Pseudogap Metal Phenomena

• Pseudogap metal is a metallic state characterized by a selective depletion of low-energy spectral weight near the Fermi level while retaining compressibility and conduction.
• Its emergence can result from diverse mechanisms including band-structure reconstruction, strong electronic correlations, nonlocal Coulomb interactions, and magnetic criticality.
• Diagnostic signatures include suppressed tunneling conductance, the formation of Fermi arcs or pockets, and anomalous transport properties typical of non-Fermi liquids.

A pseudogap metal is a metallic state in which low-energy electronic spectral weight is strongly suppressed near the Fermi level without the universal appearance of a full insulating gap. Across the literature, the term covers several distinct but related situations: structural low-temperature phases of elemental metals with partial depletion of the density of states, strongly correlated doped Mott systems with momentum-selective loss of quasiparticles, metals near spin-density-wave instabilities, Coulomb-frustrated metals proximate to Wigner crystallization, and phases in which the physical electron is gapped while composite or fractionalized carriers still form a Fermi surface (Prigara, 2011, Faye et al., 2017, Driscoll et al., 2020, Zhang et al., 2022, Zhao et al., 24 Feb 2025).

1. Definition and conceptual scope

In the narrowest sense, a pseudogap metal is distinguished from an ordinary metal by a depletion of the single-particle density of states at the chemical potential, and from an insulator by the persistence of metallic conduction or finite compressibility. That definition is explicit in several settings: a depleted but nonvanishing density of states in doped Hubbard models, a soft Coulomb pseudogap in clean lattice electrons with unscreened long-range interactions, and a depression in tunneling conductance with finite zero-bias conductance in manganites (Faye et al., 2017, Driscoll et al., 2020, 0808.0067).

The phrase is nevertheless not used uniformly. In triangular-lattice moiré Hubbard systems under intermediate Zeeman field, the pseudogap metal is a conducting, compressible state with a Fermi surface of spin-$\tfrac{3}{2}$ spin polarons but a finite single-particle gap for adding or removing a physical spin-$\tfrac{1}{2}$ electron (Zhang et al., 2022). In ancilla-based descriptions of cuprates and twisted bilayer graphene, it denotes a metallic state with pocket Fermi surfaces, suppressed physical-electron spectral weight, and violation of the perturbative Luttinger theorem because the low-energy carriers are composite or fractionalized (Christos et al., 2023, Zhao et al., 24 Feb 2025). In studies of half-filled twisted transition-metal dichalcogenides, the pseudogap is identified more sharply through the vanishing of quasiparticle weights over parts of the Fermi surface, with the remaining parts forming disconnected Fermi arcs or pockets (Zong et al., 2024).

A useful unifying description is therefore phenomenological rather than microscopic: a pseudogap metal is a metallic phase whose low-energy electron spectrum is selectively or globally depleted near $E_F$, often with pronounced momentum differentiation, non-Fermi-liquid self-energies, or composite low-energy carriers, but without the fully developed hard gap of a conventional insulator.

2. Microscopic routes to pseudogap metallicity

One route is band-structure reconstruction driven by structural order. In elemental transition metals and some $f$-metals, structural transitions are associated with splitting of a $d$-band into subbands; in $sp$-metals they are associated with relative shifts of $s$- and $p$-bands. In this framework, the low-temperature ordered phase is a pseudogap metal because the density of states near $E_F$ is depleted but metallic conduction remains possible. For $d$-band transitions the characteristic zero-temperature pseudogap satisfies $\tfrac{1}{2}$0, while for $\tfrac{1}{2}$1-band transitions $\tfrac{1}{2}$2 (Prigara, 2011).

