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

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.

Figures (3)

• Figure 1: Free energy phase diagram from static mean-field theory of t/U model \ref{['tUmodel']} including antiferromagnetism, q=0 altermagnetism, superconductivity, and the Fermi gas (white). Altermagnetism here is supported by a kinetic interaction that is deactivated by the purely localized Mott insulator, so is more like a Pomeranchuk instability of a Fermi liquid than a consequence of antiferromagnetism, but all orders are siblings that arise together from a Hubbard-commuting dynamic. Dynamical parameters $U, J$ are effectively renormalized to compensate for lack of correlations, $U/|t|=0.80, J/|t|=1.1, t'/t=-1/7$. Metastable phase boundaries of d-AM and d-SC are presented as $T^*$ and $T_{pair}$. $T^*$ cleaves the hole-doped superconductor into underdoped and overdoped sides, while in the altermagnetic phase, $T_{pair}$ signals onset of strong Cooper pair fluctuations. The altermagnetic phase is fully concealed by AFM for $\nu>1$.
• Figure 2: a) Tuning from non-interacting band to Hubbard-commuting kinetic, $T(\eta)=T_h+T_d+(1-\eta)(T_++T_-)$, first and second neighbor mean-field hoppings diminish in scale, $c_s, c_{s'}$, as non-commuting processes are removed. When $\eta \sim1$, altermagnetism condenses in energetic sympathy with the s-wave band. b) The overdoped superconductor is like standard BCS in that the pairing gap vanishes at $T_c$. The underdoped d-SC is distinguished by its melting transition to another ordered phase. A potentially higher $T_c$ could be unlocked by the targeted suppression of altermagnetism.
• Figure 3: a) Transverse susceptibility spectrum of the altermagnet within TDHF theory, for a simplified Hamiltonian with $U=J=0$. A purely d-wave Goldstone boson becomes unstable and anisotropic away from $\bm{q}=\Gamma$, and disperses mostly as an s-wave paramagnon near $\bm{q}=M$. b) The most severe instability is common to the AM and the Fermi gas, appearing in the charge sector at the antinodes $\bm{q}=X,Y$ nucleating $\pi$-flux order. Superposition of $X$ and $Y$ modes on top of background s-wave hopping leads to a checkerboard of fluxes, as in d). More particuar to the AM is a secondary instability at $\bm{q}=X,Y$ intertwining longitudinal currents with transverse modulation of hopping, as in c).