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Register a new userThe Three Component Electronic Structure of the Cuprates Derived from SI-STM
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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.
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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.
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.
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.
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.
One of the key motivations for the development of atomically resolved spectroscopic imaging STM (SI-STM) has been to probe the electronic structure of cuprate high temperature superconductors. In both the d-wave superconducting (dSC) and the pseudogap (PG) phases of underdoped cuprates, two distinct classes of electronic states are observed using SI-STM. The first class consists of the dispersive Bogoliubov quasiparticles of a homogeneous d-wave superconductor. These are detected below a lower energy scale |E|={Delta}0 and only upon a momentum space (k-space) arc which terminates near the lines connecting k=pm({pi}/a0,0) to k=pm(0, {pi}/a0). In both the dSC and PG phases, the only broken symmetries detected in the |E|leq {Delta}0 states are those of a d-wave superconductor. The second class of states occurs at energies near the pseudogap energy scale |E| {Delta}1 which is associated conventionally with the antinodal states near k=pm({pi}/a0,0) and k=pm(0, {pi}/a0). We find that these states break the 90o-rotational (C4) symmetry of electronic structure within CuO2 unit cells, at least down to 180o rotational (C2) symmetry (nematic) but in a spatially disordered fashion. This intra-unit-cell C4 symmetry breaking coexists at |E| {Delta}1 with incommensurate conductance modulations locally breaking both rotational and translational symmetries (smectic). The properties of these two classes of |E| {Delta}1 states are indistinguishable in the dSC and PG phases. To explain this segregation of k-space into the two regimes distinguished by the symmetries of their electronic states and their energy scales |E| {Delta}1 and |E|leq{Delta}0, and to understand how this impacts the electronic phase diagram and the mechanism of high-Tc superconductivity, represents one of a key challenges for cuprate studies.
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