Fluctuations and Phase Separation in a Quasi-One-Dimensional System

Phase transitions in a quasi-one-dimensional surface system on a metal substrate are investigated as a function of temperature. Upon cooling the system shows a loss of long-range order, fluctuations, and a transition into an inhomogeneous ground state due to competition of local adsorbate-adsorbate interactions with an incommensurate charge density wave. This agrees with a general phase diagram for correlated systems and high-temperature superconductors. The model surface system allows direct imaging of the fluctuations and the glassy inhomogeneous ground state by scanning tunneling microscopy.

Figure 1

(a) STM image of the $c(2\times 2)\mathrm{\text{−}}\mathrm{Br}/\mathrm{Pt}(110)$ surface ($T=300\mathrm{K}$, $55\times 41{\AA }^2$, 0.63 V, 1.13 nA). White arrows mark the direction of the close-packed Pt rows. The inset shows a simulated STM image based on DFT calculations and displaying contours of constant charge density. (b) Ball model of the Pt(110) surface (gray balls) with the ($1\times 1$) unit cell (upper left), as well as Br (orange balls) $c(2\times 2)$ (lower left), ($2\times 1$) (upper right), and ($3\times 2$) (lower right) domains. The unit cells are shown as black rectangles, the dashed black lines mark the domain boundaries. Br atom 1 occupies a short-bridge, Br atom 2 a long-bridge site. (c) STM image ($T=300\mathrm{K}$, $75\times 65\AA {}^2$, 0.162 V, 1.10 nA) of an area close to a defect (dark spot at lower right of the image). (d) STM image of a $c(2\times 2)$ preparation recorded at $T=110\mathrm{K}$ ($105\times 90{\AA }^2$, 0.92 V, 1.96 nA) showing $c(2\times 2)$ and ($2\times 1$) contrast. (e) Different area of the same preparation as shown in (d) ($T=110\mathrm{K}$, 0.84 V, 0.12 nA). (f) STM image of a $c(2\times 2)$ preparation recorded at $T=50\mathrm{K}$ ($78\times 59{\AA }^2$), showing in addition ($3\times 2$) structural elements. (g) Large-area STM scan recorded at $T=50\mathrm{K}$ ($415\times 251{\AA }^2$, 0.51 V, 0.33 nA) showing three terraces separated by monatomic steps. $c(2\times 2)$, ($2\times 1$) and ($3\times 2$) domains form a striped phase without long-range order.

Figure 2

LEED spot-profile analysis. All peak heights have been corrected by the Debye-Waller factor obtained from the integer-order peak intensity. (a) Height of the Gaussian component in the peak profile measured perpendicular to the close-packed row direction for the ($1/2$, $1/2$) and the (0,1) spot. Inset: Theoretical power-law dependence of the order parameter in the Ising model, which is isomorphous to the $c(2\times 2)$ structure. (b) Height of the Lorentzian component in the peak profile measured perpendicular to the close-packed row direction for the ($1/2$, $1/2$) and the (0,1) spot. Inset: Monte Carlo calculation of critical fluctuations in the Ising model. The divergence at $T_c$ is rounded off due to the finite size of the grid. (c) Correlation length of the critical fluctuations in the adsorbate system perpendicular to the close-packed row direction. (d) Height of the Gaussian component in the peak profile measured parallel to the close-packed row direction for the ($1/2$, $1/2$) and the (0,1) spot. For comparison, the behavior in the orthogonal direction is displayed as the thin red curve. (e) Height of the Lorentzian component in the peak profile measured parallel to the close-packed row direction for the ($1/2$, $1/2$) and the (0,1) spot. (f) Correlation length of the critical fluctuations parallel to the close-packed row direction.

Figure 3

Generic phase diagram of quasi-one-dimensional systems. $t_{\perp }$ is the hopping matrix element which couples the 1D subunits. $T_{\mathrm{MF}}$ is the Peierls mean-field temperature which separates the CDW phase ($T<T_{\mathrm{MF}}$) from the parent phase ($T>T_{\mathrm{MF}}$). $T_{\mathrm{CH}}$ is the coherence temperature above which the coherence between the 1D subunits is lost.