Lower Pseudogap Phase in Cuprates

• Lower Pseudogap Phase (LPP) is a distinct low-temperature regime in cuprates characterized by incoherent pairing, emerging symmetry breaking, and Fermi-surface reconstruction.
• Spectroscopic techniques, particularly ARPES, reveal a departure from linear spectral weight trends and scaling laws that indicate the onset of pairing without full coherence.
• The LPP plays a critical role in the interplay between pseudogap phenomena and superconductivity, as theories link it to charge order, nematicity, and Fermi-surface changes.

Lower Pseudogap Phase (LPP) is a term used for the lower-temperature sector of the cuprate pseudogap regime, but its precise definition depends on context. In one influential spectroscopic usage, the LPP is the interval $T_c<T<T_{\rm pair}$, where a finite pairing amplitude exists without long-range phase coherence. In a broader usage common in pseudogap phenomenology, it denotes the lower-temperature pseudogap regime below $T^{**}$ or below $T^*$, where additional broken symmetries such as charge order, nematicity, or odd-parity order become prominent. Across these usages, the LPP is distinguished from a higher-temperature pseudogap sector by extra low-energy structure—pairing signatures, Fermi-surface reconstruction, or symmetry breaking—and by a close, but disputed, relation to superconductivity (Kondo et al., 2010, Chowdhury et al., 2014).

1. Terminology and phase-diagram placement

A central feature of the LPP literature is terminological nonuniformity. In the ARPES-based formulation of Kondo, Khasanov, Takeuchi, Schmalian, and Kaminski, the pseudogap regime is split into an Upper Pseudogap Phase and a Lower Pseudogap Phase. The LPP is then identified specifically with $T_c<T<T_{\rm pair}$, while the higher-temperature interval $T_{\rm pair}<T<T^*$ is the “proper” pseudogap without pair formation. In this mapping, $T_c$ marks macroscopic phase coherence, $T_{\rm pair}$ marks the onset of incoherent pairing, and $T^*$ marks the onset of the proper pseudogap (Kondo et al., 2010).

A broader cuprate-literature usage places the LPP inside the pseudogap below a lower crossover or ordering scale such as $T^{**}$ or below $T^*$ itself. In that usage, the Upper Pseudogap Phase is the higher-temperature pseudogap without static charge order, whereas the LPP is the lower-temperature regime in which translational symmetry is broken by charge-density-wave correlations that can become static or quasi-static, especially under magnetic field (Chowdhury et al., 2014).

This distinction is visible in YBa$T^{**}$0Cu$T^{**}$1O$T^{**}$2 as well. Resonant ultrasound spectroscopy identifies a thermodynamic phase-transition line at $T^{**}$3 that bounds the pseudogap from above and terminates at $T^{**}$4 near $T^{**}$5 inside the superconducting dome. Within the phase below $T^{**}$6, additional onsets such as Kerr and charge order can occur at lower temperature without a corresponding elastic anomaly in that study. Optical rotational-anisotropy measurements further show that below $T^{**}$7 YBa$T^{**}$8Cu$T^{**}$9O$T^*$0 enters a non-centrosymmetric state that breaks inversion and $T^*$1 while preserving $T^*$2 in the minimal point-group assignment, and this regime can be mapped to the LPP if the LPP is defined as the part of the pseudogap where new broken symmetries develop (Shekhter et al., 2012, Zhao et al., 2016).

2. Spectroscopic identification of pairing-dominated LPP

In the spectroscopic formulation, the LPP is defined by ARPES at the antinode through the temperature dependence of the spectral weight at the Fermi level, $T^*$3. Symmetrized antinodal energy-distribution curves show that the proper pseudogap opens below $T^*$4 as a two-peak structure, while $T^*$5 decreases linearly with cooling below $T^*$6 and above $T^*$7. At $T^*$8, $T^*$9 departs downward from that linear trend, signaling an additional loss of spectral weight attributed to incoherent pairing. The pairing contribution is isolated by subtracting the extrapolated pseudogap background, and for Bi2201 and Bi2212 it obeys the empirical scaling law

