English Abstract: We investigate an analytical framework bridging the weakly coupled Bardeen-Cooper-Schrieffer (BCS) regime and strongly correlated macroscopic quantum states, with a focus on single-band Mott-Hubbard systems. To address the finite-temperature thermodynamic challenges inherent in standard Gutzwiller projections, we embed the pairing wavefunction within a Slave-Boson Mean-Field Theory (SBMFT). Incorporating a doping-scaled inter-layer coupling to satisfy the Mermin-Wagner restrictions provides a mechanism for finite-temperature holon condensation to remain thermodynamically stable. Subject to the nearest-neighbor pairing boundary condition and the zero-integral constraint dictated by the restricted Hilbert space, we find that the B1g irreducible representation (d-wave) optimizes the ground state energy in the Mott limit. Furthermore, evaluating emergent U(1) gauge fluctuations elucidates the distinction between the Anderson-Higgs gapped superconducting state and the gapless pseudogap phase. By mapping holon dynamics onto the Bardeen-Stephen vortex flow via the Ioffe-Larkin composition rule, we construct a descriptive model for AC microwave dissipation. Selective polaronic dressing of charged holons, driven by anti-adiabatic timescale separation, yields a spatially dependent pinning functional for pancake vortices and a doping-gated isotope coefficient. This Polaronic Fractionalization Model (PFM) provides a consistent perspective on the superconducting dome and captures the qualitative phenomenology of strongly correlated quasi-two-dimensional systems. 中文摘要: 我們探討一個橋接弱耦合 Bardeen-Cooper-Schrieffer (BCS) 區間與強關聯宏觀量子態的解析框架,並聚焦於單帶 Mott-Hubbard 系統。為了處理標準 Gutzwiller 投影中固有的有限溫度熱力學挑戰,我們將配對波函數嵌入奴隸玻色子平均場理論 (SBMFT) 中。透過引入隨摻雜調節的層間耦合以滿足 Mermin-Wagner 限制,為有限溫度下的空穴子 (holon) 凝聚保持熱力學穩定提供了一種機制。在受限希爾伯特空間 (Hilbert space) 所決定的最近鄰配對邊界條件與積分為零約束 (zero-integral constraint) 下,我們發現 B1g 不可約表示 (d波) 在 Mott 極限下能最佳化基態能量。此外,透過評估湧現的 U(1) 規範漲落,闡明了具備 Anderson-Higgs 能隙的超導態與無能隙贗能隙相之間的物理區別。藉由 Ioffe-Larkin 複合規則將空穴子動力學映射至 Bardeen-Stephen 渦旋流,我們建構了一個描述交流微波耗散的模型。由反絕熱 (anti-adiabatic) 時間尺度分離所驅動的帶電空穴子選擇性極化子修飾,產生了適用於餅狀渦旋 (pancake vortices) 的空間相依釘扎泛函 (pinning functional),以及受摻雜調控的同位素係數。此極化子分數化模型 (PFM) 對超導穹頂提供了一致的視角,並捕捉了強關聯準二維系統的定性現象學。
English Abstract: We investigate an analytical framework bridging the weakly coupled Bardeen-Cooper-Schrieffer (BCS) regime and strongly correlated macroscopic quantum states, with a focus on single-band Mott-Hubbard systems. To address the finite-temperature thermodynamic challenges inherent in standard Gutzwiller projections, we embed the pairing wavefunction within a Slave-Boson Mean-Field Theory (SBMFT). Incorporating a doping-scaled inter-layer coupling to satisfy the Mermin-Wagner restrictions provides a mechanism for finite-temperature holon condensation to remain thermodynamically stable. Subject to the nearest-neighbor pairing boundary condition and the zero-integral constraint dictated by the restricted Hilbert space, we find that the B1g irreducible representation (d-wave) optimizes the ground state energy in the Mott limit. Furthermore, evaluating emergent U(1) gauge fluctuations elucidates the distinction between the Anderson-Higgs gapped superconducting state and the gapless pseudogap phase. By mapping holon dynamics onto the Bardeen-Stephen vortex flow via the Ioffe-Larkin composition rule, we construct a descriptive model for AC microwave dissipation. Selective polaronic dressing of charged holons, driven by anti-adiabatic timescale separation, yields a spatially dependent pinning functional for pancake vortices and a doping-gated isotope coefficient. This Polaronic Fractionalization Model (PFM) provides a consistent perspective on the superconducting dome and captures the qualitative phenomenology of strongly correlated quasi-two-dimensional systems. 中文摘要: 我們探討一個橋接弱耦合 Bardeen-Cooper-Schrieffer (BCS) 區間與強關聯宏觀量子態的解析框架,並聚焦於單帶 Mott-Hubbard 系統。為了處理標準 Gutzwiller 投影中固有的有限溫度熱力學挑戰,我們將配對波函數嵌入奴隸玻色子平均場理論 (SBMFT) 中。透過引入隨摻雜調節的層間耦合以滿足 Mermin-Wagner 限制,為有限溫度下的空穴子 (holon) 凝聚保持熱力學穩定提供了一種機制。在受限希爾伯特空間 (Hilbert space) 所決定的最近鄰配對邊界條件與積分為零約束 (zero-integral constraint) 下,我們發現 B1g 不可約表示 (d波) 在 Mott 極限下能最佳化基態能量。此外,透過評估湧現的 U(1) 規範漲落,闡明了具備 Anderson-Higgs 能隙的超導態與無能隙贗能隙相之間的物理區別。藉由 Ioffe-Larkin 複合規則將空穴子動力學映射至 Bardeen-Stephen 渦旋流,我們建構了一個描述交流微波耗散的模型。由反絕熱 (anti-adiabatic) 時間尺度分離所驅動的帶電空穴子選擇性極化子修飾,產生了適用於餅狀渦旋 (pancake vortices) 的空間相依釘扎泛函 (pinning functional),以及受摻雜調控的同位素係數。此極化子分數化模型 (PFM) 對超導穹頂提供了一致的視角,並捕捉了強關聯準二維系統的定性現象學。
