Fixed points and critical temperature near quantum critical points in d-wave cuprate superconductors
Qi-Qi Yue, Yi-Sheng Fu, Jing Wang
DOI 10.1103/qfwt-y132 · Physical Review B
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Abstract
We study the critical behavior driven by potential quantum critical points (QCPs) termed as τ0,x,y,z-type QCPs beneath the superconducting dome of the d-wave cuprate superconductors. To comprehensively capture the distinct degrees of freedom in the vicinity of these QCPs, we construct a phenomenological effective theory based on the Landau-Ginzburg-Wilson framework and then employ the renormalization group approach to derive the coupled flow equations of all interaction parameters, incorporating all relevant one-loop corrections. Decoding these flow equations yields a series of unique properties arising from strong quantum fluctuations around QCPs. 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: FP-IIA, FP-IIB, FP-IIC, FP-IID, and FP-IIE. In addition, we find that disorder scattering can influence fermion velocities and critical energy scales, and even destabilize certain FPs around the 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 (Tc) as the system approaches these QCPs. Near the τx QCP, Tc is considerably suppressed for both FP-I and FP-II. In contrast, near the τ0 QCP, Tc undergoes a substantial decrease for FP-I but only a slight decrease for FP-II. Conversely, Tc exhibits an increasing trend near the τy QCP, with a pronounced peak at vΔ0/vF0∼0.25. However, numerical analysis suggests that the τz QCP is unlikely to be physically realizable. Additionally, we realize that Tc can also be modified by the emergence of disorder-induced FPs in the vicinity of the τx QCP. These findings would provide valuable insights into the critical low-energy properties of d-wave cuprate superconductors and related materials.