Equation 2 can be rewritten as (3) where we consider the effective Lande g-factor g *. We can see that Equation 3 corresponds to two straight line fits

through the origin for a pair of spin-split Landau levels in the E-B plane as shown in Figure 2a,b. Such an approach was applied to a GaN-based 2DEG in our previous work [19]. We note that our method does depend on the exact functional form of the Landau band since the peak positions of the Landau level is only related to the carrier density in our system. Let us now consider the region ν = 3 between the two linear fits corresponding to two spin-split Landau levels n = 1↓ and n = 1↑. According to Equation 3, the difference between the Tariquidar slopes of the spin-split Landau levels is given by g * Φ06Δ B B. Thus we are able to measure g * for different Landau level indices (n = 1, 2, 3,…). In our system, the spin gap value is proportional to the magnetic field with good accuracy and corresponds to a constant g * for a pair of given spin-split Landau

levels. Figure 4 shows the measured g * as a function of Landau level index n for samples A and B. In all cases, the measured g * is greatly enhanced over its bulk value in GaAs (0.44). We ascribe this enhancement to exchange interactions. We suggest that the determined g * is in the zero disorder limit since the positions of the spin-split Landau levels are located using Equation 2. Figure 4 The measured g * as a function of Landau level index n. The measured Methocarbamol g * as SYN-117 a function of Landau level index n for samples A and B at T = 0.3 K. It is worth mentioning

that conventional activation energy studies are not selleckchem applicable to our data obtained on sample A, sample B as well as the GaN-based 2DEG in our previous work [19]. The reason for this is that the values of the R xx (and σ xx ) minima are high; therefore, it is not appropriate to speak of electrons being thermally activated from the localized states to the extended states. In order to provide further understanding on the measurements of the spin gap, we have studied the slopes of the spin-split Landau levels in the E-B plane and have also performed conventional activation energy measurements on sample C over the same magnetic field range. Sample C is a more disordered device compared with samples A and B thus we can only perform measurements in the regime where the ρ xx corresponding to a spin-split ν = 3 state is resolved. Figure 5 shows the evolution of the n = 1↓ and n = 1↑ resistivity peaks at different magnetic fields for sample C. From the difference between the two slopes of n = 1↓ and n = 1↑ spin-split Landau levels, the exchange-enhanced g-factor for the n = 1 Landau level is measured to be 11.65 ± 0.14, which is in close agreement with those obtained on a much higher mobility in samples A and B.