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Topological quantum phase transitions and topological quantum criticality in superfluids and superconductors Yang, Fan


Superfluids and superconductors can be either fully gapped or gapless with nodal structures in momentum space. Both the gapped and nodal phases can be topologically protected and possess nontrivial topological invariants. Topological quantum phase transitions exist at zero temperature between different gapped phases or between gapped and nodal phases. These phase transitions can be driven by chemical potential and/or spin exchange fields. The two phases separated by the phase transition can have the same local order but differ in global topology. Thus, these topological quantum phase transitions cannot be described by the Landau paradigm of symmetry breaking. Although some aspects of these transitions, such as the change of topological invariants and gapless boundary states, have been discussed before, a complete theory of these transitions has yet to be developed. In this dissertation, we construct effective field theories to study the universality and thermodynamic signatures of these transitions. We find four different universality classes in superfluids and superconductors. Certain thermodynamic quantities, such as compressibility or spin susceptibility, change non-analytically across the transitions. For certain time-reversal symmetry breaking fields that lead to bulk phase transitions, there also exist topological phase transitions on the surface. All the topological phase transitions studied in this dissertation only exist at zero temperature. At finite temperature, different states are connected by smooth crossovers. There exists a quantum critical region at finite temperature near the quantum critical point (QCP). In this quantum critical region, thermodynamic quantities have universal scaling dependence on temperature dictated by the universality class of the QCP. We argue that these scaling properties can be used to probe and differentiate these QCPs. These bulk and surface topological quantum phase transitions are discussed in various concrete models, such as chiral and time-reversal invariant p-wave superfluids, topological superconductors of emergent Dirac fermions, and topological superconducting model of CuₓBi₂Se₃.

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