Observation of Coulomb repulsion between Cu intercalants in ${\mathrm{Cu}}_x{\mathrm{Bi}}_2$${\text{Se}}_3$

Using scanning tunneling microscopy and ab initio simulations, we have identified several configurations for Cu dopants in ${\text{Cu}}_x$${\text{Bi}}_2$${\text{Se}}_3$, with Cu intercalants being the most abundant. Through statistical analysis, we show strong short-range repulsive interactions between Cu intercalants. At intermediate range (>5 nm), the pair distribution function shows oscillatory structure along the $\langle 10\overline{1}\rangle$ directions, which appear to be influenced by different diffusion barriers along the $\langle 10\overline{1}\rangle$ and $\langle 2\overline{1}\overline{1}\rangle$ directions.

Figure 1

${\text{Cu}}_{0.05}$${\text{Bi}}_2$${\text{Se}}_3$ after a room temperature cleave shows nodules on the surface. To prevent the tip from changing, we take data between these larger features. The nodule count appears to scale linearly with the nominal Cu doping level.

Figure 2

Topography (top) and dI/dV (bottom) at +0.5 V (left) and $-0.5$ V (right) of the same region of ${\text{Cu}}_{0.2}$${\text{Bi}}_2$${\text{Se}}_3$ at 500 pA. At $-0.5$ V, the ${\text{Bi}}_{\mathrm{Se}}$ antisite defects are weak features in the topography (c), though are prominent features in the dI/dV image (d). Additional defects are present, but are not well structured. They are likely multidefect complexes.

Figure 3

Detailed defect analysis. (a) Defect A atomic resolution topograph at 1 V, 480 pA. (b) Defect B topograph which we have associated with an H-site intercalant. (c) Defect C topograph which we have associated with a T4-site intercalant. (d) Newly identified defect D and (e) newly identified defect E. Color range for (e) is 18 pm; all others are 43 pm.

Figure 4

Simulated STM images for bias of $-0.5$ and +0.5 V for Fermi energy 0.3 eV above the CBM and corresponding defect structures. ${\text{Cu}}_{\mathrm{Bi}}$ in the second atomic layer is the closest match for defect A. Both ${\text{Cu}}_{\mathrm{Se}}$ (fifth layer) and ${\text{Cu}}_{\mathrm{Bi}}$ (fourth layer) have features common to defect D. Defects B and C are best associated with intercalant defects.

Figure 5

 (a) $200\mathrm{nm}\times 200\mathrm{nm}$ topography of nominally ${\text{Cu}}_{0.05}$${\text{Bi}}_2$${\text{Se}}_3$ showing 1020 Cu intercalants, white spots, and Cu clusters, red dots. (b) Radial distribution function of Cu intercalants extracted from (a) along directions of major symmetry. (c) A repulsive interaction is shown by the potential of mean force, determined by taking the log of the radial distribution function (solid line). The dotted line is a fit to the Yukawa potential; the screening length was found to be 3.9 ± 0.4 nm. The normalization factor was determined by computing the radial distribution function for an ensemble of random distributions and is plotted with its pointwise standard deviation in (d). To determine whether the structure within the radial distribution functions is within 1σ, we normalized the distribution functions along $\langle 10\overline{1}\rangle$ and $\langle 2\overline{1}\overline{1}\rangle$ by $R^{*}\left({\mathbf{r}}_1,{\mathbf{r}}_2\right)\pm \sigma$, as shown in (e) and (f). The lattice vectors are plotted on top of a C-type defect (g). The observed structure indicates that the preferred ordering at this intercalant density is similar to that shown in (h). The observed directional anisotropy is attributed to diffusion barrier anisotropy: hopping along sites in the $\langle 10\overline{1}\rangle$ direction has a lower barrier than the $\langle 2\overline{1}\overline{1}\rangle$ direction, as shown by the lattice sites in (i).

Figure 6

(a) Climbing image nudged elastic band calculation [34] of the kinetic barrier for diffusion of intercalated Cu directly in the $\langle 211\rangle$ direction. Eight images are chosen between each metastable minima, the energies of which are shown by the points. A spline is added between points as a guide to the eye. The small insets show the atomic structures at the ${\text{H}}_3$, ${\text{T}}_4$, and ${\text{T}}_1$ metastable configurations. The large inset is a top-down view depicting the successive hops taken into consideration in the calculation. (b) Schematic representation of the lattice where black lines are drawn between lattice registries which have a small barrier for Cu diffusion. Diffusion along the $\langle 10\overline{1}\rangle$ and $\langle 2\overline{1}\overline{1}\rangle$ directions are indicated by paths highlighted in blue and red, respectively.