A second route is strong local correlation in doped Mott systems. Cluster treatments of the square-lattice and anisotropic Hubbard models describe a low-doping pseudogap metal continuously connected to the Mott insulator, with short-range antiferromagnetism, cluster singlets, or orbital- and momentum-selective Mottness suppressing spectral weight at the Fermi level (Faye et al., 2017, Fratino et al., 2021). In half-filled twisted $\tfrac{1}{2}$3, the pseudogap phases with Fermi arcs and Fermi pockets are produced by correlation-driven band reconstruction marked by the coexistence of poles and zeros of the single-particle Green’s function (Zong et al., 2024). In a recent confinement-based formulation, the pseudogap is identified with a long-range entangled pseudogap-Mott metal whose nodal arcs support a non-Fermi liquid and whose transition to the Mott insulator is the confinement of holon-doublon excitations (Mukherjee et al., 23 Jul 2025).

A third route is nonlocal Coulomb physics. For spinless fermions on the triangular lattice with $\tfrac{1}{2}$4, unscreened long-range Coulomb interactions generate a pseudogap metal characterized by a soft Coulomb pseudogap, self-generated randomness, electronic polarons, suppression of the Drude weight, and divergence of the quasiparticle effective mass as the system approaches a stripe-ordered Wigner crystal (Driscoll et al., 2020).

A fourth route is magnetic criticality. In one square-lattice Hubbard analysis, the pseudogap state is magnetically in the renormalized classical regime and forms near the $\tfrac{1}{2}$5 point where the nesting condition of short-range antiferromagnetic order is fulfilled, whereas the strange metal has nearly quantum-critical spin fluctuations, overdamped spin waves with $\tfrac{1}{2}$6 scaling, and $\tfrac{1}{2}$7-linear resistivity (Tanaka, 11 Nov 2025). Related work on thermal SDW fluctuations shows that a magnetic pseudogap at finite $\tfrac{1}{2}$8 emerges only if the ground state is magnetically ordered, and that the pseudogap above $\tfrac{1}{2}$9 requires summation of infinite series of diagrams for both the fermionic self-energy and the magnetic correlation length (Ye et al., 2023). A distinct quantum-critical construction yields a pseudogap state as a superposition of $E_F$0-wave superconductivity and a quadrupole-density wave, with certain areas of the Fermi surface closed by a large gap even after antiferromagnetic long-range order is destroyed (Efetov et al., 2012).

A fifth route replaces bare electrons by composite objects. In the moiré spin-polaron metal, the basic carriers are spin-$E_F$1 bound states of a hole and a spin-flip, so the physical electron is gapped even though the system remains metallic and compressible (Zhang et al., 2022). In ancilla theories of cuprates and twisted bilayer graphene, the pseudogap arises from hybridization with ancillary fermions and emergent gauge structure, producing small pocket Fermi surfaces, suppressed physical-electron weight, and composite fermions that dominate the low-energy metallic response (Christos et al., 2023, Zhao et al., 24 Feb 2025).

3. Electronic structure and diagnostic signatures

The most common diagnostic is a suppression of $E_F$2 or $E_F$3 near $E_F$4. In Hubbard-model pseudogap metals, the spectral function at hot or antinodal momenta develops two peaks at finite $E_F$5 with a local minimum at $E_F$6, and the global density of states shows a clear dip rather than a hard gap (Faye et al., 2017, Ye et al., 2023). In the anisotropic triangular moiré Hubbard model, the defining criterion is sharper: quasiparticle weights vanish over parts of the Fermi surface, while the remaining coherent pieces form disconnected Fermi arcs or closed pockets (Zong et al., 2024).

Closely related is the language of poles and zeros of the Green’s function. In the moiré Hubbard analysis, the pseudogap phases are reconstructed by coexistence of poles and zeros of $E_F$7; the zeros form Luttinger surfaces that cut up the large Fermi surface and bound the surviving arcs or pockets (Zong et al., 2024). In the pseudogap-Mott metal, Luttinger surfaces likewise accompany a non-Fermi-liquid metal on nodal arcs and antinodal gapping without conventional symmetry breaking (Mukherjee et al., 23 Jul 2025).

