Hole-doped cuprate pseudogap

Shine light on a copper-oxide crystal and measure the energy and direction of the electrons it ejects. In some of these materials, the signal from low-energy electronic states weakens in some directions while remaining visible in others—even above the temperature where electrical resistance vanishes. This partial depletion is the pseudogap. Changing the composition to reduce the electron count is called hole doping. What causes the depletion, and why does it change with doping?[1] [3]

In hole-doped copper-oxide superconductors, low-energy electron spectral weight can disappear unevenly before superconducting order appears. Which correlations cause this pseudogap and its doping evolution? Angle-resolved photoemission ejects electrons with light and resolves their energy and momentum. Near the Fermi energy—the boundary between mostly occupied and mostly empty states—an underdoped Bi2212 experiment found depleted intensity near one part of the momentum contour while a portion closer to its diagonal remained gapless. On cooling above the superconducting transition, the remaining portions shrink into arcs. The contrast is between electronic momenta, not dark and bright patches on the crystal.

The Emery model retains one copper and two oxygen electronic orbitals per copper-oxygen unit. A 2026 calculation of its normal state includes repulsion and correlated spin fluctuations: nearby spins tend toward opposite orientations without requiring long-range magnetic order. These fluctuations alter electron propagation differently at different momenta and produce a pseudogap over part of the modeled doping range. It is a concrete candidate mechanism, with qualitative comparisons to spectra and magnetic response.[1] [3]

One calculation produces a pseudogap when neighboring electron spins fluctuate with a tendency to point oppositely. That shows a possible mechanism in the model. It does not establish whether this mechanism, electron pairing without superconducting order, or another form of electronic order explains the hole-doped crystals.[1] [2]

Producing the depletion in a chosen model does not show that the same correlations dominate every hole-doped material. The calculation assumes a clean system and makes approximations to the electronic interactions. Pairing-precursor and competing-order accounts still require discrimination by their temperature, momentum and doping predictions. The separate electron-doped thermal-magnetic result addresses a different regime; it is useful for comparison, not a solution of the hole-doped question.[1] [2]

The depleted states are part of the electronic response from which superconductivity develops. Knowing what removes their low-energy weight would help distinguish correlations that obstruct superconductivity from those that participate in its formation.[1] [2] [3]

The pseudogap changes which low-energy electronic states remain available before pairing becomes coherent across the crystal. A mechanism that also accounts for spin and charge measurements would constrain the starting point for a pairing theory and help determine whether the depleted spectrum reflects competition with superconductivity or part of its development. Spectral agreement alone cannot establish that connection.[1] [2] [3]