Pseudogap Phase — Cuprate Superconductors

Fermi Arcs, Spectral Weight Loss, Preformed Pairs vs Phase Fluctuations

Spectral Weight A(k,ω=0) on Fermi Surface

Phase Diagram

Temperature T/Tc T/Tc = 1.20

Doping p p = 0.100

Pseudogap Scenario

Scattering Rate γ/EF γ/EF = 0.08

Pseudogap Δ*/EF Δ* = 0.120

Arc length (preformed pairs):

L_arc ~ T/T* (nodes open last)

MFL self-energy:

Σ''(ω) ∝ max(|ω|, T)

Spectral function:

A(k,ω) = −(1/π) Im G(k,ω)

BCS weight:

uk² = ½(1 + ξk/Ek)

Pseudogap T* line:

T*(p) ≈ T*₀(1 − p/p*)

Below T* but above Tc, cuprates exhibit a pseudogap: spectral weight is lost near (π,0) but "Fermi arcs" survive near the nodal direction. Two main theories: (1) Preformed Cooper pairs without long-range phase coherence (BEC-BCS crossover); (2) A competing order (CDW/SDW) that gaps the Brillouin zone. The arc length shrinks on cooling and collapses to a point at Tc.