$T_c<T<T_{\rm pair}$0

For optimally doped Bi2212, the reported values are $T_c<T<T_{\rm pair}$1 K, $T_c<T<T_{\rm pair}$2 K, and $T_c<T<T_{\rm pair}$3 K at the antinode; in Bi2201, $T_c<T<T_{\rm pair}$4 rises from overdoped toward optimal doping and then saturates at $T_c<T<T_{\rm pair}$5 K on the underdoped side. The paper emphasizes that $T_c<T<T_{\rm pair}$6 has a universal value around $T_c<T<T_{\rm pair}$7–$T_c<T<T_{\rm pair}$8 K even for materials with very different $T_c<T<T_{\rm pair}$9, and argues that the scaling indicates a breakdown of a purely classical phase-fluctuation picture (Kondo et al., 2010).

In moderately underdoped Bi$T_{\rm pair}<T<T^*$0Sr$T_{\rm pair}<T<T^*$1CaCu$T_{\rm pair}<T<T^*$2O$T_{\rm pair}<T<T^*$3, autocorrelated ARPES gives a closely related picture from the joint density of states. Below and above $T_{\rm pair}<T<T^*$4, the constant-$T_{\rm pair}<T<T^*$5 maps show similar banana-shaped contours and similar octet dispersions, and above $T_{\rm pair}<T<T^*$6 the dispersions of the principal octet vectors $T_{\rm pair}<T<T^*$7 and $T_{\rm pair}<T<T^*$8 are particle-hole symmetric within experimental uncertainty over $T_{\rm pair}<T<T^*$9 meV. The authors interpret this as evidence that Bogoliubov-like excitations persist above $T_c$0 in the LPP and support a preformed-pair scenario at least in the moderately underdoped regime (Shah et al., 16 Sep 2025).

A local probe reaches a stronger one-gap conclusion for Bi-2212. Shot-noise spectroscopy identifies a pairing-onset energy $T_c$1 from a step-like increase in the effective charge $T_c$2 due to Andreev processes, and finds $T_c$3 at each measured position and across underdoped to optimally doped samples. The pseudogap energies are spatially heterogeneous, ranging roughly from $T_c$4 meV to above $T_c$5 meV, and the paper argues that the limiting factor for higher $T_c$6 is phase coherence rather than the pairing scale. The measurements were performed below $T_c$7, so the link to the above-$T_c$8 LPP is made through the energy scale rather than direct normal-state spectroscopy (Niu et al., 2024).

3. Symmetry breaking, charge order, and vestigial order

In the broader LPP literature, the phase is often characterized by additional broken symmetries. For non-Lanthanum-based cuprates such as YBCO and Bi-based compounds, the low-temperature pseudogap is associated with incommensurate axial charge-density-wave correlations with wavevectors $T_c$9 and $T_{\rm pair}$0, a predominantly bond-centered $T_{\rm pair}$1-form factor, and strong competition with superconductivity. Resonant and hard X-ray measurements find that the onset is gradual, $T_{\rm pair}$2, that the CDW intensity decreases below $T_{\rm pair}$3 at zero field, and that magnetic field enhances the intensity and correlation length (Chowdhury et al., 2014).

YBa$T_{\rm pair}$4Cu$T_{\rm pair}$5O$T_{\rm pair}$6 exhibits a different symmetry signature. Linear and second-harmonic optical anisotropy measurements show that above $T_{\rm pair}$7 the crystal is monoclinic and centrosymmetric with point group $T_{\rm pair}$8, whereas below $T_{\rm pair}$9 a bulk electric-dipole second-harmonic contribution appears, implying global inversion-symmetry breaking. The low-temperature SHG anisotropy is consistent with non-centrosymmetric subgroups of $T^*$0 that do not contain $T^*$1, specifically $T^*$2 or $T^*$3, or their subgroups. The onset temperatures reported for this inversion-breaking transition are approximately $T^*$4 K at $T^*$5, $T^*$6 K at $T^*$7, $T^*$8 K at $T^*$9, and $T^{**}$0 K at $T^{**}$1, and the signal evolves smoothly through both $T^{**}$2 and the charge-order onset without detectable anomalies (Zhao et al., 2016).