A d-wave superconducting ground state for a doped Mott insulator is obtained. It is distinguished from a Gutzwiller-projected Bardeen–Cooper–Schrieffer (BCS) superconductor by an explicit separation of Cooper pairing and resonating valence bond (RVB) pairing. Such a state satisfies the precise sign structure of the t–J model, just as a BCS state satisfies the Fermi–Dirac statistics. This new class of wavefunctions can be intrinsically characterized and effectively manipulated by electron fractionalization with neutral spinons and 'backflow' spinons forming a two-component RVB structure. While the former spinon is bosonic, originating from the superexchange correlation, the latter spinon is found to be fermionic, accompanying the hopping of bosonic holons. The low-lying emergent gauge fields associated with such a specific fractionalization are of mutual Chern–Simons type. Corresponding to this superconducting ground state, three types of elementary excitations are identified. Among them a Bogoliubov nodal quasiparticle is conventional, while the other two are neutral excitations of non-BCS type that play crucial roles in higher-energy/temperature regimes. Their unique experimental implications for the cuprates are briefly discussed.
The principal purpose of this topical review is to single out some of the universal features of high-temperature (high-Tc) and related strongly-correlated systems, which can be compared with experiment in a quantitative manner. The description starts with the concept of exchange-interaction-mediated (real-space) pairing, combined with strong correlations among narrow band electrons, for which the reference state is that of the Mott–Hubbard insulator. The physical discussion of concrete properties relies on variational approach, starting from generalized renormalized mean-field theory (RMFT) in the form of statistically-consistent Gutzwiller approximation (SGA), and its subsequent generalization, i.e., a systematic Diagrammatic Expansion of the Variational (Gutzwiller-type) Wave Function (DE-GWF). The solution leads to the two energy scales, one involving unconventional quasiparticles close to the Fermi energy, and the other reflecting the fully correlated state, involving electrons deeper below the Fermi surface. Those two regimes are separated by a kink in the dispersion relation, which is observed in photoemission. As a result, one obtains both the doping dependent properties in the correlated state, and effective renormalized quasiparticles. The reviewed ground-state characteristics for high-Tc systems encompass high-Tc superconductivity, nematicity, charge- (and pair-) density-wave effects, as well as non-BCS kinetic energy gain in the paired state. The calculated dynamic properties are: the universal Fermi velocity, the Fermi wave-vector, the effective mass enhancement, the pseudogap; and the d-wave gap magnitude. We discuss that, within the variational approach, the minimal realistic model is represented by the so-called t-J-U Hamiltonian. Inadequacy of the t-J and Hubbard models, particularly of their RMFT versions, is discussed explicitly. For heavy fermion systems, modeled by the Anderson lattice model and with the DE-GWF approach, we discuss the phase diagram, encompassing superconducting, Kondo insulating, ferro- and anti-ferromagnetic states. The superconducting state is then a two-d-wave gap system. If the orbital degeneracy of f-electrons is included, the coexistent ferromagnetic- (spin–triplet) superconducting phases appear and match those observed for UGe2 in a semiquantitative manner. Finally, in the second part, we generalize our approach to the collective spin and charge fluctuations in high-Tc systems, starting from variational approach, defining the saddle-point state, and combining it with 1/N expansion. The present scheme differs essentially from that starting from the saddle-point Hartree–Fock approximation, and incorporating the fluctuations in the random phase approximation (RPA). The spectrum of collective spin and charge excitations is determined for the Hubbard and t-J-U models, and subsequently compared quantitatively with recent experiments. The Appendices provide formal details to make this review self-contained.
