Sensing an electromagnetic field with photon-assisted Fano resonance in a two-branch carbon nanotube junction

A photon-assisted Fano resonance in a two-branch single wall carbon nanotube junction (NJ) is considered. The NJ branches are misaligned by a finite angle $\vartheta$ and represent two coupled one-dimensional quantum dots where quantized electron states are formed. The inter-dot tunneling coupling causes a Fano resonance. When an external electromagnetic field (EF) is applied, the interdot tunneling becomes photon assisted. The resulting dc conductivity of each NJ branch shows series of satellite singularities arising in addition to the steady state Fano peaks. Magnitudes and positions of the singularities depend on the frequency, amplitude, and polarization of the EF, which may be used for sensing purposes.

Figure 1

(a) A carbon nanotube junction (NJ). (b) A $\Lambda$ sensor of the electromagnetic field. We also indicate the components of electric field vector, $E_x$ and $E_y$.

Figure 2

The dimensionless stationary transmission coefficient ${\mathcal{T}}_0$ as a function of the electron energy $\epsilon$ (in units of the sum level energy $\overline{\epsilon }$): (a) for different magnitude of the linewidth $\Gamma$ (see text), (b) for various field polarizations, (c) for various level energy differences $\Delta$, and (d) for various sum level energies $\overline{\epsilon }$.

Figure 3

Calculation results for the linear conductivity $G$ (in units of $4e^2∕\hslash$) of the $\Lambda$ sensor versus the source-drain bias voltage $V_{\mathrm{SD}}$ (in units of $\overline{\epsilon }∕e$). (a) The $G\left(V_{\mathrm{SD}}\right)$ curves for three different external electromagnetic field amplitudes $V_{\mathrm{ac}}$ (see text). The splitting between adjacent satellite peaks is $\propto \hslash \Omega ∕e$. (b) $G\left(V_{\mathrm{SD}}\right)$ for three different field frequencies. (c) Universal dependence of the dimensionless ratio $\alpha =e{V}_{\mathrm{ac}}∕\hslash \Omega$ versus another dimensionless ratio $\kappa =J_1^2\left(\alpha \right)∕J_0^2\left(\alpha \right)$. (d) The $\Lambda$ nanosensor with antennas attached to the NJ branches.

Figure 4

(a) The atomic lattice displacement inside the nanotube section C changes the quantum well profile $U\left(x\right)\to U^{\prime }\left(x\right)$, which affects the energy level position $E_0\to E_0^{\prime }$. (b) Broadening ${\Gamma }_{\mathrm{ph}}\left(T\right)$ of the localized level $E_0=1$ due to electron-phonon coupling at energies $\epsilon =0.01$, 0.2, 0.4, and 1.5 (curves 1–4, respectively). (c) Energy dependence of ${\Gamma }_{\mathrm{ph}}\left(\epsilon \right)$ at different temperatures $T=0.15$, 0.45, 0.65, and 0.85 (curves 1–4). (d) Limits of the Fano sensor sensitivity are shown as $\Omega \text{−}T$ curves corresponding to different ac field harmonics $(m=1,2,3)$. The sensitivity condition (16) is observed below each of the $\Omega \text{−}T$ curves. Here, the field frequency and all the energy quantities are expressed in units of $E_0$, while the temperature is expressed in units of $E_0∕k_B$ ($k_B$ is the Boltzmann constant).