Transport gap in suspended bilayer graphene at zero magnetic field

We report a change of three orders of magnitude in the resistance of a suspended bilayer graphene flake which varies from a few k$\Omega$ in the high-carrier-density regime to several M$\Omega$ around the charge neutrality point (CNP). The corresponding transport gap is 8 meV at 0.3 K. The sequence of quantum Hall plateaus appearing at filling factor $\nu =2$ followed by $\nu =1$ suggests that the observed gap is caused by the symmetry breaking of the lowest Landau level. Investigation of the gap in a tilted magnetic fields indicates that the resistance at the CNP shows a weak linear decrease for increasing total magnetic field. Those observations are in agreement with a spontaneous valley splitting at zero magnetic field followed by splitting of the spins originating from different valleys with increasing magnetic field. Both the transport gap and $B$ field response point toward the spin-polarized layer-antiferromagnetic state as the ground state in the bilayer graphene sample. The observed nontrivial dependence of the gap value on the normal component of $B$ suggests possible exchange mechanisms in the system.

Figure 1

Four-probe resistance of the suspended bilayer graphene. (a) Gate dependence of the sample at the temperatures of 4.2 (black), 1.3 (red), 0.7 (green), and 0.3 K (blue). Inset: Resistance at 4.2 K on a logarithmic scale showing the dramatic change from the CNP to the metallic regime. (b) Transport gap extraction at 4.2 and 0.3 K. The energy gap in the bias direction is highlighted by the conductance crossover (fitted with dashed lines) at zero. The values of the transport gap are 3 meV (4.2 K) and 8 meV (0.3 K). (c) An Arrhenius plot of the resistance. The value of the extracted thermal gap is 0.33 meV.

Figure 2

Quantum transport at 1.3 K. (a) Quantum Hall conductance of the suspended bilayer at $B=0$ and 5 T.(b) Quantum Hall conductance of the suspended bilayer at $B=7$ and 11 T. The exact filling factors $\nu$ corresponding to the observed plateaus are shown. (c) Resistance of the sample in the quantum Hall regime. (d) Scaling of the filling factor positions in graph of gate voltage ($V_{g\nu }$) vs magnetic field. (e) LL hierarchy of the symmetry breaking of the lowest LL in bilayer graphene. Suggested scenario of spontaneous valley splitting followed by spin splitting at high $B$.

Figure 3

(a) Behavior of the resistance at the charge neutrality point at fixed $B_n$ with increasing $B_{\mathrm{tot}}$. From top to bottom, angle and total field are 27${}^{\circ }$ (6 T), 45${}^{\circ }$ (8 T), 63${}^{\circ }$ (12 T), 27${}^{\circ }$ (6 T), 72${}^{\circ }$ (16 T), and 81${}^{\circ }$ (30 T). (b) Behavior of the resistance at the charge neutrality point when $B$ has only the in-plane field component ($\theta =$ ${90}^{\circ }$). (c) Suggested scheme of spontaneously split valley followed by spin splitting induced by $B$.

Figure 4

(a) Change in the $R_{\max }$ of the middle peak with total magnetic field $B_{\mathrm{tot}}$. (b) ln($R_{\max }$) as a function of $B_{\mathrm{tot}}$ at different $B_n$. The values of $B_n$ from left to right are 1, 4, 9, 13.7, 17, 21.2, and 25 T. (c) The slope of the linear fit from (b) as a function of the normal component $B_n$.

Figure 5

Electrical scheme of the setup we use to perform our measurements. Inset: Scanning electron micrograph of a typical suspended bilayer membrane between two contacts.