Tunable magnetoresistance behavior in suspended graphitic multilayers through ion implantation

We report a tunable magnetoresistance (MR) behavior in suspended graphitic multilayers through point-defect engineering by ion implantation. We find that ion implantation drastically changes the MR behavior: the linear positive MR in pure graphitic multilayers transforms into a negative MR after introducing significant short-range disorders (implanted boron or carbon atoms), consistent with recent non-Markovian transport theory. Our experiments suggest the important role of the non-Markovian process in the intriguing MR behavior for graphitic systems, and open a new window for understanding transport phenomena beyond the Drude-Boltzmann approach and tailoring the electronic properties of graphitic layers.

Figure 1

Diagrams of cyclotron motion in a 2D system in perpendicular $B$ fields and device schemes for this work. (a) Guiding center drift of cyclotron orbits along the constant-energy contours of a long-range smooth disorder potential, which leads to localization at high-$B$ fields. (b) Localization of electrons by repeated scattering with the same hard-disk (short-range) scatterer. (c) Transition of cyclotron motion between equipotential contours in the presence of both long-range disorders and short-range (hard-disk) scatterers, leading to electron delocalization. (d) Cross section (upper panel) and top view (lower panel) of the device geometry illustrating a graphitic multilayer suspended ∼ 110 nm above the SiO${}_2$/Si substrate. (e) Scanning electron microscope image of a typical device with a suspended graphitic multilayer bridging two electrodes spaced ∼ 500 nm apart. Scale bar: 1 μm.

Figure 2

Electron-transport behavior of a multilayer graphitic device before boron implantation. (a) Differential conductance ($\mathit{dI}$/$\mathit{dV}$) as a function of gate voltage $V_g$ with drain-source bias $V_d$ $=$ 0 for a graphitic multilayer at temperature $T$ $=$ 4.2 K and magnetic field $B$ $=$ 0. (b) $\mathit{dI}$/$\mathit{dV}$ vs $V_d$ with $V_g$ $=$ 0 at $T$ $=$ 4.2 K and $B$ $=$ 0. (c) Differential resistance $R$ (symbols), which is the inverse of measured $\mathit{dI}$/$\mathit{dV}$, as a function of $B$ field at various source-drain bias $V_d$ at $T$ $=$ 4.2 K. Lines are the best fittings to the experimental data by a power-law behavior ($R\propto B^{\alpha }$) for $B$ > 2.15 T. The fitting parameter is α $=$ 0.81, 0.65, 0.47, 0.52, 0.60, and 0.64, for the data with $V_d=0,\hspace{0.5em}-8,\hspace{0.5em}-16,\hspace{0.5em}-24,\hspace{0.5em}-32,\hspace{0.5em}\mathrm{and}\hspace{0.5em}-40\hspace{0.5em}\mathrm{mV}$, respectively (from top to bottom). The vertical line is a guide to the eye at $B$ $=$ 2.15 T. Inset: Low-field negative magnetoresistance data for $V_d$ $=$ 0 (symbols) and the best fitting (line) according to the weak localization theory for graphene in Ref. 24 with fitting parameters: dephasing length $L_{\mathrm{\phi }}$ $=$ 68 nm, intervalley scattering length $L_i$ $=$ 50 nm, and scattering length $L_{*}=1$ nm characterizing the trigonal warping effect and chirality-breaking, elastic intravalley scattering.

Figure 3

Differential conductance $\mathit{dI}$/$\mathit{dV}$ as a function of drain-source bias $V_d$ with gate voltage $V_g$ $=$ 0 at different temperature $T$ (a) before and (b) after a boron implantation for the device of Fig. 2 (from bottom to top based on the $\mathit{dI}$/$\mathit{dV}$ values at $V_d$ $=$ 0: $T$ $=$ 4.2, 10, 20, 40, 60, 80, 110, and 295 K); $\mathit{dI}$/$\mathit{dV}$ as a function of temperature with $V_g$ $=$ 0 at different $V_d$ (c) before and (d) after the boron implantation (from bottom to top: $V_d$ from 0 to 200 mV in a step of 20 mV).

Figure 4

SdH oscillations for the device of Fig. 2 at different drain-source bias $V_d$ obtained by subtracting the original data with the fitted positive magnetoresistance background [Fig. 2c]. For clarity, the curves are stacked with an offset of $-0.04\hspace{0.5em}\mathrm{k}\Omega$ from top to bottom.

Figure 5

Raman-scattering spectra and electron-transport behavior for the device of Fig. 2 after a boron implantation (with a boron density per layer ∼$n_S\hspace{0.5em}1.4\times {10}^{12}/{\mathrm{cm}}^2$). (a) Raman spectra after (red/dark gray) and before (black marked with arrow) the implantation. Inset: a zoomed-in view of the $G$ band, showing a shift of Δω${}_G$ $=$ 5.5 cm${}^{-1}$. (b) $\mathit{dI}$/$\mathit{dV}$ vs $V_g$ with $V_d$ $=$ 0 at different temperatures after the implantation. (c) Comparison of $\mathit{dI}$/$\mathit{dV}$ vs $V_d$ with $V_g$ $=$ 0 after (red/dark gray) and before (black marked with arrow) the implantation.

Figure 6

Differential resistance $R$ (symbols) as a function of $B$ field with $V_d$ $=$ 0 at $T$ $=$ 4.2 K for the device in Fig. 5 after the boron implantation. The solid line and the dashed line show fittings with a quadratic and a linear $B$ dependence for the MR, respectively.

Figure 7

MR behavior for a suspended graphitic multilayer device (a) before and (b) after the implantation of ${\mathrm{C}}^{12}$ ions (8 keV) with a total dosage of 1.2×10${}^{14}$ ions/cm${}^2$ in experiments (the implanted ${\mathrm{C}}^{12}$ density per layer cannot be estimated since unfortunately we were not able to determine the thickness for this sample). (c) $\mathit{dI}$/$\mathit{dV}$ vs $V_g$ and (d) $\mathit{dI}$/$\mathit{dV}$ vs $V_d$ before and after the implantation for the device.

Figure 8

MR behavior for a suspended graphitic multilayer device (∼ 49 nm thick) before and after the implantation of boron ions with a lower density ∼ 10${}^{10}$ /cm${}^2$ per layer for the bottom layer (according to the SRIM simulation with a dosage of 1.2×10${}^{14}$ ions/cm${}^2$ for implantation with 7 keV boron ions in experiments).