Imaging the atomic orbitals of carbon atomic chains with field-emission electron microscopy

A recently developed high-field technique of atomic chains preparation has made it possible to attain the ultrahigh resolution of field-emission electron microscopy (FEEM), which can be used to direct imaging the intra-atomic electronic structure. By applying cryogenic FEEM, we are able to resolve the spatial configuration of atomic orbitals, which correspond to quantized states of the end atom in free-standing carbon atomic chains. Knowledge of the intra-atomic structure will make it possible to visualize generic aspects of quantum mechanics and also lead to approaches for a wide range of nanotechnological applications.

Figure 1

(Color online) Characterization of high-resolution field-emission electron microscopy. (a) A schematic drawing of electron emission from a self-standing atomic chain anchored at the graphite parabolic tip, mounted opposite a luminescent screen. (b) The dependence of theoretical resolution of FEEM on the radius of the supporting parabolic electrode for carbon atomic chains, closed carbon nanotubes with fullerene end caps and conventional parabolic emitters. (c) The calculated resolution of FEEM as a function of the length of carbon atomic chains and nanotubes.

Figure 2

(Color online) FEEM images of the end atoms of carbon chains. (a) Singlet and (b), doublet of bright spots were acquired with a voltage 425 V. The singlet patterns represent the most stable configuration. (c) $s$-like images of two atoms at the end of chains. (d) Spontaneous $s\to p$ transformation of the FEEM pattern at constant voltage of one of atoms shown in c.

Figure 3

(Color online) Transformation of atomic FEEM patterns. (a) A mixed FEEM state transforms successively to (b) $p$-like and (c) $s$-like states. The field-emission current from the end atom increases was increased by about 85 times at the $p\to s$ transformation. A considerable elliptical distortion of the FEEM patterns could be connected with the asymmetry of the supporting graphite tip. (d) A spatial map of lines of equal brightness corresponding to the mixed FEEM pattern (a).

Figure 4

(Color online) Spatial variations of squared wave functions of the end atom of the carbon chain. (a) and (b), FEEM image is formed by the calculated $s$ and $p$ orbitals, respectively. (c–e) Calculated maps of ${\left|\Phi \right|}^2$ based on Eqs. (3, 5). The dashed and solid traces in (c), (d) indicate experimental data and calculation probability amplitudes of the eigenfunctions, respectively. The vertical axis is approximately proportional to the LDOS. (e) The calculated two-dimensional contour plot of the wave function density corresponding to an equal superposition of the $s$ and $p$ orbitals.

Figure 5

(Color online) FEEM images of the end atoms of carbon chain at 300 K acquired with voltages (a) 330, (b) 340, and (c) 360 V. Thermal vibrations of the end atom of chain at this temperature shown in panel (d).

Figure 6

Forming of the branched carbon nanowire during the unraveling of a graphene sheet. Labels (a)–(c) denote the various unraveling stages.

Figure 7

Relaxed configuration of branched atomic chains with the numbers of carbon atoms equal to: 12 (a), 10 (b), and 9 (c).