Transport and thermodynamics often remain metallic but anomalous. In the Coulomb-induced pseudogap metal, $E_F$8 and $E_F$9 at the metal-insulator transition, the effective mass diverges, and the charge fluctuation spectrum develops soft collective modes at $f$0, far below the bare bandwidth $f$1 (Driscoll et al., 2020). In the dimer Hubbard model, the pseudogap metal is an orbital-selective bad metal: the bonding orbital remains Fermi-liquid-like while the antibonding orbital shows a pseudogap and a non-Fermi-liquid self-energy peak at $f$2 (Fratino et al., 2021).

The observable used depends on platform. In a 2D Fermi-Hubbard quantum simulator, the underdoped pseudogapped metal is identified thermodynamically by a pronounced maximum in the isothermal compressibility $f$3 at low temperature and large $f$4, and spectroscopically by a loss of low-energy spectral weight in the $f$5 channel that emphasizes antinodal regions (Kendrick et al., 22 Sep 2025). In manganite thin films, a depression in the density of states with finite zero-bias conductance over $f$6 K defines a pseudogap metallic phase (0808.0067). In 1T-TaS$f$7Se$f$8, symmetrized energy-distribution curves are fit by $f$9 with $d$0, giving a V-shaped pseudogap (Jung et al., 15 Mar 2025).

A notable variation is that the physical electron itself may be gapped while the system remains metallic because the true low-energy carriers are composite. That is explicit for spin-polaron metals and for ancilla-based fractionalized metals, and it expands the standard density-of-states definition into a broader statement about operator dependence of low-energy coherence (Zhang et al., 2022, Zhao et al., 24 Feb 2025).

4. Canonical theoretical realizations

Several model studies treat the pseudogap metal as a distinct phase rather than a crossover. In the anisotropic two-dimensional Hubbard model, Cluster Dynamical Impurity Approximation yields a first-order transition at zero temperature between a low-doping pseudogap metal and a higher-doping correlated metal, with a coexistence region and a quantum critical endpoint around $d$1 (Faye et al., 2017). In the dimer Hubbard model solved exactly within DMFT, doping drives a first-order transition from an orbital-selective pseudogap metal to a conventional Fermi liquid; the compressibility becomes strongly enhanced near the endpoint (Fratino et al., 2021).

Bandwidth-tuned moiré Hubbard systems expose a particularly rich sequence. For half-filled twisted $d$2, the ground state evolves from a pseudogap state with Fermi arcs to a $d$3 Néel ordered Mott insulator, then to another pseudogap state with Fermi pockets, and eventually to a Fermi liquid via a Lifshitz transition (Zong et al., 2024). In semiconductor moiré triangular lattices, small hole doping of a Mott insulator under intermediate Zeeman field yields a pseudogap metal whose total spin is locked to doping by $d$4, reflecting a magnetization plateau and spin gap (Zhang et al., 2022).

Other theories place the pseudogap metal inside a broader phase architecture. The square-lattice Hubbard study of pseudogap and strange metal states ties the pseudogap to short-range antiferromagnetic order near the $d$5 point and the strange metal to nearly quantum-critical spin fluctuations, with the coincidence of the Mott–Heisenberg/Slater localization scale $d$6 and the Van Hove singularity doping playing a central role (Tanaka, 11 Nov 2025). The confinement-based theory regards the pseudogap phase as a distinct long-range entangled quantum phase whose eventual confinement yields a continuous transition into the Mott insulator (Mukherjee et al., 23 Jul 2025).

Taken together, these works support a recurrent structural claim: the pseudogap metal often intervenes between a more coherent Fermi liquid and a Mott or Wigner-crystal-like insulator, but the mechanism of intervention—short-range antiferromagnetism, Kondo breakdown, long-range Coulomb frustration, or composite-carrier formation—depends strongly on the model.

5. Materials and experimental manifestations

Elemental and simple metals furnish one end of the spectrum. In the structural-transition framework, hcp–bcc Ti, Zr, and Hf, $d$7 Mn, hcp–bcc Be, and several alkaline-earth and rare-earth metals are described as entering low-temperature phases with an energy pseudogap produced by $d$8-band splitting or $d$9-band shifts (Prigara, 2011). This usage keeps the system within conventional metallic chemistry but assigns pseudogap behavior to structural ordering itself.

