Effect of orbital symmetry of the tip on scanning tunneling spectra of Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$

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 the tunneling spectrum.

Figure 1

(a) Geometry of the simulated system. Left-hand panel gives the arrangement of the CuO${}_2$ layer, while the right panel depicts the BiO and SrO layers on top of the CuO${}_2$ layer. (b)–(e) Topographic STM images for different tip symmetries. (b) $s$ orbital, (c) $p_z$ orbital, (d) $p_r$ orbital, and (e) $p_b$ orbital. Indicated also are Bi and O positions and the top (T), bridge (B), and hollow (H) sites. In (d) and (e) the tip symmetry is further indicated with a schematic of the corresponding $p$ orbital.

Figure 2

Corrugation curves for various tip orbitals along the route ($A\to B\to C\to A$) shown in the inset. The vertical scale represents the height change the tip experiences along the route. Curves for $p_r$ and $p_b$ are similar in overall shape yet they differ strongly in relative amplitude. This shows that they connect at least partially to different surface orbitals. Note that each curve was shifted downward by its own average tip surface distance thus making all curves zero centered.

Figure 3

(a) LDOS of $p_z$ of Bi, $p_{x/y}$ of O(Bi), and $p_z$ of O(Bi). The first orbital hybridizes with the CuO${}_2$ bands, the second is dominant in BiO bands (Bi pocket states), and the third is rather localized. (b), (c), and (d) show the $dI/dV$ curves with different tip orbitals at the high-symmetry sites B, H, and T, respectively.

Figure 4

(a) $dI/dV$ spectra of the regular and modified bonding oxygen using $s$-symmetric tip above the oxygen. (b) The same spectra using $p_b$-symmetric tip above the oxygen. (c) LDOS of the $p$ orbital of the bonding oxygen in the cuprate layer. Regular case (red) is compared with an orbital with a modified on-site energy (blue). (d) Two competing channels from the bonding oxygen ($o$) through $d_z$ orbitals ($a$ or $b$), apical oxygens ($f$ and $g$), and the surface bismuths (1 and 2) to the tip ($t$).