Mott-Proximate Cuprate Model

• The Mott-Proximate Cuprate Model is a theoretical paradigm that explains high-temperature superconductivity by emphasizing strong electron correlations near a Mott insulating state.
• It employs a minimal S = 1 pseudospin Hamiltonian incorporating local correlations, inter-site interactions, and composite boson transport to capture competing orders.
• The model accounts for experimental phenomena such as the pseudogap onset, phase separation, and d-wave superconductivity emerging from composite boson dynamics.

The Mott-Proximate Cuprate Model is a theoretical paradigm for understanding the complex phase diagram of high-temperature superconducting (HTSC) cuprates. It centers on their proximity to a Mott insulating state and the profound consequences of strong electron correlations for their electronic, magnetic, and superconducting properties. Rather than viewing cuprates as conventional Fermi liquids or simple Mott insulators, this model situates them in a crossover regime, where the interplay of Mottness, itinerancy, and competing orders dynamically shapes the phenomenology of the normal and superconducting states.

1. Theoretical Framework: Minimal Models and Pseudospin Algebra

At the heart of the Mott-Proximate Cuprate Model is a minimal non-BCS spin-pseudospin Hamiltonian acting on CuO₂ planes. The on-site Hilbert space is truncated to three effective charge states—[CuO₄]⁷⁻, [CuO₄]⁶⁻, and [CuO₄]⁵⁻—mapping onto a S = 1 pseudospin “charge triplet” (Moskvin et al., 2021). The Hamiltonian includes terms for:

• Local correlations (single-ion anisotropy Δ = U/2, chemical potential μ),
• Inter-site Coulomb interactions (V_{ij}),
• Single-particle and two-particle kinetic processes (with kinetic integrals t_{ij}^{(p)}, t_{ij}^{(n)}, t_{ij}^{(b)} for particle and composite boson transport),
• Exchange interactions (J_{ij}) involving on-site spin densities.

The full S = 1 operator algebra yields a complete set of eight pseudospin operators (dipolar and quadrupolar), making it possible to address local charge ordering, AFM order, unusual metallicity, and d-wave superconductivity from a unified basis.

2. Competing Orders, Phase Separation, and Free Energy Landscape

A defining property of Mott-proximate cuprates is the prevalence of competing local order parameters. The formalism naturally yields multiple symmetry-broken phases:

• Antiferromagnetic insulation (AFMI: ⟨S_z⟩ order),
• Charge order (CO: long-range alternation of charge states),
• d-wave Bose superfluidity (BS: ⟨S_±²⟩ order; local “glueless” composite bosons),
• Unusual metallic (“Fermi liquid”/FL) regime.

Crucially, phase diagrams derived by mean-field, Bethe cluster, and Monte Carlo methods show that the global free energy minimum is often realized by phase separated (PS) states (Moskvin et al., 2021). Such PS states are bounded by a third-order phase transition line T*(n), demarcating the pure (gapless) metallic state from regions supporting true coexisting orders. The existence of Maxwell constructions in the free energy (i.e., negative compressibility for systems with competing orders) is the hallmark of such phase separation, which is ubiquitous when local Coulomb, exchange, and pairing interactions are comparable.

3. Phase Diagram and Pseudogap Phenomenon

The resulting T–n phase diagrams display regions of single-order homogeneous phases (AFMI, CO, BS, FL), but the dominant phase across extended doping and temperature intervals is phase separated (Moskvin et al., 2021). Each homogeneous region is characterized by a single nonzero local order parameter, while PS phases exhibit local coexistence—with fluctuating (nanoscale) domains of different order.

The third-order transition line T*(n) is interpreted as the onset of the pseudogap phenomenon: it is here that the pure (gapless) Fermi liquid gives way to gapped phases with one or more coexisting local orders. Experimentally, T*(n) tracks the opening of the pseudogap in underdoped cuprates, while the corresponding regions in the model coincide with the experimentally established pseudogap regime in T- and T′-cuprates and nickelates.

4. Superconductivity: Composite Bosons and d-wave Bose Superfluid

Superconductivity, in this framework, is not the consequence of conventional Cooper pairing of doped holes or electrons but arises from the coherent transport of on-site composite bosons (local S_±² operators). The quadratic expectation value ⟨S_±²⟩ serves as the superconducting order parameter and is identified with a local d-wave order due to symmetry. This provides a non-BCS superconducting phase—the d-wave Bose superfluid—arising intrinsically from the on-site electronic configuration, not from pairing of itinerant carriers (Moskvin et al., 2021). In this sense, the superconducting phase is an emergent property of the parent complex, stabilized by the intricate balance among local correlation energy Δ, kinetic terms, and exchange.

5. Pseudogap, Unusual Metallic Phase, and Experimental Comparison

The model identifies the pseudogap as an intrinsic feature, demarcated by T*(n), and attributes its origin to phase separation and competition among local order parameters. When T drops below T*(n), the system transitions from a gapless metallic (Fermi liquid) phase to a mixed state with gapped magnetic, charge, or superconducting order parameters. This matches the experimental observation of the pseudogap’s onset, where finite-density regions exhibit incomplete gaps.

Quantitatively, by varying the local correlation strength Δ, kinetic integrals (t^{(b)}, t^{(p)}), and exchange J, the phase diagrams generated by the model can closely reproduce the main experimental features of T- and T′-cuprates, including:

• Antiferromagnetic and charge order at low doping,
• A superconducting (BS) dome that appears at all fillings (even in some parent compounds),
• The location and slope of the pseudogap T*(n),
• A phase-separated regime dominating a wide part of the phase diagram.

6. Implications for Superconductivity and Competing Orders

The Mott-Proximate Cuprate Model challenges the conventional BCS/Cooper pair view. The superconducting phase emerges from a distinct local mechanism—involving on-site composite bosons—decoupled from the usual “pairing” of itinerant Fermions. It is one phase among several possible ground states of the parent system, stabilized by the interplay of charge, spin, and local bosonic degrees of freedom. The model also provides a rationale for unusual metallic properties (including strange-metal behavior), consistent with a metallic phase defined locally by a vanishing order parameter but globally stabilized by the proximity to competing, spatially segregated orders.

This landscape of self-organized phase separation, composite boson superconductivity, and complex order parameter competition provides a coherent account of the rich, multifaceted phenomenology observed in cuprates. Notably, the connection between phase separation (and its third-order boundary T*(n)) and the pseudogap provides an organizing principle for interpreting disparate experimental findings across materials.

7. Relation to Broader Cuprate and Nickelate Physics

While formulated for cuprates, this model (with suitable parameter choices) can be applied to T- and T′-cuprates and nickelates (Moskvin et al., 2021). The universality of the main physical ingredients—on-site correlations, local bosonic degrees of freedom, competition between metallic and insulating orders, and d-wave symmetry—highlights the broad applicability of the Mott-Proximate framework to layered transition metal oxides that are close to Mottness but support unconventional metallic and superconducting phases.

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In summary, the Mott-Proximate Cuprate Model, via a minimal S = 1 pseudospin Hamiltonian, encapsulates the essential physics of phase separation, competing orders, local boson-driven superconductivity, and the pseudogap in high-Tₙ cuprates. Its intrinsic phase diagrams, validated by experimental correspondence, elucidate why cuprates evade classification as either pure Mott insulators or conventional metals, instead realizing a multifaceted “proximity” regime that underpins high-temperature superconductivity and its intertwined orders.