Colloquium: Electronic instabilities in self-assembled atom wires

Many quasi-one-dimensional (1D) materials are experimental approximations to the textbook models of Peierls instabilities and collective excitations in 1D electronic systems. The recently observed self-assembly of atom wires on solid surfaces has provided fascinating new insights into the nature of their structural and electronic instabilities, from both real-space and momentum-space perspectives. In this Colloquium, three of the most studied atom wire arrays are highlighted, all featuring multiple surface-state bands. One of these is made of indium atoms on a flat silicon (111) surface, while the two others consist of gold atoms on surfaces that are vicinal to Si(111). The experimental and theoretical results are discussed with a focus on the detailed mechanisms of the observed phase transitions and on the role of microscopic defects.

Figure 1

The effect of a Peierls distortion on (a) a half-filled 1D band structure and (b) the charge density and the atomic structure. In (a) the thin continuous band belongs to the undistorted metal and the bold printed gapped band belongs to the Peierls distorted system. (b) The periodic modulation of the charge density and the period doubling of the lattice structure are shown.

Figure 2

Nesting and dielectric response of free electron gases. (a) Lindhard response function for a free-electron gas in one, two, and three dimensions. (b) Fermi surface nesting for a free-electron gas in one and two dimensions. From 8.

Figure 3

(Color online) The $\mathrm{Si}\left(111\right)\text{−}5\times 2\text{−}\mathrm{Au}$ reconstruction. (a) Structural model for $\mathrm{Si}\left(111\right)\text{−}5\times 2\text{−}\mathrm{Au}$. Large, light circles are Au atoms, dark circles are Si adatoms. A $5\times 2$ unit cell and a Si (and a mixed additional Au-Si) honeycomb are indicated. (b) STM image ($-1.5\mathrm{V}$, $200\mathrm{pA}$) of the $\mathrm{Si}\left(111\right)\text{−}5\times 2\text{−}\mathrm{Au}$ wire reconstruction with Si adatoms visible as dots. From 24 and 43.

Figure 4

(Color online) The $\mathrm{Si}\left(557\right)\text{−}\mathrm{Au}$ reconstruction. (a) Structural model for Si(557)-Au. Large light circles are Au atoms, darker circles at the step edges are Si honeycomb atoms, very dark circles are Si adatoms. (b) STM image of the Si(557)-Au surface at room temperature. Tunneling voltage $V=1.5\mathrm{V}$; tunneling current $I_t=300\mathrm{pA}$. From 21 and 92.

Figure 5

Band dispersion and reciprocal lattice of $\mathrm{Si}\left(557\right)\text{−}\mathrm{Au}$. (a) ARPES spectra of Si(557)-Au, showing a split half-filled band dispersing to $E_F$. (b) LEED pattern of the surface, revealing an ordered anisotropic structure. From 91.

Figure 6

Band structure of the Si(557)-Au surface measured with ARPES. (a) Full Brillouin zone along $k_x$, with the zone boundaries at $\pi ∕a$ and (b) a zoom-in image of the doublet of $S1$ and $S2$ bands. Adapted from 7 and 20.

Figure 7

(Color online) STM and STS data from the $\mathrm{Si}\left(557\right)\text{−}\mathrm{Au}$ surface. (a) STM images $(V=1\mathrm{V})$ and (b) STS normalized $dI∕dV$ data of Si(557)-Au at 300 and at $78\mathrm{K}$ revealing a doubling of the periodicity in the step-edge wire and the appearance of a gap at low temperature. The inset in (b) is a zoomed-in spectrum near zero bias. From 6 and 113.

Figure 8

(Color online) Model of the order-disorder transition in $\mathrm{Si}\left(557\right)\text{−}\mathrm{Au}$ surface. (a) Detailed structural model of the Si(557)-Au surface showing buckled step-edge atoms. Schematic band structure (b) below and (c) above $T_c$, showing the empty step-edge bands and energy gap in the spin-split Si-Au bands. Adapted from 81.

Figure 9

(Color online) Final $4\mathrm{ps}$ (of a total of $8\mathrm{ps}$) of a molecular dynamics simulation of the Si(557)-Au reconstruction performed at $\sim 300\mathrm{K}$. (a) The height of different atoms as a function of time (see also Fig. 8): adatom ($ad$, dashed line), rest atom (res, solid line), and the step-edge atoms ($a$, solid line and $b$, dashed line). (b) The two inequivalent Si-Au-Si bond angles ($\alpha$ and $\beta$). Adapted from 81.

Figure 10

(Color online) The $\mathrm{Si}\left(553\right)\text{−}\mathrm{Au}$ reconstruction. (a) Structural model for the Si(553)-Au. Atoms indicated as in Fig. 4. (b) Empty state and (c) filled state STM images of the Si(553)-Au surface at room temperature. $V\pm 0.5\mathrm{V}$, $I_t=50\mathrm{pA}$. From 21 and 94.

Figure 11

Electronic structure of the $\mathrm{Si}\left(553\right)\text{−}\mathrm{Au}$ reconstruction. Band dispersion (bottom) and Fermi surface (top) of the Si(553)-Au surface as measured by ARPES. Adapted from 20.

Figure 12

(Color online) High-pass filtered high-resolution band dispersion of the doublet of bands close to the $\times 2$ zone boundary at $0.41{\mathrm{\AA }}^{-1}$ revealing a pattern of horizontally displaced avoided crossings. Adapted from 12.

