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Physical review. B./Physical review. B

Fixed points and critical temperature near quantum critical points in d -wave cuprate superconductors

Qi-Qi Yue, Yi-sheng Fu, Jing Wang

Published Apr 24, 2026• 0 citations
Publisher
DOI
10.1103/qfwt-y132

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Fixed points and critical temperature near quantum critical points in ddd-wave cuprate superconductors
We study the critical behavior driven by potential quantum critical points (QCPs) termed as τ0,x,y,zτ_{0,x,y,z}τ0,x,y,z​-Type QCPs in the ddd-wave cuprate superconductors. Within the framework of the renormalization group approach, we construct the coupled flow equations of all interaction parameters and obtain several unique properties. On one hand, the interaction parameters flow toward several fixed points (FPs) at certain critical energy scales. We identify two different types of FPs designated at the clean limit. FP-I is characterized by the divergence of the quadratic parameter and exhibits robustness against variations in interaction parameters. In contrast, FP-II is dominated by the cubic and quartic interaction parameters, and it is sensitive to initial conditions, leading to five subclasses. Besides, we find that disorder scattering can influence fermion velocities and critical energy scales, and even destabilize certain FPs around the τx,zτ_{x,z}τx,z​-QCPs, driving the system toward a preempted disorder-induced FP. On the other hand, we find that quantum fluctuations play a critical role in shaping the critical temperature (TcT_cTc​) as the system approaches these QCPs. Near the τxτ_xτx​-QCP, TcT_cTc​ is considerably suppressed for both FP-I and FP-II. In contrast, near the τ0τ_0τ0​-QCP, TcT_cTc​ undergoes a substantial decrease for FP-I but only a slight decrease for FP-II. Conversely, TcT_cTc​ exhibits an increasing trend near the τyτ_yτy​-QCP, with a pronounced peak at vΔ0/vF0∼0.25v_{Δ0}/v_{F0} \sim 0.25vΔ0​/vF0​∼0.25. However, numerical analysis suggests that the τzτ_zτz​-QCP is unlikely to be physically realizable. Additionally, we realize that TcT_cTc​ can also be modified by the emergence of disorder-induced FPs in the vicinity of the τxτ_xτx​-QCP. These findings would provide valuable insights into the critical low-energy properties of ddd-wave cuprate superconductors and related materials.
The ddd-wave high-temperature cuprate superconductor may exhibit a nematic ordering transition at zero temperature. Near the quantum critical point, the coupling between gapless nodal quasiparticles and nematic order parameter fluctuation can result in unusual behaviors, such as extreme anisotropy of fermion velocities. We study the disorder effects on the nematic quantum critical behavior and especially on the flow of fermion velocities. The disorders that couple to nodal quasiparticles are divided into three types: random mass, random gauge field, and random chemical potential. A renormalization-group analysis shows that random mass and random gauge field are both irrelevant and, thus, do not change the fixed point of extreme velocity anisotropy. However, the marginal interaction due to random chemical potential destroys this fixed point and makes the nematic phase transition unstable.