Photon-assisted transport in bilayer graphene flakes

The electronic conductance of graphene-based bilayer flake systems reveals different quantum interference effects, such as Fabry-Pérot resonances and sharp Fano antiresonances on account of competing electronic paths through the device. These properties may be exploited to obtain spin-polarized currents when the same nanostructure is deposited above a ferromagnetic insulator. Here, we study how the spin-dependent conductance is affected when a time-dependent gate potential is applied to the bilayer flake. Following a Tien-Gordon formalism, we explore how to modulate the transport properties of such systems via appropriate choices of the ac-field gate parameters. The presence of an oscillating field opens the possibility of tuning the original antiresonances for a large set of field parameters. We show that interference patterns can be partially or fully removed by the time-dependent gate voltage. The results are reflected in the corresponding weighted spin polarization, which can reach maximum values for a given spin component. We found that differential conductance maps as functions of bias and gate potentials show interference patterns for different ac-field parameter configurations. The proposed bilayer graphene flake systems may be used as a frequency detector in the THz range.

Figure 1

Sketch of the model of a finite graphene flake of width $W$ deposited onto a graphene nanoribbon. The bilayer portion of the system ($L$) is placed on the proximity of a ferromagnetic material (blue). An ac field of intensity $V_{\text{ac}}$ and frequency $\omega$ is applied to the bilayer flake.

Figure 2

Spin-dependent conductance vs energy for two BGFs with lengths $N=40$ in (a) and (b) and $N=120$ in (c) and (d). Solid red/black curves denote spins down/up. The systems are probed by an ac field of intensity $e{V}_{\text{ac}}=0.046{\gamma }_0$ and frequencies $\hslash \omega =\mathrm{\Delta }{E}_{40}=0.153{\gamma }_0$ in (a), and $\hslash \omega =\mathrm{\Delta }{E}_{120}=0.052{\gamma }_0$ in (c); dashed blue lines are used for the pristine system ($V_{\text{ac}}=0$ and ${\mathrm{\Delta }}_{\text{ex}}=0$). In (b) and (d) the systems are probed with the same frequency, $\hslash \omega =0.012{\gamma }_0$, and dashed red/black lines stand for $V_{\text{ac}}=0$.

Figure 3

Spin-dependent conductance as a function of the intensity of the ac-field intensity ($e{V}_{\text{ac}}$) for a BGF of length $N=40$, for different values of the ac-field frequency ($\hslash \omega$). The curves are calculated for a fixed energy $E=\mathrm{\Delta }{E}_{{}_N}/2-{\mathrm{\Delta }}_{\text{ex}}\approx 0.06{\gamma }_0$ corresponding to a minimum of the spin-down conductance.

Figure 4

Contour plots of the conductance (upper panels) and weighted spin polarization (bottom panels) for an $N=40$ BGF as function of the ac-field parameters, $e{V}_{\text{ac}}$ and $\hslash \omega$. The energy is fixed at $E=\mathrm{\Delta }{E}_{40}/2-{\mathrm{\Delta }}_{\text{ex}}\approx 0.06{\gamma }_0$; (a) and (c) correspond to spin down, and (b) and (d) to spin up.

Figure 5

Spin-dependent conductance [(a)–(d)] and weighted spin polarization [(e)–(h)] vs energy for a BFG of length $\mathrm{N}=120$. The ac frequency is fixed at $\hslash \omega =3\mathrm{\Delta }{E}_{120}/2\approx 0.08\left({\gamma }_0\right)$ and the ac-field intensity is increasing: (a) $e{V}_{\text{ac}}=0$, (b) $0.04{\gamma }_0$, (c) $0.08{\gamma }_0$, and (d) and (e) $0012{\gamma }_0$. Red and black curves stand for spin down and spin up, respectively.

Figure 6

Contour plots for the spin-down conductance (a), and for weighted spin polarization (b), as a function of the ac-field intensity. The parameters are the same as in Fig. 5.

Figure 7

Contour plots of the (a) spin-down conductance and (b) weighted spin-up polarization as a function of the ac-field frequency $\hslash \omega$ and the ac-field potential $e{V}_{\text{ac}}$, for a $N=120$ BGF. The energy is fixed at $E=\mathrm{\Delta }{E}_{120}/2-{\mathrm{\Delta }}_{\text{ex}}\approx 0.006{\gamma }_0$.

Figure 8

Differential conductance contour plots as a function of bias and gate voltages. Top panels: Null ac field for $N=40$ (left) and $N=120$ (right). Middle panels: $e{V}_{\text{ac}}=0.172{\gamma }_0$ for $N=40$. Bottom panels: $e{V}_{\text{ac}}=0.046{\gamma }_0$ for $N=120$ and from left to right frequencies: $\hslash \omega =\mathrm{\Delta }{E}_{{}_N}/4$, $\mathrm{\Delta }{E}_{{}_N}/2$, and $\mathrm{\Delta }{E}_{{}_N}$, for spin down.

Figure 9

BGF conductance vs energy for $A\text{−}A$ (blue curves) and $A\text{−}B$ (red curves) stacking. Conductances for the pristine systems are marked with dashed lines and in the presence of an ac field with solid lines. The parameters are the same as in Fig. 2, with ${\mathrm{\Delta }}_{\text{ex}}=0$.