  The key to unraveling the nature of high-temperature superconductivity (HTS)
lies in resolving the enigma of the pseudogap state. The pseudogap state in the
underdoped region is a distinct thermodynamic phase characterized by
nematicity, temperature-quadratic resistive behavior, and magnetoelectric
effects. Till present, a general description of the observed universal features
of the pseudogap phase and their connection with HTS was lacking. The proposed
work constructs a unifying effective field theory capturing all universal
characteristics of HTS materials and explaining the observed phase diagram. The
pseudogap state is established to be a phase where a charged magnetic monopole
condensate confines Cooper pairs to form an oblique version of a
superinsulator. The HTS phase diagram is dominated by a tricritical point (TCP)
at which the first order transition between a fundamental Cooper pair
condensate and a charged magnetic monopole condensate merges with the
continuous superconductor-normal metal and superconductor-pseudogap state phase
transitions. The universality of the HTS phase diagram reflects a unique
topological mechanism of competition between the magnetic monopole condensate,
inherent to antiferromagnetic-order-induced Mott insulators and the Cooper pair
condensate. The obtained results establish the topological nature of the HTS
and provide a platform for devising materials with the enhanced superconducting
transition temperature.
