Out-of-plane bond-order phase, superconductivity, and their competition in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> </mml:math> - <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>J</mml:mi> <mml:mo>∥</mml:mo> </mml:msub> <mml:mtext>−</mml:mtext> <mml:msub> <mml:mi>J</mml:mi> <mml:mo>⊥</mml:mo> </mml:msub> </mml:math> model: Possible implications for bilayer nickelates
Matías Bejas, Xianxin Wu, Debmalya Chakraborty, Andreas P. Schnyder, A. Greco
Abstract
Almost four decades of intense research have been invested to study the physics of high-${T}_{c}$ cuprate superconductors. The recent discovery of high-${T}_{c}$ superconductivity in pressurized bilayer nickelates and its potential similarities with cuprate superconductors may open a new window to understand this long-standing problem. We have studied the proposed bilayer $t\text{\ensuremath{-}}{J}_{\ensuremath{\parallel}}\text{\ensuremath{-}}{J}_{\ensuremath{\perp}}$ model [where ${J}_{\ensuremath{\parallel}}$ (${J}_{\ensuremath{\perp}}$) is the in-plane (out-of-plane) magnetic exchange] in a large-$N$ approach on the basis of the path integral representation for Hubbard operators, which allows to obtain results at mean-field and beyond mean-field level. We find that ${J}_{\ensuremath{\perp}}$ is a candidate for triggering high superconducting ${T}_{c}$ values at quarter filling (hole doping $\ensuremath{\delta}=0.5$) of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbitals. Beyond mean-field level, we find a new phase, an out-of-plane bond-order phase (z-BOP), triggered also by ${J}_{\ensuremath{\perp}}$. z-BOP develops below a critical temperature which decreases with increasing doping and vanishes at a quantum critical point below quarter filling. The occurrence of this phase and its competition with superconductivity leads to a superconducting dome-shaped behavior as a function of doping and as a function of ${J}_{\ensuremath{\perp}}$. Qualitative comparisons with the physics of cuprates and the recent literature on the new pressurized nickelates are given along the paper.