Significance Most metals display an electron-scattering rate 1 / τ that follows 1 / τ ∼ T 2 at low temperatures, as prescribed by Fermi liquid theory. But there are important exceptions. One of the most prominent examples is the “strange” metal regime in overdoped cuprate supercondcutors, which exhibits a linear T dependence of the scattering rate 1 / τ ∼ T that reaches a putative Planckian limit. Here, using cutting-edge computational approaches, we show that T -linear scattering rate can emerge from the overdoped Hubbard model at low temperatures. Our results agree with cuprate experiments in various aspects but challenge the Planckian limit. Finally, by identifying antiferromagnetic fluctuations as the physical origin of the T -linear scattering rate, we discover the microscopic mechanism of strange metallicity in cuprates.
Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one-particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (\ensuremath{\pi},0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. A self-consistent solution with singlet ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is found and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest-neighbor antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favoring superconductivity. However, the mechanism for superconductivity is a local one, in contrast to spin-fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature
Tc is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/
kTc\ensuremath{\simeq}4.
We study the temperature and doping dependence of the two-dimensional (2D) Hubbard model in the intermediate coupling regime
(U=4). As temperature is decreased for a half-filled band, 2D critical spin fluctuations give rise to a strong local maximum in $|\mathrm{Im}\ensuremath{\Sigma}({k}_{F},\ensuremath{\omega})|$ at $\ensuremath{\omega}=0,$ leading to a split peak in the spectral function. These strong fluctuations dominating near half filling are completely destroyed by 12% doping concentration. Below this concentration the imaginary part of the self-energy vanishes nearly quadratically in frequency at the Fermi energy, a Fermi-liquid-like feature. With varying the temperature at this concentration, we present numerical evidence for the band Kondo effect in the doped 2D Hubbard model by showing at low temperatures a growing peak in the density of states, nearly quadratically vanishing (in frequency) scattering rates at the Fermi energy and a linearly vanishing (in temperature) effective magnetic moment.
Quantum Monte Carlo (QMC) and maximum-entropy techniques are used to study the spectral function $A(\mathbf{p},\ensuremath{\omega})$ of the one-band Hubbard model with strong coupling including a next-nearest-neighbor electronic hopping with amplitude ${t}^{\ensuremath{'}}/t=\ensuremath{-}0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for
Sr2CuO2Cl2. A narrow quasiparticle (qp) band is observed in the QMC analysis at the temperature of the simulation
T=t/3, both at and away from half-filling. Such a narrow band produces a large accumulation of weight in the density of states at the top of the valence band. As the electronic density
〈n〉 decreases further away from half-filling, the chemical potential travels through this energy window with a large number of states, and by $〈n〉\ensuremath{\sim}0.70$ it has crossed it entirely. The region near momentum $(0,\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ in the spectral function is more sensitive to doping than momenta along the diagonal from
(0,0) to $(\ensuremath{\pi},\ensuremath{\pi})$. The evolution with hole density of the quasiparticle dispersion contains some of the features observed in recent ARPES data in the underdoped regime. For sufficiently large hole densities the ``flat'' bands at $(\ensuremath{\pi},0)$ cross the Fermi energy, a prediction that could be tested with ARPES techniques applied to overdoped cuprates. The population of the qp band introduces a hidden density in the system which produces interesting consequences when the quasiparticles are assumed to interact through antiferromagnetic fluctuations and studied with the BCS gap-equation formalism. In particular, a region of extended
s-wave character is found to compete with the
d wave in the overdoped regime, i.e., when the chemical potential has almost entirely crossed the qp band as
〈n〉 is reduced. The present study also shows that previous ``real-space'' pairing theories for the cuprates, such as the antiferromagnetic Van Hove scenario, originally constructed based on information gathered at half-filling, do not change their predictions if hole dispersions resembling noninteracting electrons with renormalized parameters are used.
We examine the quasiparticle lifetime and spectral weight near the Fermi surface in the two-dimensional Hubbard model. We use the FLEX approximation to self-consistently generate the Matsubara Green's functions and then we analytically continue to the real axis to obtain the quasiparticle spectral functions. We compare the spectral functions found in the nearest neighbor hopping only Hubbard model with those found when second neighbor hopping is included. This separates the effects of nesting, the Van Hove singularity and the short-ranged antiferromagnetic correlations. The quasiparticle scattering rate is enhanced along the (0,pi) to (pi,pi) Brillouin zone diagonal. When the density is close to half-filling these 'hot-spots' lie on the Fermi surface and the scattering rate increases with decreasing temperature. For the next-nearest neighbor hopping scenario we observe a large range of doping where there is no antiferromagnetism but the scattering rate has a linear temperature dependence. On decreasing the interaction this non-Fermi liquid behavior is confined to doping levels where the Fermi energy lies near to the Van Hove singularity. We conclude that the 'hot-spots' are associated with the antiferromagnetic phase transition while the linear temperature dependence of the scattering rate is associated with the Van Hove singularity.
We examine a two-dimensional Fermi liquid with a Fermi surface which touches the Umklapp surface first at the four points as the electron density is increased. Umklapp processes at the four patches near lead the renormalization group equations to scale to strong coupling, resembling the behaviour of a two-leg ladder at half-filling. The incompressible character of the fixed point causes a breakdown of Landau theory at these patches. A further increase in density spreads the incompressible regions so that the open Fermi surface shrinks to four disconnected segments. This non-Landau state, in which parts of the Fermi surface are truncated to form an insulating spin liquid, has many features in common with phenomenological models recently proposed for the cuprate superconductors.