Figure 1
(a) The first Brillouin zone and conduction band constant energy surfaces for bulk AlAs. (b) Schematic diagram showing that electrons are transferred from the
to the
valley upon the application of strain while the total 2DES density is independent of strain. (c) Experimental setup for the valley susceptibility measurements. (d) Energy diagram showing the spin (
) and valley (
) subband splittings with applied magnetic field or strain, respectively. (e) Sample resistance,
, vs the piezo bias,
at various filling factors
. The traces are offset for clarity. The dashed and dotted lines, respectively, mark
at which
and
are equally populated, and
beyond which all the electrons are transferred to the
valley. The top axis shows the strain as measured by the strain gauge. (f) Same data as in (e) but now plotted vs a normalized horizontal (top) axis
, showing that the oscillations have the same period. The traces are offset for clarity and, for
, 10, and 12, a smooth, parabolic background is subtracted from the traces to highlight the oscillations. (g) Plot of the coincidence index,
normalized by
, showing linearity with
. From the slopes of the lines fitted through the data points we obtain
, and the
intercepts give the value of
at which the
and
valleys are equally populated (
). Three data sets A, B, and C correspond to densities of: 2.8, 4.8, and
, respectively. (h) Schematic energy fan diagram showing the relevant energies: the cyclotron (
), Zeeman (
) and valley splitting (
).
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