Topological Nature of High Temperature Superconductivity

Abstract

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 is 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 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.

Signatures of two-dimensional superconductivity emerging within a three-dimensional host superconductor

“…Our results also raise the question of whether the origin of V-shape conductance spectra is due to d-wave pairing as in the case of cuprates, or simply due to electronic disorder. Notably, the 3D superinsulator phase has been conjectured to be associated with the pseudogap phase of high-temperature superconductors (52). Very recently, numerical calculations have suggested that a disordered superconductor driven through the 3D Anderson transition shares some of the 2D phenomenology, including strong spatial fluctuations and enhancements of the order parameter, although only in the weak-coupling limit, and specific connections to local variables accessible via STM/STS are out of reach (53).…”

Magnetic monopole mechanism for localized electron pairing in HTS

“…It thus occurs as the temperature compares with the coupling energy, and our estimate gives T c = O 10 2 K for a typical granule size of O(1) nm. We stress that these purely magnetic monopoles are different from the dyons in the pseudogap condensate 4 excitations which become stable since electron pairing reduces their repulsive energy and hence the total energy of the system. The pseudogapresiding monopoles are the endpoints of Josephson-like vortices residing in the granular array.…”

“…A field-theoretical approach establishing the long sought unified theory of HTS and accounting for all universal features within the superconducting dome and in the pseudogap state in a consistent whole 4 , stemmed from the topological gauge theory of the SIT 24,26 and its generalization to three dimensions 27 . A fundamental mechanism of the HTS was identified as the formation of a condensate of dyons, electrically charged magnetic monopoles 4 . The superconducting state is a coexistence phase of dyon and pure charge condensates.…”

“…Crucial in this picture is the emergent self-induced granularity 4,27 characterizing the SIT at the antiferromagnetic quantum critical point (AFM-QCP) 12,20 . Superconducting granules of the spatial scale of order of a few superconducting coherence lengths ξ and connected by tunnelling links produce a medium supporting magnetic monopoles [27][28][29] and dyons 4 . The last missing piece to complete this picture of HTS is a mechanism of localized electron pairing in real space.…”

Topological Model of the Pseudogap State: Experimental Signatures

“…The monopoles that we consider carry both the electric charge 2e and magnetic charge π/e (h/2e in physical units) and are called dyons. The topological theory of high-temperature superconductivity [16] establishes that the pseudogap state is the state harboring a condensate of dyons and that the charges carrying the electric current in this state are stable symmetryprotected fermionic edge dyons. We propose that edge dyons can be detected by measuring magnetic and electric fields that encircle currents carried by these excitations.…”