Anomalous insulator-metal transition in boron nitride-graphene hybrid atomic layers

The study of two-dimensional (2D) electronic systems is of great fundamental significance in physics. Atomic layers containing hybridized domains of graphene and hexagonal boron nitride (h-BNC) constitute a new kind of disordered 2D electronic system. Magnetoelectric transport measurements performed at low temperature in vapor phase synthesized h-BNC atomic layers show a clear and anomalous transition from an insulating to a metallic behavior upon cooling. The observed insulator to metal transition can be modulated by electron and hole doping and by the application of an external magnetic field. These results supported by ab initio calculations suggest that this transition in h-BNC has distinctly different characteristics when compared to other 2D electron systems and is the result of the coexistence between two distinct mechanisms, namely, percolation through metallic graphene networks and hopping conduction between edge states on randomly distributed insulating h-BN domains.

Figure 1

Optical microscopy images of a transferred h-BNC film (a) and ribbon (b) on a silicon substrate. The patterned ribbon was fabricated by using optical lithography and oxygen plasma etching. (c) Optical image of a typical h-BNC ribbon electrically contacted with Ti/Au pads of thickness ranging from 3 to 30 nm.

Figure 2

Scanning electron microscope image of one of our experimental devices.

Figure 3

Schematic diagram of the hybridized h-BN graphene device geometry.

Figure 4

(a) High-resolution transmission electron microscopy (HRTEM) image taken on the edge of the sample indicates most of our tested films are composed of three layers. (b) The fast Fourier transform reveals a three-layer packing region with rotational angle of 11${}^{\circ }$ in our sample. (c) The core electron energy loss spectra (EELS) clearly shows B, C, and N are uniformly distributed throughout the film.

Figure 5

Low-temperature transport of h-BNC and pristine graphene FETs. Temperature dependence of the resistance of a pristine graphene (a) and a hybridized BNC with 90 at. % carbon (b) under zero-magnetic field in a cooling run. The curve of h-BNC exhibits a peak at $T_{\mathrm{peak}}=12$ K, signaling the insulator-metal transition. A negative derivative of the resistance ($\frac{dR}{dT}<0$) corresponds to an insulating phase, and a positive sign ($\frac{dR}{dT}>0$) is empirically associated with the metallic phase. It should be clarified that graphene was measured in a four terminal configuration while h-BNC was measured in a two terminal one. The insert images of (a) and (b) are atomic models for pure graphene and hybridized h-BN graphene, respectively.

Figure 6

Temperature dependence of the resistance for h-BNC films with (a) 90 at. % carbon under zero gate voltage and under various magnetic fields measured either in warming up or cooling down sweeps. Insulator to metal transition observed in different h-BNC devices with (b) 65 at. %, (c) 94 at. %, and (d) 56 at. % carbon.

Figure 7

Temperature dependence of the resistance of a h-BNC film under gate voltages of $V_{\mathrm{gate}}=+40$, 0, $-$40 V, and under fixed magnetic field of 0 T for a 40 at. % carbon device.

Figure 8

Temperature dependence of the resistance of a h-BNC film under gate voltages of $V_{\mathrm{gate}}=+40$, $+$28, 0, $-$40 V, and under fixed magnetic field of (a) 6 T and (b) 9 T for a 90 at. % carbon device.

Figure 9

Electric field dependence of the insulator-metal transition in h-BNC at 90 at. % carbon. (a) Temperature dependence of the h-BNCs resistance at gate voltage $V_{\mathrm{gate}}=+40$, $+$28, 0, $-$28, $-$40 V in a fixed magnetic field of 3 T. (b) The variation of resistance as a function of gate voltage measured at a temperature of 37.5 K. The vertical line marks the neutrality point (Dirac point) of h-BNC FET. (c) The corresponding changes of peak position and FWHM in abnormal IMT peak as a function of gate voltage in (a). (d) Room temperature $I$-$V$ curves for h-BNC under different bias voltages.

Figure 10

Temperature dependence of the resistance of a h-BNC film under magnetic fields of $B=0$, 3, 6, and 9 T, measured for backgate voltage values of (a) $-$40 V and (b) $+$40 V for a 90 at. % carbon device.

Figure 11

Magnetic field dependence of the insulator-metal transition in h-BNC at 90 at. % carbon. (a) Temperature dependence of the h-BNCs resistance at magnetic field $B=0$, 3, 6, and 9 T measured in zero gate voltage. The abnormal IMT point down-shifts to lower temperature with the increasing magnetic field. The dashed lines are guides to the eye. (b) Changes of peak position and FWHM in the abnormal IMT peak as a function of magnetic field measured in a gate voltage of 28 V.

Figure 12

Schematic of a h-BN nanoribbon embedded in graphene. Two degenerate states localized at the N and B terminated zigzag edges of the h-BN nanoribbon are depicted by isosurfaces of $\pm$0.1 $e$/Å${}^{3/2}$. B, N, and C atoms are depicted by red, blue, and gray balls, respectively.

Figure 13

Schematics of a N terminated zigzag edged nanodomain in h-BNC with wave functions depicted as isosurfaces of $\pm 0.025$ Å${}^{-3/2}$ for (a) localized edge states at the nanodomain boundaries and (b) extended graphenelike states. B, N, and C atoms are colored red, blue, and gray, respectively.

Figure 14

Transmission through a N terminated zigzag edged h-BN nanodomain embedded in graphene (shown as inset) as a function of energy $\varepsilon$ relative to the Fermi level ${\varepsilon }_F$ in eV. Note the peak in the transmission at $\sim$0.2 eV corresponding to the state localized on the edge of the h-BN nanodomain, shown in Fig. 13a.

Figure 15

Schematic of a (a) h-BN zigzag terminated nanoribbon and a (b) N terminated zigzag edged h-BN nanodomain embedded in graphene. The change in charge density $\Delta \rho$ upon removal of one electron is shown by isosurfaces of $\pm$0.006 25 $e$/Å${}^3$. Red regions depict positive charge, while blue regions depict negative charge. B, N, and C atoms are depicted by red, blue, and gray balls, respectively.

Figure 16

Theoretical model for the insulator-metal transition in h-BNC: (a) Phenomenological parallel-resistor model for the IMT. (b) Single-parameter scaling leading to the collapse of all five $R\left(T\right)$ curves shown in Fig. 9a, for different doping levels, into a single universal curve. The parallel-resistor model (black line) is compared to the experimental resistance for the five different gate voltages.

Figure 17

Data fitting of the insulating portion of the $R\left(T\right)$ data. Black, red, green, and blue curves correspond to $x$ values of 1, 1/2, 1/3, and 1/4, respectively. The ES-VRH mechanism ($x=1/2$) gives the best fit of our data to a straight line.

Figure 18

Data fitting of the metallic portion of the $R\left(T\right)$ data.