Analysis of scanning tunneling microscopy images of the charge-density-wave phase in quasi-one-dimensional ${\mathrm{Rb}}_{0.3}\mathrm{Mo}{\mathrm{O}}_3$

The experimental scanning tunneling microscopy (STM) images for the charge-density-wave (CDW) phase of the blue bronze ${\mathrm{Rb}}_{0.3}\mathrm{Mo}{\mathrm{O}}_3$ have been successfully explained on the basis of first-principles density functional theory calculations. Although the density of states near the Fermi level strongly concentrates in two of the three types of Mo atoms (${\mathrm{Mo}}_{\mathrm{II}}$ and ${\mathrm{Mo}}_{\mathrm{III}}$), the STM measurement mostly probes the contribution of the uppermost O atoms of the surface, associated with the ${\mathrm{Mo}}_{\mathrm{I}}{\mathrm{O}}_6$ octahedra. In addition, it is found that the surface concentration of Rb atoms plays a key role in determining the surface nesting vector and hence, the periodicity of the CDW modulation. Significant experimental inhomogeneities of the ${\mathit{b}}^{*}$ surface component of the wave vector of the modulation probed by STM are reported. The calculated changes in the surface nesting vector are consistent with the observed experimental inhomogeneities.

Figure 1

(Color online) (a) An idealized surface structure of ${\mathrm{Rb}}_{0.3}\mathrm{Mo}{\mathrm{O}}_3$ in the $\left(\overline{2}01\right)$ plane. The filled and dashed square units are in the first $\mathrm{Mo}{\mathrm{O}}_6$ sublayer. (b) Idealized sideview of the room temperature ${\mathrm{Rb}}_{0.3}\mathrm{Mo}{\mathrm{O}}_3$ structure projected onto the plane perpendicular to the $\mathit{b}$ axis. Each square represents a $\mathrm{Mo}{\mathrm{O}}_6$ octahedron with the Mo located at the center of oxygen octahedron. Closed circles are Rb atoms at the uppermost positions of the “surface” (labeled 1) and empty circles are Rb atoms $1.2\mathrm{\AA }$ below (labeled 2). The three highest octahedra with respect to the “surface” are the dashed squares indicated by the arrows. Their centers lie at levels 1.8, 2.4, and $3.5\mathrm{\AA }$ below the surface.

Figure 2

The band structure for (a) bulk ${\mathrm{Rb}}_{0.3}\mathrm{Mo}{\mathrm{O}}_3$; (b) a slab preserving the bulk stoichiometry at the surface, and (c) a slab with a defect of Rb atoms (one every three) at the surface. In (a) $\Gamma =(0,0,0)$, $X^{\prime }=(\frac{1}{2},0,0)$, and $Y^{\prime }=(0,\frac{1}{2},0)$ in units of the ${\mathit{a}}^{\mathbf{\prime }\mathbf{*}}$, ${\mathit{b}}^{\mathbf{\prime }\mathbf{*}}$, and ${\mathit{c}}^{\mathbf{\prime }\mathbf{*}}$ reciprocal lattice vectors (Ref. 4). In (b) and (c) $\Gamma =(0,0)$, $X=(\frac{1}{2},0)$, and $Y=(0,\frac{1}{2})$ in units of the corresponding oblique reciprocal lattice vectors.

Figure 3

The ${\mathit{b}}^{\mathbf{*}}$ component of the surface nesting vector of the $\left(\overline{2}01\right)$ surface of rubidium blue bronze versus the density of alkali atoms at the surface. The horizontal axis indicates the number of excess Rb atoms at the surface per unit cell, with the zero corresponding to the stoichiometric Rb composition. The continuous line corresponds to the calculated values. The empty circles refer to the experimental values of ${\mathit{q}}^{\mathbf{*}}$ probed by STM (See text).

Figure 4

(Color online) (a) The constant current STM image of about $30\times 30{\mathrm{nm}}^2$ of an in situ cleaved $\left(\overline{2}01\right)$ surface of ${\mathrm{Rb}}_{0.3}\mathrm{Mo}{\mathrm{O}}_3$ in the CDW ground state at $63\mathrm{K}$ with molecular and CDW resolution. The tunneling conditions are $\mathrm{Vbias}=+420\mathrm{mV}$ and $I_t=110\mathrm{pA}$. (b) A 2D Fourier transform of (a) showing surface lattice spots indicated by vectors $\mathbf{2}{\mathit{b}}^{\mathbf{*}}$ and $\mathbf{2}{(\mathit{a}+\mathbf{2}\mathit{c})}^{\mathbf{*}}$ and CDW superlattice spots around each lattice spot indicated by ${\mathit{q}}_{\mathit{C}\mathit{D}\mathit{W}}$ short white arrows. In this scanned zone the ${\mathit{b}}^{\mathbf{*}}$ component of ${\mathit{q}}_{\mathit{C}\mathit{D}\mathit{W}}$ equals the 0.25 bulk value. (c) The constant current STM image with similar parameters as indicated in (a) but measured on another sample. (d) A 2D Fourier transform of (c) showing the same spots as those appearing in (b) but with the ${\mathit{b}}^{\mathbf{*}}$ component of ${\mathit{q}}_{\mathit{C}\mathit{D}\mathit{W}}$ equals 0.30, showing significant clear deviation from the 0.25 bulk value.

Figure 5

(Color online) (a) The constant current mode topographical image of $6.2\times 6.2{\mathrm{nm}}^2$ on $\left(\overline{2}01\right)$ plane of ${\mathrm{Rb}}_{0.3}\mathrm{Mo}{\mathrm{O}}_3$ at $63\mathrm{K}$ (raw data image). The bias voltage applied on the sample is $+420\mathrm{mV}$ and the set-up tunneling current is $110\mathrm{pA}$. Molecular lattice and CDW superlattice coexist in the image. The three arrows indicate (from left to right) , respectively, the observed type I, II $\mathrm{Mo}{\mathrm{O}}_6$ octahedra, and the expected position of the ${\mathrm{Mo}}_{\mathrm{III}}{\mathrm{O}}_6$ octahedra. An associated profile along ${\mathrm{Mo}}_{\mathrm{I}}{\mathrm{O}}_6$ octahedra indicated by a left arrow (from Ref. 3). (b) (Color online) The calculated image and associated profile along the ${\mathrm{Mo}}_{\mathrm{I}}{\mathrm{O}}_6$ octahedra for the modulated phase of ${\mathrm{Rb}}_{0.3}\mathrm{Mo}{\mathrm{O}}_3$.

Figure 6

(Color online) The isocharge density, represented as the gray surface [sideview as in Fig. 1b] integrated from the Fermi level to $0.5\mathrm{eV}$ above. All the relevant atoms have been labeled. In the image in color the Rb, Mo, and O atoms are shown as black, yellow (light gray), and red (gray) balls, respectively.