Combined spectroscopic imaging STM and ARPES study of different gaps measured in the cuprate phase diagram

A comparative study of the gaps measured in two techniques, angle-resolved photoelectron spectroscopy and spectroscopic imaging scanning tunneling microscopy, is presented. In particular the study focuses on the more overdoped region of the cuprate phase diagram in the superconducting state. While the total densities of states measured in the two techniques agree very well, it is shown that the peak in the density of states, ${\mathrm{\Delta }}_{\mathrm{DOS}}$, is consistently displaced to higher energies relative to the maximal superconducting gap, ${\mathrm{\Delta }}_0$, determined in photoemission. The difference between the two gaps is more evident for the less doped samples reflecting increased normalization of bands. This observation will clearly influence the boundaries in the phase diagrams of the cuprates defined by these two techniques.

Figure 1

(a) Schematic of the ARPES process involving the photoexcitation of electrons and the subsequent detection of the latter in free space and schematic of the SI-STM process involving the application of an electric field between a scanning tip and the surface under investigation enabling the tunneling of electrons back and forth between the tip and the surface. We indicate the amplifier (a) in the STM circuit. (b) The sample mounting required to enable the growth and modification of the surface in the MBE system and transfer of the latter to either the ARPES facility or the SI-STM facility. The scale is indicated.

Figure 2

(a) Topography and (b) gap map measured from the OD91 $(T_c=91\mathrm{K})$ sample over an area $25\times 25\mathrm{nm}$ area using SI-STM. The inset shows the distribution of different gap sizes measured in the sampling area. The blue arrow indicates the peak energy determined in the DOS measurement from both techniques. (c) Gap-sorted averaged $dI/dV$ spectra from SI-STM. (d) ARPES measured constant energy surface corresponding to 15 meV below the chemical potential along with tight binding fits, indicated by the solid and dashed lines. (e) Shows a cut in the antinodal region in the direction indicated by the solid line in (d). (f) Shows two EDC cuts indicated in (e) by the blue and red lines.

Figure 3

(a) Comparison of the integrated DOS measured in SI-STM (red curve) and the integrated DOS measured in ARPES (blue curve) from the OD91 sample. Also shown is the ARPES spectrum, $A(k,\omega )$, measured exactly at $(\pi ,k_{\mathrm{F}})$. (b) The same as in (a) but now for the OD50 sample. (c) Comparison of the integrated DOS measured in ARPES from the slightly underdoped UD85 sample with the ARPES spectrum, $A(k,\omega )$, measured exactly at $(\pi ,k_{\mathrm{F}})$.