Dome structure in pressure dependence of superconducting transition temperature for HgBa2Ca2Cu3O8: Studies by ab initio low-energy effective Hamiltonian

The superconducting (SC) cuprate HgBa2Ca2Cu3O8 (Hg1223) has the highest SC transition temperature T-c among cuprates at ambient pressure P-amb, namely, T-c(opt) similar or equal to 138 K experimentally at the optimal hole doping concentration. T-c(opt) further increases under pressure P and reaches 164 K at optimal pressure P-opt similar or equal to 30 GPa, then T-c(opt) decreases with increasing P > P-opt generating a dome structure [Gao et al., Phys. Rev. B 50, 4260(R) (1994)]. This nontrivial and nonmonotonic P dependence of T-c(opt) calls for a theoretical understanding and mechanism. To answer this open question, we consider the ab initio low-energy effective Hamiltonian (LEH) for the antibonding (AB) Cu3d(x2-y2)/O2p(sigma) band derived generally for the cuprates. In the AB LEH for cuprates with N-l <= 2 laminated CuO2 planes between block layers, it was proposed that T-c(opt) is determined by a universal scaling T-c(opt) similar or equal to 0.16 vertical bar t(1)vertical bar F-SC [Schmid et al., Phys. Rev. X 13, 041036 (2023)], where t(1) is the nearest-neighbor hopping, and the SC order parameter at optimal hole doping F-SC mainly depends on the ratio u = U/vertical bar t(1)vertical bar where U is the onsite effective Coulomb repulsion: The u dependence of F-SC has a peak at u(opt) similar or equal to 8.5 and a steep decrease with decreasing u in the region u < u(opt) irrespective of materials dependent on other ab initio parameters. In this paper, we show that vertical bar t(1)vertical bar increases with P, whereas u decreases with P in the ab initio Hamiltonian of Hg1223. Based on these facts, we show that the domelike P dependence of T-c(opt) can emerge at least qualitatively if we assume Hg1223 with N-l = 3 follows the same universal scaling for T-c(opt), and Hg1223 is located at the slightly strong coupling region u greater than or similar to u(opt) at P-amb and u similar or equal to u(opt) at P-opt by taking account of expected corrections to our ab initio calculation. The consequence of these assumptions is the following: With increasing P within the range P < P-opt, the increase in T-c(opt) is accounted for by the increase in vertical bar t(1)vertical bar, whereas F-SC is insensitive to the decrease in u around similar or equal to u(opt) and hence to P as well. At P > P-opt, the decrease in T-c(opt) is accounted for by the decrease in u below uopt, which causes a rapid decrease in FSC dominating over the increase in vertical bar t(1)vertical bar. We further argue the appropriateness of these assumptions based on the insight from studies on other cuprate compounds in the literature. In addition, we discuss the dependencies of u and vertical bar t(1)vertical bar on each crystal parameter (CP), which provides hints for design of even higher T opt c materials.