Dynamical Local Lattice Instability Triggered High Tc Superconductivity

Julius Ranninger (1)

1 NEEL - TMC - Théorie de la Matière Condensée

High Tc cuprate superconductors are characterized by two robust features: their strong electronic correlations and their intrinsic dynamical local lattice instabilities. Focusing on exclusively that latter, we picture their parent state in form of a quantum vacuum representing an electronic magma in which bound diamagnetic spin-singlet pairs pop in and out of existence in a Fermi sea of itinerant electrons. The mechanism behind that resides in the structural incompatibility of two stereo-chemical configurations Cu II O4 and Cu III O4 which compose the CuO2 planes. It leads to spontaneously fluctuating Cu-O-Cu valence bonds which establish a local Feshbach resonance exchange coupling between bound and unbound electron pairs. The coupling, being the only free parameter in this scenario, the hole doping of the parent state is monitored by varying the total number of unpaired and paired electrons, in chemical equilibrium with each other. Upon lowering the temperature to below a certain T * , bound and unbound electron pairs lock together in a local quantum superposition, generating transient localized bound electron pairs and a concomitant opening of a pseudo-gap in the single-particle density of states. At low temperature, this pseudo-gap state transits via a first order hole doping induced phase transition into a superconducting state in which the localized transient bound electron pairs get spatially phase correlated. The mechanism driving that transition is a phase separation between two phases having different relative densities of bound and unbound electron pairs, which is reminiscent of the physics of 4 He-3 He mixtures. PACS numbers: I INTRODUCTION Quite independent on any microscopic mechanism leading to superconductivity, this phenomenon is generated by establishing a macroscopic coherent quantum state in which an ensemble of transient bosonic charge carriers (composed of diamagnetic electron-pairs), having arbitrary phases in the parent state above T c , undergoes a global spontaneous symmetry breaking (SSB). The arbitrary phases of these virtual bosonic entities are thereby locked together into a unique global (though arbitrary) phase, the excitations of which are symmetry restoring collective Goldstone modes. In a current carrying state their existence assures the persistence of the resistance-less conduction through the Anderson-Higgs mechanism, by which they contribute to set up a longitudinal component of the electromagnetic vector potential driving this current, as recently reviewed [1] in commemorating the centennial anniversary of the discovery of superconduc-tivity [2]. The value of the critical temperature T c at which a super-flow sets in, depends however sensibly on how this SSB comes about in (i) forming finite amplitudes of individual bosonic entities and (ii) establishing the phase coherence between them in order to construct a macroscopic coherent quantum state. There are two ways for that to happen. * [e-mail] (I) When the strength of the inter-pair phase correlations , locking together the bosonic entities is large compared to the pairing energy. This is the case for BCS superconductors. The interaction between the electrons, monitored by the exchange of a phonon, is too weak to guarantee real space pairing. Yet, the ensemble of such virtual pairs, existing in form of transient Cooper pairs in momentum space, situated in a thin layer around the Fermi surface and having arbitrary phases, can be phase-locked into a macroscopic coherent quantum state through a collective process [3]. It provides the required strength for pairing, mediated by inter-pair phase correlations , engaging simultaneously a macroscopic number of transient Cooper pairs. Its resulting T c is controlled by the zero temperature pairing amplitude ∆(0), tantamount to the energy of the single-particle gap ∆(0) ≃ 1.76k B T BCS c with T c being given by T BCS c ≃ ω D exp − 1 λ/(1 + λ) − µ * (1) µ * = µ/[1 + µ ln(ε F /ω D)] (2) µ − λ = ρ(ε F)V el−ph (q, ω = 0) F S (3) V el−ph (q, ω = 0) = 4πe 2 q 2 ε(q, ω = 0) , (4) T c sensibly depends on the difference between the attractive phonon-mediated electron-electron interaction λ and the repulsive bare Coulomb interaction µ, given by the electron lattice coupling V el−ph (q, ω = 0). Appearing in form of the average over the Fermi surface, V el−ph con

Domaines: Matière Condensée [cond-mat]

Julius Ranninger. Dynamical Local Lattice Instability Triggered High Tc Superconductivity. Acta Physica Polonica A, 2015, 127 (2), pp.176 - 184. ⟨10.12693/APhysPolA.127.176⟩. ⟨hal-01734791⟩