monopoles being realized as excitations in emergent condensed matter states, where they would be much lighter and easier to create. This book is about the physical effects of such emergent magnetic monopoles. These range from a new mechanism for local, strong pairing of electrons possibly relevant for high-T superconductivity, to the formation of a new quantum phase of matter when monopoles condense. In such a condensate the electric interaction becomes extremely strong, so much so that only extended neutral states survive, with the consequence of an infinite resistance, even at finite temperatures. This state, called a superinsulator, is a dual superconductor and has been experimentally detected in various materials. In a superinsulator the electric interaction becomes analogous to the strong interaction holding quarks together in colour-neutral hadrons. Even more interesting is the case when the condensate carries both magnetic and electric charge. The ensuing state has properties that are strikingly reminiscent of the mysterious pseudogap state of high-T superconductors. Magnetic monopoles might thus have been hiding in plain sight where no one was looking for them for a long time. Contents Preface 1. Introduction 1.1. Units and notation 2. Gauge theories and magnetic monopoles: A first encounter with superinsulators 3. Gauge theories in 2+1 dimensions: The Chern–Simons term 4. Lattice Chern–Simons term 5. Saddle points, topological excitations and instantons 5.1. The XY model and vortices 5.2. Quantum wires and phase slips 5.3. Compact QED in 2D 6. Effective Chern–Simons gauge theories of emergent condensed matter systems 7. The superconductor-to-insulator transition 8. Effective field theory of the SIT tricritical point 9. The nature of the phases in the vicinity of the SIT tricritical point 9.1. Superconductors 9.2. Superinsulators 9.3. Bose metals 10. Bose metals, a.k.a. bosonic topological insulators 11. Josephson junction arrays 12. Fractional Bose metals 13. Symmetry classification of superinsulator excitations 14. Three dimensions: A gauge theory for vortices 14.1. The 3D SIT 14.2. Topologically ordered (Higgsless) superconductivity 14.3. 3D superinsulators 14.4. 3D bosonic insulators 14.5. Finite-temperature phase transitions 15. Gauging spin 16. Dyons and the θ-term 17. The electric Meissner effect, antiscreening and confining strings 18. Electric pions and asymptotic freedom 19. Oblique superinsulators, strong superinsulators, and high-Tc superconductivity 20. Real-space electron pairing by magnetic monopoles 21. Magnetic monopoles in loop-current Mott insulators 22. Interplay of disorder, topology, and interactions: Endogenous vs. exogenous disorder 23. Synthesis Bibliography