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(a) Fermi surfaces of electrons in bulk Si. Only the two out-of-plane valleys are occupied in our 2D system. (b) Sample structure. (c) Wave functions of the ground and upper confinement subbands in a symmetrical potential. is the difference in confinement energy of the two subbands. (d) Energy levels of the valley-split ground state and upper confinement state in an asymmetrical potential. The valley-splitting energy is increased by the asymmetrical bias. (e) Energy levels of these states separated by the Zeeman splitting in an in-plane magnetic field.
and at , 1.5 K, without magnetic field (a) and with (c). (b) and (d) are grayscale plots of at and , respectively, and green dashed lines mark , , and . Arrow labeled A indicates the threshold of conduction. Arrows labeled B and C mark features arising from the occupation of the upper-valley and upper confinement subbands, respectively. Under in-plane magnetic field, B evolves into D and E while C evolves into F and G due to spin splitting. The lines at in all the figures are experimental artifacts.
(a) Schematic diagram of subband edges as a function of : (I), (II), (III). (b) DOS under in region (III). Left- and right-hand sides correspond to the DOS of lower- and upper-valleys, respectively. Up and down arrows denote spin up and down states. (i), (ii), (iii) and (iv) correspond to the Fermi energy in regions (i), (ii), (iii), and (iv) in (a). and correspond to the Fermi energy at D and E, respectively, in Figs. 2(c) and 2(d).
dependence of using data taken at 0.3 K, . The dashed line shows a fit using Eq. (2) giving .
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