Half–Bogoliubons as the intermediate states for phase coherence in underdoped cuprates

Superconductivity is achieved by the pairing of electrons and phase coherence between the Cooper pairs. According to the Bardeen-Cooper-Schrieffer theory, quasiparticles with Bogoliubov dispersion exist in the superconducting state, leading to the particle-hole symmetric coherence peaks on the single particle tunneling spectrum. Here we report the observation of two kinds of tunneling spectra showing only one side of the coherence peak in the underdoped cuprate superconductor Bi₂Sr_2-xLa_xCuO₆, and we name the electronic states as half-Bogoliubons. Based on the model that two doped holes bind into a local pair within the 4a₀ × 4a₀ plaquette, we attribute the half-Bogoliubons to one-hole or three-hole intermediate states for phase coherence. An entanglement of distinct half-Bogoliubons would lead to the dynamic hopping of charge freedom, resulting in the phase coherence between the local pairs. Our results unravel a unique process for establishing the phase coherence through exchanging a charge between regions with local pairs.