How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+d

Abstract: The antiferromagnetic ground state of copper oxide Mott insulators is achieved by localizing an electron at each copper atom in real space (r-space). Removing a small fraction of these electrons (hole doping) transforms this system into a superconducting fluid of delocalized Cooper pairs in momentum space (k-space). During this transformation, two distinctive classes of electronic excitations appear. At high energies, the enigmatic 'pseudogap' excitations are found, whereas, at lower energies, Bogoliubov quasi-particles -- the excitations resulting from the breaking of Cooper pairs -- should exist. To explore this transformation, and to identify the two excitation types, we have imaged the electronic structure of Bi2Sr2CaCu2O8+d in r-space and k-space simultaneously. We find that although the low energy excitations are indeed Bogoliubov quasi-particles, they occupy only a restricted region of k-space that shrinks rapidly with diminishing hole density. Concomitantly, spectral weight is transferred to higher energy r-space states that lack the characteristics of excitations from delocalized Cooper pairs. Instead, these states break translational and rotational symmetries locally at the atomic scale in an energy independent fashion. We demonstrate that these unusual r-space excitations are, in fact, the pseudogap states. Thus, as the Mott insulating state is approached by decreasing the hole density, the delocalized Cooper pairs vanish from k-space, to be replaced by locally translational- and rotational-symmetry-breaking pseudogap states in r-space.

• The paper reveals a rapid extinction of Bogoliubov quasi-particles within a narrowing k-space region as Bi2Sr2CaCu2O8+d approaches the Mott insulator.
• It identifies the emergence of pseudo-localized r-space states forming a pseudogap, indicative of local symmetry breaking in the underdoped regime.
• The study shows diverging energy scales between superconducting and pseudogap states, challenging traditional applications of Luttinger’s theorem.

Insights into Cooper Pair Transition Near Mott Insulators in Cuprates

This paper meticulously examines the transition of copper oxide compounds, particularly Bi₂Sr₂Ca₂CuO₈₊ₜ, from high-temperature superconductors to Mott insulators. Detailed analysis of electronic excitations using scanning tunneling microscopy (STM) and quasi-particle interference (QPI) imaging provides a nuanced understanding of the transformation process, focusing especially on the behavior of Cooper pairs as hole density is reduced.

The study reveals that, as these materials approach the Mott insulating state, there is a rapid reduction in the region of the momentum space (k-space) that supports Bogoliubov quasi-particles (BQPs), which are essential to the superconducting state. The remaining spectral weight transitions to high-energy, quasi-localized states in real space (r-space), characterized as pseudogap states. Importantly, these pseudogap states manifest a local symmetry-breaking nature, lacking the delocalized nature of Cooper pair excitations.

Key Findings

1. Bogoliubov Quasi-Particle Extinction: The BQP excitations, responsible for superconductivity, vanish outside a narrowing "Bogoliubov arc" in k-space as hole doping is reduced. This extinction occurs near specific k-space loci connecting k = (0, ±π/a) and k = (±π/a, 0).
2. Pseudogap Formation: At higher energies than the critical energy for BQPs, the system exhibits r-space dominated pseudo-localized states. These states have a consistent pattern across the atomic scale but show intensity fluctuations that correlate with the pseudogap energy.
3. Diverging Energy Scales: As hole density reduces, the energy scales between the superconducting state and the pseudogap state increasingly diverge—highlighting a critical connection between electronic segregation and superconductivity loss.
4. Violation of Luttinger’s Theorem: Observations indicate a breakdown of the traditional Luttinger theorem, necessitating its amendment to include zeros of Green's functions arising from the strong electronic correlations inherent in these systems.

Implications and Speculations

The findings provide a comprehensive insight into the two distinct electronic excitation classes within underdoped cuprates. The duality of high-energy pseudogap states and low-energy BQPs suggests a complex landscape where electronic correlations play a crucial role. The spatial symmetry breaking associated with pseudogap states could be pivotal in developing theoretical frameworks for understanding high-Tc superconductivity.

For the future, this research highlights several avenues. Exploration into the alterations in quasiparticle dispersions could yield new insights into the mechanism of Cooper pair localization. Furthermore, understanding the intrinsic link between these pseudogap characteristics and physical properties, such as thermal conductivity and magnetic behavior, remains an area ripe for exploration. As computational models of the Hubbard-type gain resolution, corroborating these experimental observations will be crucial for advancing cuprate superconductivity theories.

In conclusion, this paper systematically delineates the trajectory from superconducting to insulating phases in copper oxides, establishing a platform for future inquiries into correlated electronic systems and contributing significantly to the broader understanding of high-temperature superconductivity.