First-principles Study Of The Superconductivity Of Metallic La And Ca Under Pressure

Lanthanum metal is the first member of the rare-earth series of elements and experiences a series of phase transitions under pressure. At ambient pressure,La exhibits a double hexagonal close packed (dhcp)structure and transforms to face-centered cubic(fcc)phase at 2.3GPa.Low-temperature resistivity and superconductivity measurements showed that there was a transformation from fcc to distorted fcc phase at～5.4 GPa.However,the room-temperature high-pressure x-ray diffraction(XRD)experiment suggested that this phase transition occurred at about 7GPa.The temperature effects mainly contribute to the difference among the three experimental measurements.Through XRD experiment,a soft phonon mode at the L point of Brillouin zone(BZ)in fcc-La is speculated to be responsible for this phase transition.Using frozen-phonon calculations,the theory also predicted that the transverse acoustic(TA)phonon at L-point softens with pressure,but no direct evidence was available in the literature.More interestingly,Lanthanum is a superconductor at ambient pressure with a relatively high superconducting transition temperature (T_c)of 4.9K.Experimental measurements demonstrated that T_c increases dramatically with pressure from 5 K at zero pressure to 13 K at 10GPa.Pickett et al.calculated the electron-phonon coupling(EPC) constantλwith the rigid muffin-tin approximation(RMTA)and suggested that the drastic increase in T_c under pressure can be attributed primarily to the changes in the electronic stiffness.Wang et al. suggested that the softening of the transverse L-point phonon frequency might lead to the increased T_c,however,there is no any theoretical data supporting their conclusion.In the current study,we systemically studied the lattice dynamics and the EPC with pressure using the linear-response approach based on the density-functional perturbation theory to reveal the nature of the pressure-induced phase transition from fcc to distorted fcc and to uncover the physical origin for the increased T_c in fcc La with pressure.A pressure-induced softening TA phonon mode at the L point of Brillouin zone is identified and the phonon softening pressure was predicted to be～4.92GPa,which coincides with the experimentally observed second-order phase transition pressure of～5.3GPa from fcc to distorted fcc.Moreover.no elastic instability is found under compression.Analysis of the calculated results suggested that the TA phonon instability is the driven force for this second-order phase transition.Furthermore,the current EPC calculations suggested that the experimental observation of elevated T_c with pressure is from the increased EPC strength and the softening TA phonon.In addition to lanthanum,we also studied calcium(Ca)metal due to its interesting phenomenon under pressure.Calcium adopts an fcc (Ca-Ⅰ)lattice at ambient conditions.Under compression,it transforms to body-centered cubic(bcc)(Ca-Ⅱ)and a very unique simple cubic(sc) (Ca-Ⅲ)structures at 20 GPa and 32 GPa,respectively.The existence of sc phase in Ca has been theoretically confirmed by the total energy calculations.Further experimental measurement suggests that the sc phase exists in a large pressure range of 32 to 109 GPa.Beyond 110 GPa,two new high-pressure phases of Ca-Ⅳ(113- 139 GPa)and Ca-Ⅴ(＞139GPa)have been observed experimentally but not explained theoretically.The experimental measurements on the electrical resistances of Ca with pressure show two remarkable anomalies.One is the resistance maximum in the 12-19 GPa pressure range within the fcc phase.This abnormal behavior is understandable with the metal-nonmetal transition predicted by the band structure calculations.The second anomaly is the obvious discontinuity in resistance at～40 GPa within the sc phase.The physical origin for this anomaly remains unknown. More importantly,Ca was found to become a superconductor under pressure.Superconductivity of Ca was firstly observed as a small drop in the electrical resistance at 2 K and 44 GPa within the sc structure. Later,Shingo et al.measured that T_c of Ca is below 3 K above 85 GPa and increases linearly with pressure up to 15 K at 150 GPa.A newly published experimental study further showed that T_c reached 25 K at 161 GPa.However.the only theoretical study on the superconductivity of Ca is performed within the RMTA and the mean-square phonon frequency <ω~2> is approximated through the formula <ω~2> = 0.5θ_D~2 without considering the distribution of the phonon density of states (DOS),which leads to much higher T_c than that in experiment.Normally,the anomaly in the electrical resistance is related to the changes of the electronic properties.This stimulates us to explore the band structures and Fermi surface of sc Ca under compression.In addition,lattice dynamics and EPC are calculated to uncover the origin of the pressure-induced T_c enhancement in sc Ca.Analysis of the calculated band structure and Fermi surface with pressure suggests that the predicted electronic topology transitions(ETT)atⅩpoint is mainly responsible for the observed anomaly of the electrical resistance.The phonon calculations for sc Ca with both supercell and linear response methods reveal large imaginary frequencies in the pressure range of 32 -109 GPa.This phonon instability might imply the existence of significant anharmonic effect in sc Ca needed to stabilize the crystal.In addition,EPC calculation demonstrates that the observed increase of T_c with pressure is mainly attributed to the enhancement of the electron DOS at the Fermi level N(E_F)and the EPC matrix element .