Correlated oxides provide a more familiar condensed-matter setting. In La$sp$0Ca$sp$1MnO$sp$2 thin films, tunneling spectroscopy shows a pseudogap throughout $sp$3 K together with finite zero-bias conductance that increases on cooling, consistent with metallic free carriers in a polaronic background (0808.0067). In 1T-TaS$sp$4Se$sp$5, isoelectronic Se substitution drives a transition from a CDW-Mott insulator to a pseudogap metallic phase with preserved CDW order, V-shaped density of states, strong spectral broadening, and momentum-space asymmetry that reflects the chiral CDW structure (Jung et al., 15 Mar 2025).

Disorder-driven pseudogap metals can appear even at crystalline–disordered interfaces. At the surface of black phosphorus doped by disordered alkali metals, ARPES reveals back-bending of an otherwise parabolic conduction band and a pseudogap of $sp$6 meV from the Fermi level. The interpretation is resonance scattering by alkali-metal ions, with quasi-bound states and $sp$7-renormalization leading to $sp$8-wave or $sp$9-wave resonance pseudogaps depending on the dopant species (Ryu et al., 10 Jul 2025).

Cold-atom quantum simulation now realizes closely related phenomenology in a controlled Hubbard setting. In the square-lattice Fermi-Hubbard simulator, low-temperature measurements show a line of compressibility anomalies separating underdoped and overdoped metals, while lattice-modulation spectroscopy detects a sharp loss of low-energy spectral weight in the antinodal $s$0 channel; together these establish a pseudogap phase diagram as a function of interaction strength and doping (Kendrick et al., 22 Sep 2025).

These realizations demonstrate that pseudogap metallicity is not confined to a single family of materials. It appears in structural metals, transition-metal oxides, van der Waals Mott systems, doped semiconducting interfaces, and synthetic Hubbard platforms.

6. Relation to neighboring phases and unresolved boundaries

Pseudogap metals are frequently adjacent to superconductivity, but the relation is not unique. In the quantum-critical spin-fermion theory, the pseudogap state is a fluctuating superposition of $s$1-wave superconductivity and a quadrupole-density wave; thermal fluctuations destroy long-range order at moderate temperature, and superconductivity becomes stable only below a critical temperature (Efetov et al., 2012). In the ancilla theory of cuprates, the pseudogap metal is a fractionalized Fermi liquid, and condensing a charge-$s$2 Higgs boson produces a conventional $s$3-wave superconductor with four nodal Bogoliubov quasiparticles even when the normal pseudogap metal contains only antinodal electron pockets (Christos et al., 2023).

Magnetic scenarios remain sharply delimited. One finite-temperature SDW analysis argues that a magnetic pseudogap emerges only if the ground state is magnetically ordered; above that ordered ground state the pseudogap survives over a temperature window split into strong and weak pseudogap regimes, while outside it SDW fluctuations alone do not produce a pseudogap metal (Ye et al., 2023). Other studies instead attribute pseudogap behavior to Mottness without conventional symmetry breaking, to disorder in a Mott insulator, to long-range Coulomb frustration, or to composite fermions formed from ancilla sectors (Fratino et al., 2021, Jung et al., 15 Mar 2025, Driscoll et al., 2020, Zhao et al., 24 Feb 2025).

Across these works, the phrase “pseudogap metal” therefore denotes a class of metallic states unified by partial low-energy suppression but not by a single universality class. Some are best viewed as electronically reconstructed metals, some as bad metals with divergent mass and vanishing Drude weight, some as momentum-selective descendants of a Mott insulator, and some as metals whose low-energy carriers are not bare electrons at all. A plausible implication is that the pseudogap is less a unique phase label than a spectral and thermodynamic regime whose microscopic content must be specified case by case.