In Bi-2212, sublattice-phase-resolved STM/STS supports a vestigial-nematic interpretation of the pseudogap sector that contains the LPP. The $T^{**}$3 nematic signal and finite-$T^{**}$4 density-wave signal both attain maximal spectral intensity at the same energy, identified independently as the pseudogap energy $T^{**}$5. No new energy gap appears at the density-wave onset, whereas the pseudogap opening coincides with the nematic onset. For dopings $T^{**}$6, $T^{**}$7, $T^{**}$8, $T^{**}$9, and $T^*$0, the characteristic energies are approximately $T^*$1–$T^*$2 meV, $T^*$3 meV, $T^*$4 meV, $T^*$5 meV, and $T^*$6 meV, respectively. This supports a picture in which the lower pseudogap regime is a vestigial nematic state intertwined with density-wave fluctuations rather than a phase defined by a separate DW-induced gap (Mukhopadhyay et al., 2019).

4. Fermi-surface reconstruction and carrier density

A transport-based definition of the LPP emerges from angle-dependent magnetoresistance in Nd-LSCO. In the low-temperature, high-field normal state just below the pseudogap critical doping $T^*$7, superconductivity is suppressed with $T^*$8 T and the Fermi surface changes qualitatively across $T^*$9. At $T^{**}$00, outside the pseudogap, the ADMR is described by a large unreconstructed diamond-like Fermi surface consistent with ARPES. At $T^{**}$01, inside the pseudogap, the data require a reconstructed Fermi surface produced by a commensurate $T^{**}$02 reconstruction, yielding four small nodal hole pockets. Models based only on changing quasiparticle lifetimes, isotropic scattering, anisotropic scattering, or Fermi arcs without closed-pocket corners fail to reproduce the observed angular dependence (Fang et al., 2020).

This reconstruction also accounts for the carrier-density change across $T^{**}$03. Above $T^{**}$04, the large unreconstructed Fermi surface gives the conventional Luttinger count

$T^{**}$05

whereas below $T^{**}$06 the nodal hole pockets satisfy a total area consistent with $T^{**}$07. In Nd-LSCO at $T^{**}$08, the Hall and Seebeck coefficients remain positive, favoring nodal hole pockets without a dominant electron pocket (Fang et al., 2020).

A different small-pocket route is provided by the fractionalized Fermi liquid framework. There, the high-temperature pseudogap metal has four small pockets whose total area is specified by $T^{**}$09 rather than $T^{**}$10, and the low-temperature pseudogap develops a $T^{**}$11-form-factor bond-density wave as an instability of that FL$T^{**}$12 state. In this formulation, the LPP is the regime in which the axial $T^{**}$13-form-factor CDW becomes prominent at low temperature and high field, reconstructing the Fermi surface into small pockets and accounting for quantum oscillations and negative Hall response in non-La-based cuprates (Chowdhury et al., 2014).

5. Microscopic theories of the LPP

One broad theoretical line relates the LPP to Mottness. Plaquette CDMFT studies of the square-lattice Hubbard model identify a finite-doping first-order transition between a pseudogap and a correlated metal—the Sordi transition—ending at a finite-temperature critical point. The Knight-shift-defined $T^{**}$14 runs parallel to the corresponding Widom line and abruptly collapses at a critical doping $T^{**}$15. Although the lower pseudogap transition $T^{**}$16 is not computed directly, the calculated $T^{**}$17 shares its main experimental phenomenology: abrupt termination at $T^{**}$18, logarithmic specific-heat coefficient $T^{**}$19 around $T^{**}$20, and a nearly vertical ridge of maximum entropy near the same doping. This framework treats the LPP as lower-temperature ordering inside a pseudogap regime organized by a finite-doping extension of the Mott transition (Reymbaut et al., 2019).

