Disorder effects on hot spots in electron-doped cuprates

C. Gauvin-Ndiaye, P.-A. Graham, and A.-M. S. Tremblay

Phys. Rev. B 105, 235133 – Published 24 June 2022

Abstract

Antiferromagnetic fluctuations in two dimensions cause a decrease in spectral weight at so-called hot spots associated with the pseudogap in electron-doped cuprates. In the $2 D$ Hubbard model, these hot spots occur when the Vilk criterion is satisfied, namely, when the spin correlation length exceeds the thermal de Broglie wavelength. Using the two-particle self-consistent approach, here we show that this criterion may be violated near the antiferromagnetic quantum critical point when sufficient disorder is added to the model. Static disorder decreases inelastic scattering, in contradiction with Matthiessen's rule, leading to a shift in the position of the quantum critical point and a modification of the conditions for the appearance of hot spots. This opens the road to a study of the interplay between disorder, antiferromagnetic fluctuations, and superconductivity in electron-doped cuprates.

Received 29 April 2022
Revised 1 June 2022
Accepted 13 June 2022

DOI:https://doi.org/10.1103/PhysRevB.105.235133

Physics Subject Headings (PhySH)

Pseudogap Quantum criticality

Cuprates Disordered systems

Hubbard model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

C. Gauvin-Ndiaye , P.-A. Graham, and A.-M. S. Tremblay

Département de Physique, Institut quantique, and RQMP Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1

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Issue

Vol. 105, Iss. 23 — 15 June 2022

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Images

Figure 1
Spectral weight computed with our NCCO-model parameters for $T = 0.02$ and $τ = 25$ to illustrate how we define the AFM pseudogap temperature $T^{*}$ . (a) and (b) show $A (k, ω = 0)$ , the spectral weight at $ω = 0$ as a function of wave vector $k$ in a quarter of the Brillouin zone at fillings $n = 1.16$ and $n = 1.165$ , respectively. The stars are placed at one of the two hot spots $k_{F}$ where the Fermi surface crosses the AFM Brillouin zone. In (a), the AFM pseudogap is clearly visible at the hot spots for $n = 1.16$ . (c) shows $A (k_{F}, ω)$ , the spectral weight as a function of the frequency $ω$ at the hot spots $k_{F}$ defined in (a) and (b). We see that, at this value of the temperature, a loss of spectral weight occurs at $ω = 0$ for $n = 1.16$ , but not for $n = 1.165$ , which defines the boundary of the AFM pseudogap at this temperature.
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Figure 2
Antiferromagnetic pseudogap temperature $T^{*}$ without disorder (red squares), with disorder $τ = 46$ (blue circles), and with disorder $τ = 25$ (green triangles). Left panel shows $T^{*}$ obtained from the spectral weight at the hot spots $A (k_{F}, ω)$ . Right panel shows $T_{C_{U}}^{*}$ obtained from the maximum value of the specific heat over temperature $C_{U, n} / T$ at each filling.
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Figure 3
Effect of disorder on the spin fluctuations. Calculations are done at $T = 0.04$ and $n = 1.20$ , the filling associated with the AFM QCP for the case without disorder. As $τ$ increases, the disorder level decreases. Here, we use the notation $Δ f = (f^{dis} - f) / f$ to signify the relative deviation in percentage between the results with and without disorder. Blue squares and green circles show, respectively, the relative deviation of $U_{sp}$ and $U_{m f}$ due to disorder. Both quantities are only slightly increased due to disorder. Red diamonds, dark-blue triangles, and dark-red triangles show, respectively, the relative deviation of $ξ_{0}$ , $ξ_{sp}$ , and $δ U$ due to disorder. The large increase in $δ U$ and decrease in $ξ_{0}$ due to disorder suppress the spin correlation length Eq. (13).
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Figure 4
Ratio of the spin correlation length $ξ_{sp}$ and the thermal de Broglie wavelength $ξ_{th}$ evaluated at $T^{*}$ . The Vilk criterion $ξ_{sp}^{*} \geq ξ_{th}^{*}$ , shown as the dashed line in the plot, is satisfied in the cases without disorder (dark-red squares) and with $τ = 46$ (dark-blue circles). For a higher disorder level of $τ = 25$ (green triangles), the criterion is not satisfied at fillings near the AFM QCP, even though an AFM pseudogap can be seen in the spectral weight (Fig. 1) in this range of parameters.
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Figure 5
Minimal value of the ratio $ξ_{sp} / ξ_{th}$ at wich an AFM pseudogap is expected to open at the hot spots from Eq. (18). The ratio $ξ_{0}^{2} / ξ_{0}^{2} (τ \to \infty)$ is taken as a free parameter in the analytic calculation. The black dashed line corresponds to the original Vilk criterion. The three other lines, calculated with disorder: $v_{F} τ = ξ_{sp} / 2$ (pink line), $v_{F} τ = ξ_{sp}$ (green line), $v_{F} τ = 10 ξ_{sp}$ (blue line) show the value of $ξ_{sp} / ξ_{th}$ at which an AFM pseudogap opens depending on the value of $ξ_{0}^{2} / ξ_{0}^{2} (τ \to \infty)$ .
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Figure 6
Temperature dependence of the spin correlation length as a function of the disorder level. Left panel shows the nondisordered case for fillings $n = 1.195$ , $n = 1.200$ , and $n = 1.205$ . The AFM QCP for this case is located around $n = 1.200$ , as seen from the behavior of the spin correlation length, which grows when $T \to 0$ for this filling, but remains very small at low temperature for a slightly larger filling $n = 1.205$ . The middle panel shows the results for $τ = 46$ and the right panel for $τ = 25$ , both cases with disorder. Similarly to the case without disorder, we find the AFM QCP for these systems by looking at the behavior of the spin correlation length at low temperature. We find that the QCP is around $n = 1.195$ for $τ = 46$ and $n = 1.170$ for $τ = 25$ . All the results shown here are obtained from calculations converged with system size $1024 \times 1024$ and for 2048 Matsubara frequencies.
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