Gate-Controlled Quantum Interference Effects in a Clean Single-Wall Carbon Nanotube $p-n$ Junction

The precise control and deep understanding of quantum interference in carbon nanotube (CNT) devices are particularly crucial not only for exploring quantum coherent phenomena in clean one-dimensional electronic systems, but also for developing carbon-based nanoelectronics or quantum devices. Here, we construct a double split-gate structure to explore the Aharonov-Bohm (AB) interference effect in individual single-wall CNT $p-n$ junction devices. For the first time, we achieve the AB modulation of conductance with coaxial magnetic fields as low as 3 T, where the flux through the tube is much smaller than the flux quantum. We further demonstrate direct electric-field control of the nonmonotonic magnetoconductance through a gate-tunable built-in electric field, which can be quantitatively understood in combination with the AB phase effect and Landau-Zener tunneling in a CNT $p-n$ junction. Moreover, the nonmonotonic magnetoconductance behavior can be strongly enhanced in the presence of Fabry-Pérot resonances. Our Letter paves the way for exploring and manipulating quantum interference effects with combining magnetic and electric field controls.

Figure 1

(a) Energy spectrum of CNT in parallel magnetic field $B_{\parallel }$ near the Dirac cone. (b) Schematics of the double split-gate device geometry. (c) False-colored SEM image of a representative device. The individual nanotube (gray) is contacted by Pd/Au electrodes (orange) with side gates (brown). Scale bar is 100 nm. (d) Schematic of the potential profile along the channel controlled by $V_{g1}$ and $V_{g2}$, illustrating the formation of the $p-n$ junction. Landau-Zener tunneling exists in a CNT device under a given bias.

Figure 2

(a) Conductance $G$ as a function of $V_{g1}$ and $V_{g2}$ at $B=0\mathrm{T}$ and $T=3.2\mathrm{K}$. Labels denote the charge carrier configuration of the four quadrants defined by split gates. (b) Magnetoconductance traces for different gate voltages, located near the $p-n$ boundary region and indicated by the colored lines in (a). With increasing built-in electric field $E_{\mathrm{in}}$, the magnetoconductance peak moves towards lower magnetic fields. Inset: Temperature evolution of nonmonotonic magnetoconductance. The red line represents the fitting to Eq. (1). (c) $E_{\mathrm{in}}$ dependence of calculated magnetoconductance based on the band tunneling model. The hollow circles mark the magnetic field position $B_{*}$ of conductance maximum. (d) $I-V$ characteristics in a $p-n$ junction region at various temperatures. Inset: a fit of typical $I-V$ curve based on the model of Landau-Zener tunneling.

Figure 3

(a) Magnetoconductance for different titled angles $\theta$. The traces are vertically offset for clarity. (b) The variation of magnetoconductance $\mathrm{\Delta }G=G(B)-G(0)$, plotted as a function of axial field, $B_{\parallel }=B\cos \theta$. The peak position of magnetoconductance is found only related to the parallel component of the field. Inset: Schematic of the measurement configuration.

Figure 4

(a) Color scale plot of $dI/dV$ as a function of $V_s$ and $V_{g1}$, taken at fixed $V_{g2}=-2.5\mathrm{V}$ and $T=2.9\mathrm{K}$. The spectroscopy exhibits a typical checkerboard pattern for the FP interference. (b) Magnetoconductance traces obtained at different gate voltages corresponding to colored circles in the inset. Inset: Conductance as a function of $V_{g2}$. The red dotted circles indicate the resonance peaks associated with the appearance of the nonmonotonic magnetoconductance. (c) Calculated differential of total transmission coefficient $T_{\mathrm{tot}}$ and magnetic field $B$ as a function of $B$ and $E_{\mathrm{in}}$. The red line is $d{T}_{\mathrm{tot}}/dB=0$, namely, $B_{*}$. (d) Calculated transmission coefficient of the CNT device, showing an enhancement near the Fermi level in the presence of Zener tunneling. Inset: The transmission coefficient is strongly modulated by varying the length of the doping region.