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Register a new userEffect of orbital symmetry of the tip on Scanning Tunneling Spectra of Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$
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We discuss how variations in the scanning tunneling microscope (STM) tip, whether unintentional or intentional, can lead to changes in topographic images and dI/dV spectra. We consider the possibility of utilizing functionalized tips in order to improve the sensitivity of STM experiments to local irregularities at the surface or hidden below the surface layers. The change in the tip symmetry can radically alter the contrast of the topographic image due to changes in tip-surface overlap. The dI/dV curves change their shape according to which sample bands the tip orbital tends to overlap. In addition, relative phases between competing tunneling channels can be inverted by changing the tip symmetry, which could help reveal the origin of a local irregularity in tunneling spectrum.
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We report tunneling spectra of near optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ intrinsic Josephson junctions with area of 0.09 $mu$m$^2$, which avoid some fundamental difficulties in the previous tunneling experiments and allow a stable temperature-dependent measurement. A d-wave Eliashberg analysis shows that the spectrum at 4.2 K can be well fitted by considering electron couplings to a bosonic magnetic resonance mode and a broad high-energy continuum. Above $T_c$, the spectra show a clear pseudogap that persists up to 230 K, and a crossover can be seen indicating two different pseudogap phases existing above $T_c$. The intrinsic electron tunneling nature is discussed in the analysis.
In cuprate superconductors, the doping of carriers into the parent Mott insulator induces superconductivity and various other phases whose characteristic temperatures are typically plotted versus the doping level $p$. In most materials, $p$ cannot be determined from the chemical composition, but it is derived from the superconducting transition temperature, $T_mathrm{c}$, using the assumption that $T_mathrm{c}$ dependence on doping is universal. Here, we present angle-resolved photoemission studies of Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$, cleaved and annealed in vacuum or in ozone to reduce or increase the doping from the initial value corresponding to $T_mathrm{c}=91$ K. We show that $p$ can be determined from the underlying Fermi surfaces and that $in-situ$ annealing allows mapping of a wide doping regime, covering the superconducting dome and the non-superconducting phase on the overdoped side. Our results show a surprisingly smooth dependence of the inferred Fermi surface with doping. In the highly overdoped regime, the superconducting gap approaches the value of $2Delta_0=(4pm1)k_mathrm{B}T_mathrm{c}$
We present a Greens function based framework for modeling the scanning tunneling spectrum from the normal as well as the superconducting state of complex materials where the nature of the tunneling process$-$ i.e. the effect of the tunneling matrix element, is properly taken into account. The formalism is applied to the case of optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ (Bi2212) high-Tc superconductor using a large tight-binding basis set of electron and hole orbitals. The results show clearly that the spectrum is modified strongly by the effects of the tunneling matrix element and that it is not a simple replica of the local density of states (LDOS) of the Cu-$d_{x^2-y^2}$ orbitals with other orbitals playing a key role in shaping the spectra. We show how the spectrum can be decomposed usefully in terms of tunneling channels or paths through which the current flows from various orbitals in the system to the scanning tip. Such an analysis reveals symmetry forbidden and symmetry enhanced paths between the tip and the cuprate layers. Significant contributions arise from not only the CuO$_2$ layer closest to the tip, but also from the second CuO$_2$ layer. The spectrum also contains a longer range background reflecting the non-local nature of the underlying Bloch states. In the superconducting state, coherence peaks are found to be dominated by the anomalous components of Greens function.
We analyze how the coherence peaks observed in Scanning Tunneling Spectroscopy (STS) of cuprate high temperature superconductors are transferred from the cuprate layer to the oxide layers adjacent to the STS microscope tip. For this purpose, we have carried out a realistic multiband calculation for the superconducting state of Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ (Bi2212) assuming a short range d-wave pairing interaction confined to the nearest-neighbor Cu $d_{x^2-y^2}$ orbitals. The resulting anomalous matrix elements of the Greens function allow us to monitor how pairing is then induced not only within the cuprate bilayer but also within and across other layers and sites. The symmetry properties of the various anomalous matrix elements and the related selection rules are delineated.
The effects of structural supermodulation with the period $lambda approx26$ AA along the $b$-axis of Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ have been observed in photoemission studies from the early days as the presence of diffraction replicas of the intrinsic electronic structure. Although predicted to affect the electronic structure of the Cu-O plane, the influence of supermodulation potential on Cu-O electrons has never been observed in photoemission. In the present study, we clearly see, for the first time, the effects on the Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ electronic structure - we observe a hybridization of the intrinsic bands with the supermodulation replica bands in the form of avoided crossings and a corresponding reconstruction of the Fermi surface. We estimate the hybridization gap, $2Delta_hsim25$ meV in the slightly underdoped samples. The hybridization weakens with doping and the anti-crossing can no longer be resolved in strongly overdoped samples. In contrast, the shadow replica, shifted by $(pi, pi)$, is found not to hybridize with the original bands within our detection limits.
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