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Register a new userSuperconducting mechanism for the cuprate Ba$_2$CuO$_{3+delta}$ based on a multiorbital Lieb lattice model
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For the recently discovered cuprate superconductor $mathrm{Ba_{2}CuO_{3+delta}}$, we propose a lattice structure which resembles the model considered by Lieb to represent the vastly oxygen-deficient material. We first investigate the stability of the Lieb-lattice structure, and then construct a multiorbital Hubbard model based on first-principles calculation. By applying the fluctuation-exchange approximation to the model and solving the linearized Eliashberg equation, we show that $s$-wave and $d$-wave pairings closely compete with each other, and, more interestingly, that the intra-orbital and inter-orbital pairings coexist. We further show that, if the energy of the $d_{3z^2-r^2}$ band is raised to make it incipient with the lower edge of the band close to the Fermi level within a realistic band filling regime, $spm$-wave superconductivity is strongly enhanced. We reveal an intriguing relation between the Lieb model and the two-orbital model for the usual K$_2$NiF$_4$ structure where a close competition between $s-$ and $d-$wave pairings is known to occur. The enhanced superconductivity in the present model is further shown to be related to an enhancement found previously in the bilayer Hubbard model with an incipient band.
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First principles investigations of the high temperature superconducting system Ba$_2$CuO$_{3+delta}$, recently discovered at $deltaapprox0.2$ at $T_c=70$ K, are applied to demonstrate the effects of oxygen ordering on the electronic and magnetic properties. The observed `highly over-doped superconducting phase displays stretched Cu-planar oxygen O$_{rm P}$ distances and anomalously shortened Cu-apical O$_{rm A}$ separations compared with other cuprates. The stoichiometric system $delta=0$, with its strongly one-dimensional (1D) Cu-O$_{rm P}$ chain structure, when nonmagnetic shows 1D Fermi surfaces that lead, within density functional theory, to antiferromagnetic Cu-O$_{rm P}$ chains (a spin-Peierls instability). Accounting for 1D fluctuations and small interchain coupling according to the theory of Schulz indicates this system, like Sr$_2$CuO$_3$, is near the 1D Luttinger-liquid quantum critical phase. The unusual Cu-O bond lengths per se have limited effects on other properties for $delta$=0. We find that a `doubled bilayer structure of alternating Cu-O$_{rm P}$ chains and wide rung Cu$_3$O$_4$ ladders is the energetically preferred one of three possibilities where the additional oxygen ions bridge Cu-O$_{rm P}$ chains in the superconducting phase $delta=1/4$. Nominal formal valences of the three Cu sites are discussed. The six-fold (octahedral) site is the most highly oxidized, accepting somewhat more holes in the $d_{z^2}$ orbital than in the $d_{x^2-y^2}$ orbital. The implication is that two-band physics is involved in the pairing mechanism and the superconducting carriers. The Fermi surfaces of this metallic bilayer structure show both 1D and 2D strong (incipient) nesting instabilities, possibly accounting for the lack of clean single-phase samples based on this structure and suggesting importance for the pairing mechanism.
The recently discovered cuprate superconductor Ba$_2$CuO$_{3+delta}$ exhibits a high $T_csimeq73$K at $deltasimeq0.2$. The polycrystal grown under high pressure has a structure similar to La$_2$CuO$_4$, but with dramatically different lattice parameters due to the CuO$_6$ octahedron compression. The crystal field in the compressed Ba$_2$CuO$_4$ leads to an inverted Cu $3d$ $e_g$ complex with the $d_{x^2-y^2}$ orbital sitting below the $d_{3z^2-r^2}$ and an electronic structure highly unusual compared to the conventional cuprates. We construct a two-orbital Hubbard model for the Cu $d^9$ state at hole doping $x=2delta$ and study the orbital-dependent strong correlation and superconductivity. For the undoped case at $x=0$, we found that strong correlation drives an orbital-polarized Mott insulating state with the spin-$1/2$ moment of the localized $d_{3z^2-r^2}$ orbital. In contrast to the single-band cuprates where superconductivity is suppressed in the overdoped regime, hole doping the two-orbital Mott insulator leads to orbital-dependent correlations and the robust spin and orbital exchange interactions produce a high-$T_c$ antiphase $d$-wave superconductor even in the heavily doped regime at $x=0.4$. We conjecture that Ba$_2$CuO$_{3+delta}$ realizes mixtures of such heavily hole-doped superconducting Ba$_2$CuO$_4$ and disordered Ba$_2$CuO$_{3}$ chains in a single-layer or predominately separated bilayer structure. Our findings suggest that unconventional cuprates with liberated orbitals as doped two-band Mott insulators can be a direction for realizing high-T$_c$ superconductivity with enhanced transition temperature $T_c$.
Angle-dependent magnetoresistance measurements are used to determine the isotropic and anisotropic components of the transport scattering rate in overdoped Tl$_2$Ba$_2$CuO$_{6+delta}$ for a range of $T_c$ values between 15K and 35K. The size of the anisotropic scattering term is found to scale linearly with $T_c$, establishing a link between the superconducting and normal state physics. Comparison with results from angle resolved photoemission spectroscopy indicates that the transport and quasiparticle lifetimes are distinct.
The angle-dependent interlayer magnetoresistance of overdoped Tl$_2$Ba$_2$CuO$_{6+delta}$ has been measured in high magnetic fields up to 45 Tesla. A conventional Boltzmann transport analysis with no basal-plane anisotropy in the cyclotron frequency $omega_c$ or transport lifetime $tau$ is shown to be inadequate for explaining the data. We describe in detail how the analysis can be modified to incorporate in-plane anisotropy in these two key quantities and extract the degree of anisotropy for each by assuming a simple four-fold symmetry. While anisotropy in $omega_c$ and other Fermi surface parameters may improve the fit, we demonstrate that the most important anisotropy is that in the transport lifetime, thus confirming its role in the physics of overdoped superconducting cuprates.
This article describes new polar angle-dependent magnetoresistance (ADMR) measurements in the overdoped cuprate Tl$_2$Ba$_2$CuO$_{6+delta}$ over an expanded range of temperatures and azimuthal angles. These detailed measurements re-affirm the analysis of earlier data taken over a more restricted temperature range and at a single azimuthal orientation, in particular the delineation of the intraplane scattering rate into isotropic and anisotropic components. These new measurements also reveal additional features in the temperature and momentum dependence of the scattering rate, including anisotropy in the $T^2$ component and the preservation of both the $T$-linear and $T^2$ components up to 100 K. The resultant form of the scattering rate places firm constraints on the development of any forthcoming theoretical framework for the normal state charge response of high temperature superconducting cuprates.
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