Figure 3. Angle and temperature-dependent MR in various geometries.

(a) The schematic of the local measurement geometry. (b) The schematic of the van der Pauw measurement geometry. (c) Schematic of the non-local geometry which identifies Ettingshausen-Nernst effect. An applied current (I) in the y-direction and a normal magnetic field in the z-direction (B_z) generate a charge current in the x-direction due to the Ettingshausen effect, which accumulates at the non-local electrode and raises the temperature. Owing to the Nernst effect, a voltage is generated at the non-local electrodes (V_NL) along the y-direction. (d) The MR versus magnetic field (H) at various temperatures for a graphene sample with six layers on BN. The MR is very large, ∼2,000%, even at a practical operating temperature of 400 K. The MR increases to a larger value of 6,000% at 2 K. (e) The angle dependence of the MR can be fitted with cos(θ) at 300 and 400 K (shown as solid black curves), implying a dominant classical MR effect. However, the MR at 2 K cannot be fitted with a simple cosine relationship indicating contributions from other effects. (f) The van der Pauw geometry MR at various temperatures for graphene on BN. The channel width (W) and distance of separation (L) of voltage electrodes from the current electrodes is 20 and 7 μm, respectively, yielding a L/W ratio of <1, justifying the definition of van der Pauw geometry. The MR is ∼35,000% at 50 K with a higher magnetic field sensitivity. (g) The non-local MR from a narrow channel four-layer graphene/BN device at 300 K showing the importance of magnetic field induced Ettingshausen–Nernst effect. The channel width (W) and distance of separation (L) of voltage electrodes from the current electrodes is 7 and 29 μm, respectively, yielding a L/W ratio >4, justifying the definition of non-local geometry. (h) The non-local angular MR at 9 T and 300 K suggesting the presence of Ettingshausen–Nernst effect, which is cosine dependent.