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Register a new userElectronic structure of CuTeO$_4$ and its relationship to cuprates
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Based on first principles calculations, the electronic structure of CuTeO$_4$ is discussed in the context of superconducting cuprates. Despite some significant crystallographic differences, we find that CuTeO$_4$ is similar to these cuprates, exhibiting a quasi two dimensional electronic structure that involves hybridized Cu-$d$ and O-$p$ states in the vicinity of the Fermi level, along with an antiferromagnetic insulating ground state. Hole doping this material by substituting Te$^{6+}$ with Sb$^{5+}$ would be of significant interest.
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While the beginning decade of the high-Tc cuprates era passed under domination of local theories, Abrikosov was one of the few who took seriously the electronic band structure of cuprates, stressing the importance of an extended Van Hove singularity near the Fermi level. These ideas have not been widely accepted that time mainly because of a lack of experimental evidence for correlation between saddle point position and superconductivity. In this short contribution, based on the detailed comparison of the electronic band structures of different families of cuprates and iron based superconductors I argue that a general mechanism of the Tc enhancement in all known high-Tc superconductors is likely related with the proximity of certain Van Hove singularities to the Fermi level. While this mechanism remains to be fully understood, one may conclude that it is not related with the electron density of states but likely with some kind of resonances caused by a proximity of the Fermi surface to topological Lifshitz transition. One may also notice that the electronic correlations often shifts the electronic bands to optimal for superconductivity positions.
The phenomenological Greens function developed in the works of Yang, Rice and Zhang has been very successful in understanding many of the anomalous superconducting properties of the deeply underdoped cuprates. It is based on considerations of the resonating valence bond spin liquid approximation and is designed to describe the underdoped regime of the cuprates. Here we emphasize the region of doping, $x$, just below the quantum critical point at which the pseudogap develops. In addition to Luttinger hole pockets centered around the nodal direction, there are electron pockets near the antinodes which are connected to the hole pockets by gapped bridging contours. We determine the contours of nearest approach as would be measured in angular resolved photoemission experiments and emphasize signatures of the Fermi surface reconstruction from the large Fermi contour of Fermi liquid theory (which contains $1+x$ hole states) to the Luttinger pocket (which contains $x$ hole states). We find that the quasiparticle effective mass renormalization increases strongly towards the edge of the Luttinger pockets beyond which it diverges.
The large ($10^2 - 10^5$) and strongly temperature dependent resistive anisotropy $eta = (sigma_{ab}/sigma_c)^{1/2}$ of cuprates perhaps holds the key to understanding their normal state in-plane $sigma_{ab}$ and out-of-plane $sigma_{c}$ conductivities. It can be shown that $eta$ is determined by the ratio of the phase coherence lengths $ell_i$ in the respective directions: $sigma_{ab}/sigma_c = ell_{ab}^2/ell_{c}^2$. In layered crystals in which the out-of-plane transport is incoherent, $ell_{c}$ is fixed, equal to the interlayer spacing. As a result, the T-dependence of $eta$ is determined by that of $ell_{ab}$, and vice versa, the in-plane phase coherence length can be obtained directly by measuring the resistive anisotropy. We present data for hole-doped $YBa_2Cu_3O_y$ ($6.3 < y < 6.9$) and $Y_{1-x}Pr_xBa_2Cu_3O_{7-delta }$ ($0 < x leq 0.55$) and show that $sigma_{ab}$ of crystals with different doping levels can be well described by a two parameter universal function of the in-plane phase coherence length. In the electron-doped $Nd_{2-x}Ce_{x}CuO_{4-y}$, the dependence $sigma_{ab}(eta)$ indicates a crossover from incoherent to coherent transport in the c-direction.
We present a phenomenological model that describes the low energy electronic structure of the cuprate high temperature superconductor Bi2Sr2CaCu2O8+x as observed by Spectroscopic Imagining Scanning Tunneling Microscopy (SI-STM). Our model is based on observations from Quasiparticle Interference (QPI) measurements and Local Density of States (LDOS) measurements that span a range of hole densities from critical doping, p~0.19, to extremely underdoped, p~0.06. The model presented below unifies the spectral density of states observed in QPI studies with that of the LDOS. In unifying these two separate measurements, we find that the previously reported phenomena, the Bogoliubov QPI termination, the checkerboard conductance modulations, and the pseudogap are associated with unique energy scales that have features present in both the q-space and LDOS(E) data sets.
Photoemission spectra of underdoped and lightly-doped Bi$_{2-z}$Pb$_z$Sr$_2$Ca$_{1-x}${it R}$_{x}$Cu$_2$O$_{8+y}$ ($R=$ Pr, Er) (BSCCO) have been measured and compared with those of La$_{2-x}$Sr$_x$CuO$_4$ (LSCO). The lower-Hubbard band of the insulating BSCCO, like Ca$_2$CuO$_2$Cl$_2$, shows a stronger dispersion than La$_2$CuO$_4$ from ${bf k}sim$($pi/2,pi/2$) to $sim$($pi,0$). The flat band at ${bf k}sim$($pi,0$) is found generally deeper in BSCCO. These observations together with the Fermi-surface shapes and the chemical potential shifts indicate that the next-nearest-neighbor hopping $|t^{prime}|$ of the single-band model is larger in BSCCO than in LSCO and that $|t^{prime}|$ rather than the super-exchange $J$ influences the pseudogap energy scale.
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