The pseudogap state of cuprate high-temperature superconductors has been often viewed as either a yet unknown competing order or a precursor state to superconductivity. While awaiting the resolution of the pseudogap problem in cuprates, we demonstrate that local pairing fluctuations, vortex liquid dynamics, and other precursor phenomena can emerge quite generally whenever fermionic excitations remain gapped across the superconducting transition, regardless of the gap origin. Our choice of a tractable model is a lattice band insulator with short-range attractive interactions between fermions in the s-wave channel. An effective crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensate (BEC) regimes can be identified in any band insulator above two dimensions, while in two dimensions only the BEC regime exists. The superconducting transition is ``unconventional'' (non-pair-breaking) in the BEC regime, identified by either the bosonic mean field or XY universality class. The insulator adjacent to the superconductor in the BEC regime is a bosonic Mott insulator of Cooper pairs, which may be susceptible to charge density wave ordering. We construct a function of the many-body excitation spectrum whose nonanalytic changes define a sharp distinction between band and Mott insulators. The corresponding ``second-order transition'' can be observed out of equilibrium by driving a Cooper pair laser in the Mott insulator. We explicitly show that the gap for charged bosonic excitations lies below the threshold for Cooper pair breakup in any BEC regime, despite quantum fluctuations. Our discussion ends with a view of possible consequences for cuprates, where antinodal pair dynamics has certain features in common with our simple s-wave picture.
We propose a mechanism of superconductivity from purely repulsive interactions in the strong-coupling regime, where the Bardeen-Cooper-Schrieffer mechanism such as the spin-fluctuation approach is difficult to apply. Based on the SU(2) slave-rotor representation of the Hubbard model, we find that the single energy scale for the amplitude formation of Cooper pairs and their phase coherence is separated into two energy scales, allowing the so-called pseudogap state where such Cooper pairs are coherent locally but not globally, interpreted as realization of the density-phase uncertainty principle. This superconducting state shows the temperature-linear decreasing ratio of superfluid weight, resulting from strong phase fluctuations.
Resonating valence bond states in a doped Mott insulator was proposed to explain superconductivity in cuprates in January 1987 by Anderson. A challenging task then was proving existence of this unconventional mechanism and a wealth of possibilities, with a rigor acceptable in standard condensed matter physics, in a microscopic theory and develop suitable many body techniques. Shortly, a paper by Anderson, Zou and us (BZA) undertook this task and initiated a program. Three key papers that followed, shortly, essentially completed the program, as far as superconductivity is concerned,i) a gauge theory approach by Anderson and us, that went beyond mean field theory ii) Kotliar’s d -wave solution in BZA theory iii) improvement of a renormalized Hamiltonian in BZA theory, using a Gutzwiller approximation by Zhang, Gros, Rice and Shiba. In this article I shall focus on the merits of BZA and gauge theory papers. They turned out to be a foundation for subsequent developments dealing with more aspects that were unconventional - d -wave order parameter with nodal Bogoliubov quasi particles, Affleck-Marston’s π-flux condensed spin liquid phase, unconventional spin-1 collective mode at (π, π), and other fascinating developments. Kivelson, Rokhsar and Sethna’s idea of holons and their bose condensation found expression in the slave boson formalism and lead to results similar to BZA program. At optimal doping, correlated electrons acquire sufficient fermi sea character, at the same time retain enough superexchange inherited from a Mott insulator parentage, ending in a BCS like situation with superexchange as a glue! Not surprisingly, mean field theory works well at optimal doping, even quantitatively. Further, t-J model is a minimal model only around optimal doping, where RVB superconductivity is also at its best.
We study how to incorporate Mott physics in the BCS-type superconductor, motivated by the fact that high Tc superconductivity results from a Mott insulator via hole doping. The U(1) slave-rotor representation was proposed to take local-density fluctuations into account nonperturbatively, describing the Mott-Hubbard transition at half filling. Since this decomposition cannot control local pairing fluctuations, the U(1) slave-rotor representation does not give a satisfactory treatment for charge fluctuations. Extending the U(1) slave-rotor representation, we introduce an SU(2) slave-rotor representation to allow not only local-density fluctuations but also local pairing excitations. We find an SU(2) slave-rotor gauge theory of the Hubbard model in terms of two kinds of collective boson excitations associated with density and pairing fluctuations that interact with gapless fermion excitations via SU(2) gauge fluctuations. An interesting observation in this effective description is that phase fluctuations of fermion pairs arise as SU(2) gauge fluctuations. Thus, fermion-pairing excitations can be controlled by the dynamics of collective bosons in the SU(2) slave-rotor gauge theory. Performing the standard saddle-point analysis based on the SU(2) slave-rotor action, we find an interesting phase described by partial freezing of charge fluctuations near the Mott-Hubbard critical point, where local-density-fluctuation modes are condensed but local pair-excitation modes are gapped. Partial freezing of charge fluctuations causes fermion pairing to be incoherent as a result of reconciliation of superconductivity and Mott physics. The nature of this nonsuperconducting phase is identified with an anomalous metal due to the presence of incoherent pairing.