Figure 13

(Color online) Variable temperature STM images of the $\mathrm{Si}\left(553\right)\text{−}\mathrm{Au}$ reconstruction. (a) and (b) Empty state and (c) filled state STM images of the Si(553)-Au surface at $40\mathrm{K}$, revealing $\times 3$ periodicities that are in antiphase in filled and empty state images. (d) Empty state STM image at $110\mathrm{K}$ showing both $\times 2$ (white) and $\times 3$ (black) unit cells. $V=\pm 1\mathrm{V}$, $I_t=100\mathrm{pA}$ for (a)–(c) and $1\mathrm{V}$, $50\mathrm{pA}$ for (d). Adapted from 94.

Figure 14

Metal-insulator transition in the $\mathrm{Si}\left(553\right)\text{−}\mathrm{Au}$ reconstruction. (a) STS $I\text{−}V$ and $dI∕dV\text{−}V$ curves at room temperature and $40\mathrm{K}$ showing a metal-insulator transition on the Si(553)-Au surface. (b) Temperature dependence of the (partial) energy gaps of the three bands at the Si(553)-Au surface. $S1$ and $S2$ are the outer and inner bands of the doublet and $S3$ is the quarter-filled band. $S1$ and $S3$ are fitted with the BCS function for a relatively weak electron-phonon coupling. Adapted from 4 and 94.

Figure 15

(Color online) Empty state STM image and line profile of the Si(557)-Au surface near a defect in the step-edge Si wire at (a) room temperature and (b) $78\mathrm{K}$. From 113.

Figure 16

Temperature-dependent resistance and conductivity of the (a) Si(553)-Au and (b) Si(557)-Au surface states, revealing a metal-insulator transition in the former, whereas the latter shows insulating behavior over the full temperature range. The insets show the room-temperature transport paths (dashed) in relation to the defects (dots) present on the surfaces. Adapted from 69.

Figure 17

(Color online) Structural model of the $\mathrm{Si}\left(111\right)\text{−}4\times 1\text{−}\mathrm{In}$ reconstruction. (a) Side and (b) top view. Large circles are the In atoms forming parallel zigzag wires along the [110] direction. The $4\times 1$ unit cell is indicated. Adapted from 96.

Figure 18

(Color online) ARPES band dispersions of the $4\times 1$ [(a) $300\mathrm{K}$] and $8\times 2$ [(b) $45\mathrm{K}$] phases, recorded along the In wire direction. Surface Brillouin zone and schematic of the experimentally determined Fermi contours at (c) $300\mathrm{K}$ and (d) $45\mathrm{K}$. Schematic illustrations of the surface-state band structure at (e) $300\mathrm{K}$ and (f) $45\mathrm{K}$. Adapted from 3.

Figure 19

(Color online) Trimer model for the low-temperature $8\times 2$ structure. There are two degenerate $8\times 2$ structures, arising from the two possible arrangements of In trimers. This is best seen from the registry shift of the $4\times 2$ subcells that are indicated in (a) and (b). The $8\times 2$ unit cell and glide plane of the structure are also shown. Adapted from 46.

Figure 20

(Color online) Domain fluctuations in the $\mathrm{Si}\left(111\right)\text{−}4\times 1\text{−}\mathrm{In}$ reconstructions. (a) and (b) Sequential $60\times 60{\mathrm{nm}}^2$ STM images showing $4\times 1\to 8\times 2$ domain fluctuations at $123\mathrm{K}$. Defects are indicated by arrowheads. The insets are close-up views of defects which locally induce a $4\times 2$ structure. From 72.

Figure 21

(Color online) Order parameters (a) $P_{\times 2}$ (b) $P_{SM}$, and (c) their difference in the vicinity of $T_c$. Adapted from 35.

Figure 22

(Color online) Nanophase domains in $\mathrm{Si}\left(111\right)\text{−}4\times 1\text{−}\mathrm{In}$. (a) STM image of the $\mathrm{In}∕\mathrm{Si}\left(111\right)$ interface at $110\mathrm{K}$. The electronic metal-insulator contrast (bright-dark domains) is separated by dashed lines. The $4\times 1$ domains are marked with dotted lines out of the $8\times 2$ areas. (b) The line profile along $AB$. From 35.

Figure 23

(Color online) Hexagon model for the low-temperature $4\times 2$ and $8\times 2$ structures, showing the displacement patterns for both shear distortion and dimerization. Adapted from 96.

Figure 24

(Color online) Superimposed electronic band structures for 100 different atomic configurations (one every $500\mathrm{fs}$) from molecular dynamics simulations at $450\mathrm{K}$. The light lines show the band structure of the ideal (static) $4\times 1$ structure (in a $4\times 2$) unit cell. Adapted from 29.

Figure 25

(Color online) 1D plasmon dispersion. Open circles are experimental data parallel to the wire direction; crosses (×) are data recorded at a 45° angle and the pluses (+) are their projection onto the wire direction. The solid and dashed lines are the calculated plasmon dispersions for the $m1$, $m2$, and $m3$ surface-state bands (shown in the inset) based on a parallel multiwire model. The straight dotted line is the calculated plasmon dispersion of an isolated metallic wire. Adapted from 56.