Interplay of two <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:math> orbitals in superconducting <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>La</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mi>Ni</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi mathvariant="normal">O</mml:mi> <mml:mn>7</mml:mn> </mml:msub> </mml:mrow> </mml:math> under pressure
Chen Lu, Zhiming Pan, Fan Yang, Congjun Wu
Abstract
The discovery of high-${T}_{c}$ superconductivity (SC) in ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (LNO) has aroused a great deal of interest. Previously, it was proposed that the Ni-$3{d}_{{z}^{2}}$ orbital is crucial to realize the high-${T}_{c}$ SC in LNO. The preformed Cooper pairs therein acquire coherence via hybridization with the $3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbital to form the SC. However, we held a different viewpoint that the interlayer pairing $s$-wave SC is induced by the $3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbital, driven by the strong interlayer superexchange interaction. To include effects from both ${E}_{g}$ orbitals, we establish a two-orbital bilayer $t\text{\ensuremath{-}}J$ model. Our calculations reveal that due to the no-double-occupancy constraint, the $3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ band and the $3{d}_{{z}^{2}}$ bonding band are flattened by a factor of about 2 and 10, respectively, which is consistent with recent angle-resolved photoemission spectroscopy measurements. Consequently, a high-temperature SC can be hardly induced in the $3{d}_{{z}^{2}}$ orbital due to the difficulty to develop phase coherence. However, it can be easily achieved by the $3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbital under realistic interaction strength. With electron doping, the $3{d}_{{z}^{2}}$-band gradually dives below the Fermi level, but ${T}_{c}$ continues to enhance, suggesting that it is not necessary for the high-${T}_{c}$ SC in LNO. With hole doping, ${T}_{c}$ initially drops and then rises, accompanied by the crossover from the BCS to BEC-type superconducting transitions.