A second class of theories places finite-momentum pairing at the center of the LPP. In the square-lattice $T^{**}$21–$T^{**}$22 model, a Grassmann tensor product state study finds a strongly fluctuating pair-density-wave state with $T^{**}$23 in the underdoped regime $T^{**}$24. This state has uniform hole density, uniform nearest-neighbor pairing magnitude, a $T^{**}$25 sign modulation of bond pair amplitudes, weak $T^{**}$26 breaking down to diagonal reflections, and a pairing amplitude that extrapolates to zero as bond dimension $T^{**}$27, indicating no long-range superconducting coherence. Amperean-pairing theory proposes a related PDW state in which electrons on the same side of the Fermi surface pair, automatically generating subsidiary charge order at wavevector $T^{**}$28 and producing Fermi arcs whose tips are connected by the same ordering vector (Yue et al., 2024, Lee, 2014).

Other proposals emphasize ordered magnetic textures or fractionalized vortex matter. A modulated-antiferromagnetic construction from the $T^{**}$29–$T^{**}$30 model attributes the pseudogap to rows and columns of holes that generate an internal modulated AFM field and checkerboard charge modulations; it predicts a gapless excitation spectrum despite a nonzero order parameter and a reconstructed “Fermi surface” compatible qualitatively with experiment. In a distinct mutual Chern–Simons gauge theory of doped Mott insulators, the LPP is identified with a spontaneous-vortex phase above $T^{**}$31 in which holons remain Bose condensed but superconducting phase coherence is disordered by thermally excited spinons. In that framework a Higgs-like amplitude mode of the holon condensate survives into the LPP, allowing terahertz third-harmonic generation to persist above $T^{**}$32 and producing a universal $T^{**}$33 phase shift of the THG signal across the superconducting transition (Dayan, 2010, Li et al., 10 Sep 2025).

6. Relation to superconductivity, coexistence, and unresolved questions

The LPP is universally close to superconductivity, but the form of that proximity remains disputed. In the pairing-based spectroscopic picture, the LPP contains incoherent Cooper pairs and a nonzero pairing amplitude that evolves smoothly through $T^{**}$34. The pairing spectral weight decreases with underdoping while the pseudogap spectral weight increases, and in highly underdoped samples the pseudogap can completely dominate the antinodal spectra and prevent formation of the superconducting peak. Within this formulation, the competition between the two states plays a key role in determining $T^{**}$35, and the nearly material-independent scale $T^{**}$36–$T^{**}$37 K may set a limit on the highest attainable $T^{**}$38 in cuprates (Kondo et al., 2010).

A different body of work defines the LPP not by incoherent pairing but by the appearance of lower-temperature broken symmetries inside the pseudogap. In that usage, the lower pseudogap hosts charge order, nematicity, inversion breaking, or related order parameters whose onset temperatures can be distinct from both $T^{**}$39 and one another. This is compatible with a thermodynamic pseudogap boundary at $T^{**}$40, with lower internal onsets such as Kerr or charge order, and with a pseudogap energy scale $T^{**}$41 that organizes nematic and density-wave spectral weight without being reducible to a single density-wave gap (Shekhter et al., 2012, Zhao et al., 2016, Mukhopadhyay et al., 2019).

The resulting tension is not merely semantic. In moderately underdoped Bi2212, ARPES JDOS analysis above $T^{**}$42 supports a particle-hole-symmetric, pairing-derived gap structure, and local shot-noise spectroscopy in Bi-2212 identifies the pseudogap energy with the pairing-onset energy. By contrast, the ARPES $T^{**}$43 analysis that introduced the $T^{**}$44 scale separates a proper pseudogap extending to $T^{**}$45 from a lower pairing regime that begins only at $T^{**}$46. This suggests that “LPP” is best treated as a phenomenological label for the lower-temperature pseudogap sector rather than as the name of a universally agreed microscopic phase. What remains common is that the regime lies below the upper pseudogap onset, displays additional structure absent at higher temperature, and strongly conditions the emergence, suppression, or reorganization of superconductivity (Shah et al., 16 Sep 2025, Niu et al., 2024, Kondo et al., 2010).