Anisotropic pressure dependence of the in-plane effective mass in optimally doped Hg-based cuprates: a Casimir energy approach

The effect of external pressure on Hg-based cuprate superconductors is central to understanding their anisotropic electronic behavior. While the pressure dependence of $T_c$ is well studied, its influence on the effective mass of charge carriers is poorly known, especially under uniaxial compression. Here, we analyze uniaxial and hydrostatic pressure derivatives of the in-plane effective mass ${m_{ab}}^{\ast }$ in optimally doped Hg-12(n−1)n high-$T_c$ cuprates within the Casimir energy framework. Analytical expressions are derived and applied to the first five Hg-12(n−1)n members. Calculations show that a-axis and hydrostatic pressure reduce ${m_{ab}}^{\ast }$, whereas c-axis pressure increases it. The effect's magnitude and anisotropy decrease with increasing ${\text{CuO}}_2$ layers, with Hg-1245 exhibiting an anomalous response linked to lattice instabilities and interlayer decoupling. Results agree with Uemura's universal relation and other theories, offering quantitative predictions to guide future uniaxial-pressure experiments.