Suppression of Superfluid Density and the Pseudogap State in the Cuprates by Impurities

We use scanning tunneling microscopy (STM) to study magnetic Fe impurities intentionally doped into the high-temperature superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}\mathrm{C}{\mathrm{u}}_2{\mathrm{O}}_{8+\delta }$. Our spectroscopic measurements reveal that Fe impurities introduce low-lying resonances in the density of states at ${\mathrm{\Omega }}_1\approx 4\mathrm{meV}$ and ${\mathrm{\Omega }}_2\approx 15\mathrm{meV}$, allowing us to determine that, despite having a large magnetic moment, potential scattering of quasiparticles by Fe impurities dominates magnetic scattering. In addition, using high-resolution spatial characterizations of the local density of states near and away from Fe impurities, we detail the spatial extent of impurity-affected regions as well as provide a local view of impurity-induced effects on the superconducting and pseudogap states. Our studies of Fe impurities, when combined with a reinterpretation of earlier STM work in the context of a two-gap scenario, allow us to present a unified view of the atomic-scale effects of elemental impurities on the pseudogap and superconducting states in hole-doped cuprates; this may help resolve a previously assumed dichotomy between the effects of magnetic and nonmagnetic impurities in these materials.

Figure 1

(a) Spectra group averaged based on ${\mathrm{\Delta }}_{\mathrm{PG}}$ from the region in (b). In the smallest gapped spectrum, ${\mathrm{\Delta }}_{\mathrm{PG}}\approx {\mathrm{\Delta }}_{\mathrm{SC}}\approx 24\mathrm{mV}$. Kinks at 24 mV in the larger gap spectra are associated with ${\mathrm{\Delta }}_{\mathrm{SC}}$. (b) Gap map over a 200 Å-square region showing standard inhomogeneity of ${\mathrm{\Delta }}_{\mathrm{PG}}$. ${\mathrm{\Delta }}_{\mathrm{PG}}=33\pm 5\mathrm{mV}$. Our values for ${\mathrm{\Delta }}_{\mathrm{SC}}$ and ${\mathrm{\Delta }}_{\mathrm{PG}}$ are consistent with reported near-nodal and antinodal gap sizes by ARPES on BSCCO for samples of comparable hole doping [22, 23].

Figure 2

33 Å images taken concurrently around a single Fe impurity. (a) $+16\mathrm{mV}$ differential conductance map. An orange x marks the impurity center. Yellow x’s indicate the locations of the nearest impurity bright spots to the impurity center [N, E, S, and W locations of (d)]. (b) $-16\mathrm{mV}$ map of the same location. (c) Topography showing the Bi atoms in the Bi-O layer. The impurity center is shifted $\sim 1.5\AA$ from the expected Bi atom location. (d) Naming scheme used to identify individual features in the impurity-affected region based on $+16\mathrm{mV}$ map layer. C represents the impurity center. N, E, S, and W are nearest neighbor bright spots. NW, NE, SE, SW are next-nearest-neighbor bright spots.

Figure 3

(a) Background spectra taken directly outside of the impurity-affected region of Fig. 2 ($\sim 15\AA$ from impurity center) show a ${\mathrm{\Delta }}_{\mathrm{SC}}\approx 24\mathrm{mV}$ kink and peaks indicating ${\mathrm{\Delta }}_{\mathrm{PG}}\approx 33\mathrm{mV}$. North, center, and south regions of the impurity-affected region show a single impurity-induced resonance at $\sim +16\mathrm{mV}$. (b) C2NW and C2SE spectra show similar gap-defining peaks but no clear subgap resonances. (c) Overlay of a spatially averaged spectrum taken from within the impurity region (red) with the average local background spectrum (blue). The impurity resonance near $+16\mathrm{mV}$ is clearly seen in the red curve. Both spectra originate from the same 40 Å-square spectral map (33 Å-square region of which appears in Fig. 2). The “local background” spectrum represents an average of spectra from the map which are 15 Å or further away from the impurity center.

Figure 4

(a) High-resolution impurity spectra normalized to the local background show two peaks at positive bias: ${\mathrm{\Omega }}_1\approx 4\mathrm{mV}$ and ${\mathrm{\Omega }}_2\approx 15\mathrm{mV}$. (b) Red: spatially averaged spectrum taken from within the impurity region normalized to the average local background spectrum shows four peaks: $\pm 3\mathrm{mV}$ and $\pm 15\mathrm{mV}$. The local background spectrum (blue) provided for reference.