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arXiv:2603.16311

Altermagnetic pseudogap from $\frac{t}{U}$ expansion

Rohit Hegde

Published Mar 17, 2026• 0 citations
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Abstract

Order parameter analysis of the t/U series reveals a uniform altermagnet endemic to the doped Mott insulator, driven by kinetic interactions, occupying a position between the antiferromagnet and hole-doped d-wave superconductor that is normally reserved for the pseudogap. The metastable boundary of the altermagnet punctures and divides the superconductor into underdoped and overdoped regions, reminiscent of the $T^\ast$ crossover or transition in the cuprates. Similarly, the $T_{pair}$ boundary of the superconductor divides the altermagnet, leading to a low temperature phase susceptible to Cooper fluctuations. The altermagnet is unstable to inhomegeneous spin and charge order of sites, bonds, and currents. Its leading instability is to the $π$-flux state, suggesting the possible emergence of spin-charge liquids and quantum ordered states from a physically realistic microscopic model.

DOI
10.48550/arxiv.2603.16311

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Altermagnetic pseudogap from tU\frac{t}{U}Ut​ expansion
Order parameter analysis of the t/U series reveals a uniform altermagnet endemic to the doped Mott insulator, driven by kinetic interactions, occupying a position between the antiferromagnet and hole-doped d-wave superconductor that is normally reserved for the pseudogap. The metastable boundary of the altermagnet punctures and divides the superconductor into underdoped and overdoped regions, reminiscent of the T∗T^\astT∗ crossover or transition in the cuprates. Similarly, the TpairT_{pair}Tpair​ boundary of the superconductor divides the altermagnet, leading to a low temperature phase susceptible to Cooper fluctuations. The altermagnet is unstable to inhomegeneous spin and charge order of sites, bonds, and currents. Its leading instability is to the πππ-flux state, suggesting the possible emergence of spin-charge liquids and quantum ordered states from a physically realistic microscopic model.
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 sss-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\mathit{XY}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 sss-wave picture.
An intricate interplay between superconductivity, pseudogap, and Mott transition, either bandwidth driven or doping driven, occurs in materials. Layered organic conductors and cuprates offer two prime examples. We provide a unified perspective of this interplay in the two-dimensional Hubbard model within cellular dynamical mean-field theory on a 2×2 plaquette and using the continuous-time quantum Monte Carlo method as impurity solver. Both at half filling and at finite doping, the metallic normal state close to the Mott insulator is unstable to d-wave superconductivity. Superconductivity can destroy the first-order transition that separates the pseudogap phase from the overdoped metal, yet that normal state transition leaves its marks on the dynamic properties of the superconducting phase. For example, as a function of doping one finds a rapid change in the particle-hole asymmetry of the superconducting density of states. In the doped Mott insulator, the dynamical mean-field superconducting transition temperature T(c)(d) does not scale with the order parameter when there is a normal-state pseudogap. T(c)(d) corresponds to the local pair formation temperature observed in tunneling experiments and is distinct from the pseudogap temperature.
The phase diagram of hole-doped high-temperature superconductors remains puzzling. A state of matter with unusual physical properties, dubbed pseudogap, is found below a characteristic temperature T∗T^*T∗ in a doped Mott insulator. Since the superconducting state is born out of the pseudogap over much of the phase diagram, the nature of the pseudogap is a fundamental issue in the field and it is under intense theoretical and experimental scrutiny. In many cases, it is not even clear whether T∗T^*T∗ is a crossover or a phase transition. Here we show, by constructing the normal-state phase diagram of the archetypal model of strongly correlated electron systems, that T∗T^*T∗ is a crossover line above a critical endpoint, while below that point it is a first-order phase transition between two metallic phases, one with a pseudogap and one without. Thus T∗T^*T∗ appears in a new light: it is an unexpected example of a phenomenon observed in fluids, namely a sharp crossover between different dynamical regimes along a line of thermodynamic anomalies that appears above a first-order phase transition, the Widom line. Our findings thus suggest that the critical point of a first-order transition can be the organizing principle for the rich behavior of the normal state of the cuprates.
In this paper, we try to understand the pseudogap phenomenon observed in the cuprate superconductor through a model study. Specifically, we explore the so-called low-temperature pseudogap state by turning off the superconducting (SC) off diagonal long range order in an ansatz state for the t – J model (Weng 2011 New J. Phys. 13 103039 ). Besides strong non-Gaussian SC fluctuations, the resulting state also exhibits a systematic pseudogap behavior in both spin and charge degrees of freedom, manifested in the uniform spin susceptibility, specific heat, non-Drude resistivity, Nernst effect, as well as the quantum oscillation associated with small Fermi pockets emerging in strong magnetic fields, etc. These anomalous 'normal state' properties are found in qualitative consistency with experimental measurements in the cuprates. Such a model study establishes an intrinsic connection between the peculiar pseudogap properties and the non-BCS nature of the SC ground state. A critical comparison with other approaches to the doped Mott insulator is also made.
Motivated by the growing evidence of the importance of charge fluctuations in the pseudogap phase in high-temperature cuprate superconductors, we apply a large-NNN expansion formulated in a path integral representation of the two-dimensional ttt-JJJ model on a square lattice. We study all possible charge instabilities of the paramagnetic state in leading order of the 1/N1/N1/N expansion. While the ddd-wave charge density wave (flux phase) becomes the leading instability for various choices of model parameters, we find that a ddd-wave Pomeranchuk (electronic nematic phase) instability occurs as a next leading one. In particular, the nematic state has a strong tendency to become inhomogeneous. In the presence of a large second nearest-neighbor hopping integral, the flux phase is suppressed and the electronic nematic instability becomes leading in a high doping region. Besides these two major instabilities, bond-order phases occur as weaker instabilities close to half-filling. Phase separation is also detected in a finite temperature region near half-filling.
There are two seemingly unrelated puzzles about the cuprate superconductors. The first puzzle concerns the strong non-BCS behavior around xc{x}_{c}xc​, the end point of the superconducting dome on the overdoped side, where the cuprate is believed to be well described by the Fermi-liquid theory. This is the most evident in the observed ${\ensuremath{\rho}}_{s}(0)\ensuremath{-}{T}_{c}$ scaling and the large amount of uncondensed optical spectral weight at low energy. The second puzzle concerns the remarkable robustness of the ddd-wave pairing against the inevitable disorder effect in such a doped system, which is also totally unexpected from the conventional BCS picture. Here we show that these two puzzles are deeply connected to the origin of a third puzzle about the cuprate superconductors, namely, the mysterious quantum critical behavior observed around x∗{x}^{*}x∗, the so called pseudogap end point. Through a systematic variational Monte Carlo (VMC) study of the disordered 2D $t\ensuremath{-}J$ model from the resonating valence bond (RVB) perspective, we find that the ddd-wave pairing in this model is remarkably more robust against the disorder effect than that in a conventional ddd-wave BCS superconductor. We find that such remarkable robustness can be attributed to the spin-charge separation mechanism in the RVB picture, through which the ddd-wave RVB pairing of the charge-neutral spinons becomes essentially immune to the disorder potential except for the secondary effect related to the modulation of the local doping level by the disorder. We propose that there exists a Mott transition at x∗{x}^{*}x∗, where the RVB pairing in the underdoped regime is transmuted into the increasingly more BCS-like pairing for x>x∗x>{x}^{*}x>x∗, whose increasing fragility against the disorder effect leads to the non-BCS behavior and the ultimate suppression of superconductivity around xc{x}_{c}xc​.