It is worth pointing out that previous results are obtained in the plateau-plateau transition regime [26, 27, 31] and Shubnikov-de Haas region [10], which is in contrast with our case in the weak insulating regime where Landau quantization is not significant. Nevertheless, our data indeed indicate such a universal exponent at approximately 0.5 for heating in various 2D AZD0530 in vitro systems. Moreover, our results suggest that the Dirac fermion-phonon scattering rate 1/τ DFP is proportional to T 2. It is worth noting that enhanced mobility can be achieved in semiconductor quantum wires [32] and in semiconducting graphene nanoribbons [33] by a
high dc electric field. Such interesting results are highly Ganetespib cell line desirable for practical applications in narrow graphene devices in the high current limit. In order to further study the observed Dirac fermion heating effects, we have extended our measurements to higher magnetic fields. Such results are shown in Figure 5. Interestingly, a current-independent point in ρ xx is observed. The observed fixed point is reminiscent of the I-QH transition in graphene [19,
20]. In order to confirm this interpretation, as shown in Figure 6, we perform magnetoresistivity measurements ρ xx (B) at various temperatures in the low current limit to ensure thermal equilibrium between GSK1120212 in vivo phonons and Dirac fermions. The same crossing point in ρ xx at B c ≈ 9.2 T is indeed observed. For B < B c, the resistivity decreases with increasing temperature, as is characteristic of an insulator [17]. For B > B c, the resistivity increases with increasing temperature, showing a QH conductor behavior
[17]. In the high magnetic field regime, some weak oscillatory features can be ascribed to Shubnikov-de Haas www.selleck.co.jp/products/azd9291.html oscillations in disordered graphene. However, their amplitudes are weak; therefore, it is not possible to extract important physical quantities such as the quantum mobility and effective mass in our system. The Landau level filling factor at the crossing point is estimated to be ≈94. Therefore, we have observed compelling evidence for the direct I-QH in disordered epitaxial graphene. Using the measured ρ xx as a thermometer for Dirac fermions, we are able to determine T DF and the exponent in the T DF-I relation at different magnetic fields as shown in Figure 7. Close to B c, the temperature dependence of ρ xx is so weak that reliable determination of T DF cannot be obtained. We note that in the insulating regime B < B c, the exponent is again close to one half, consistent with the results at B = 0. In the QH-like regime, the exponent is about 0.15 which is significantly smaller than one half. Such vastly different exponents observed in the two regimes provide further experimental evidence for the direct I-QH transition in disordered epitaxial graphene.