Figure 6 Logarithm of ρ xx ( B )( ν  = 3) versus the inverse of t

Figure 6 Logarithm of ρ xx ( B )( ν  = 3) versus the inverse of temperature 1/ T . The logarithm of ρ xx (B)(ν = 3) versus the inverse of temperature 1/T at different gate voltages (and hence B) for sample C. From left to right: B = PD173074 5.72 (pentagon), 5.46 (star), 5.21 (hexagon), 4.97 (diamond), 4.70 (inverted triangle), 4.55 (triangle), 4.39 (heptagon) and 4.25 (square) T, respectively. The slopes of the straight line fits Δs are shown in Figure 7. Figure 7 The experimentally determined Δ s / k B at various B . The straight line fit is discussed in the text. The dotted line is the bare Zeeman energy

assuming g 0 = 0.44. The dashed line corresponds to the spin gap using the measured g * = 11.65 by the direct measurements. The inset corresponds to a schematic diagram (density of states N(E) versus E) showing the spin gap Δ s as a result of the activated behavior from the localized states (hatched areas) to the extended states (in blue). The spin gap in the zero disorder limit Δs is the energy difference between the neighboring peaks in N(E). Conclusions In conclusion, we have performed direct measurements of the

spin gaps in gated GaAs 2DEGs by studying the slopes of spin-split Landau levels in the energy-magnetic field plane. The measured g-factor is greatly enhanced over its bulk value (0.44). Since disorder exists in any experimentally realized system, conventional activation energy studies always measure the mobility gap due to disorder which is different from the real spin gap as shown in our results. As the spin gap is one of the most important energy scales and governs find more the electron spin degree of freedom, our experimental results provide useful information in the field of spintronics, spin-related phenomena, and quantum computation applications. Acknowledgments TYH, CTL and YFC were supported by the NSC, Taiwan and National Taiwan University (grant no. 102R890932 Bcl-w and grant no. 102R7552-2).

The work at Cambridge was supported by the EPSRC, UK. This research was supported by the World Class University program funded by the Ministry of Education, Science and Technology through the National Research Foundation of Korea (R32-10204). References 1. Bader SD, Parkin SSP: Spintronics. Annual review of condensed matter. Physics 2010, 1:71. 2. Shen C, Trypiniotis T, Lee KY, Holmes SN, Mansell R, Husain M, Shah V, Li XV, Kurebayashi H, NVP-BSK805 solubility dmso Farrer I, de Groot CH, Leadley DR, Bell G, Parker EHC, Whall T, Ritchie DA, Barnes CHW: Spin transport in germanium at room temperature. Appl Phys Lett 2010, 97:162104.CrossRef 3. Watson SK, Potok RM, Marcus CM, Umansky V: Experimental realization of a quantum spin pump. Phys Rev Lett 2003, 91:258301.CrossRef 4. Khrapai S, Shashkin AA, Dolgopolov VT: Direct measurements of the spin and the cyclotron gaps in a 2D electron system in silicon. Phys Rev Lett 2003, 91:126404.CrossRef 5.

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