Electron Scattering in Intrananotube Quantum Dots

Intratube quantum dots showing particle-in-a-box-like states with level spacings up to 200 meV are realized in metallic single-walled carbon nanotubes by means of low dose medium energy ${\mathrm{Ar}}^{+}$ irradiation. Fourier-transform scanning tunneling spectroscopy compared to results of a Fabry-Perot electron resonator model yields clear signatures for inter- and intravalley scattering of electrons confined between consecutive irradiation-induced defects (interdefects distance $\le 10\mathrm{nm}$). Effects arising from lifting the degeneracy of the Dirac cones within the first Brillouin zone are also observed.

Figure 1

(a) Three-dimensional topography image [22] of a $\sim 50\mathrm{nm}$ long portion of an armchair SWNT exposed to 200 eV ${\mathrm{Ar}}^{+}$ ions, recorded in the constant current mode with a sample-tip bias voltage ($V_s$) of 1 V (sample grounded) and a tunneling current ($I_s$) of 0.1 nA, $T=5.3\mathrm{K}$. (b) Corresponding $dI/dV$ scan with background subtraction, recorded along the horizontal dashed line in (a), $\Delta x=0.34\mathrm{nm}$. The $dI/dV$ spectra are recorded through a lock-in detection of a 12 mV rms ($\sim 600\mathrm{Hz}$) ac tunneling current signal added to the dc sample bias under open-loop conditions ($V_s=0.9\mathrm{V}$, $I_s=0.3\mathrm{nA}$). (c) Energy spacings between discrete states visible in (b) in the negative bias range between defect sites d3–d4 ($\sim 7.9\mathrm{nm}$) and d5–d6 ($\sim 9.9\mathrm{nm}$).

Figure 2

(a) Three-dimensional STM topography image [22] of a metallic SWNT treated with 200 eV ${\mathrm{Ar}}^{+}$ ions, showing four defects, d1–d4. (b) Line-by-line flattened topography image of the tube in (a) including defects d2–d4, with the corresponding $dI/dV$ scan recorded along the horizontal dashed line. $V_s=0.8\mathrm{V}$, $I_s=0.32\mathrm{nA}$, $T=5.21\mathrm{K}$, $\Delta x=0.1\mathrm{nm}$. (c) $dI/dV$ line profiles of the first two modes in the negative bias range, recorded between the red arrows drawn in (b). (d) $|dI/dV(k,V){|}^2$ map calculated from the $dI/dV$ scan in (b) between the red arrows. (e) Differential conductance calculated within the Fabry-Perot electron resonator model for a (7,4) SWNT with a defect distance of 9.5 nm, intra- and intervalley scattering parameters equal to 0.35 for both impurities, with the corresponding $|dI/dV(k,V){|}^2$ map in (f).

Figure 3

(a) Outline of the experimental setup and of the Fabry-Perot resonator model. (b) Sketch of the graphene valleys at a fixed energy for a (7,4) metallic SWNT. The parallel horizontal $\mathbf{k}$ lines are reminiscent of the quantization in the circumferential direction. (c) Sketch of the 1D-scattering processes between two nonequivalent valleys: intravalley (green arrows) and intervalley scattering (red, blue, and black arrows). The processes indicated by black arrows are only relevant if a commensurability condition is fulfilled. $k_{A_i}$ and $k_{A_j}$ are the CNP axial momenta components of valleys $i$ and $j$, respectively.

Figure 4

(a) STM current error image [22] of a metallic SWNT with two defect sites d1 and d2 produced by an exposition to 1.5 keV ${\mathrm{Ar}}^{+}$ ions, with the corresponding $dI/dV$ scan recorded along the horizontal dashed line. Interference pattern visibility is improved via a background subtraction. (b) Corresponding $|dI/dV(k,V){|}^2$ map limited to low frequencies contributions. $V_s=0.8\mathrm{V}$, $I_s=0.3\mathrm{nA}$, $T=5.3\mathrm{K}$, and $\Delta x=0.22\mathrm{nm}$. (c) Calculated $dI/dV$ scan for a (10,7) SWNT with a length of 18.5 nm corresponding to the average distance between the defects d2 and d3. The intra- and intervalley impurity strengths are equal to 0.025 and 0.05 for the left and the right impurity, respectively. (d) Corresponding $|dI/dV(k,V){|}^2$ map limited to low frequencies contributions.