Two-Flux Composite Fermion Series of the Fractional Quantum Hall States in Strained Si

Abstract

Magnetotransport properties are investigated in a high-mobility two-dimensional electron system in the strained Si quantum well of a (100) Si(0.75)Ge(0.25)/Si/Si(0.75)Ge0.25 heterostructure, at temperatures down to 30 mK and in magnetic fields up to 45 T. We observe around nu=1/2 the two-flux composite fermion (CF) series of the fractional quantum Hall effect (FQHE) at nu=2/3, 3/5, 4/7, and at nu=4/9, 2/5, 1/3. Among these FQHE states, the nu=1/3, 4/7, and 4/9 states are seen for the first time in the Si/SiGe system. Interestingly, of the CF series, the 3/5 state is weaker than the nearby 4/7 state and the 3/7 state is conspicuously missing, resembling the observation in the IQHE regime that the nu=3 is weaker than the nearby nu=4 state. Our results can be quantitatively understood in the picture of CF's with the valley degree of freedom.

Fractional quantum Hall effect of two-dimensional electrons in high-mobility Si/SiGe field-effect transistors

“…1(a), are consistent with those reported previously in modulation-doped samples with much lower mobilities [12] and can be phenomenologically understood as the IQH effect of two-flux CFs with a valley degree of freedom. As discussed above, at ν = 1/2, CFs form by attaching two fictitious magnetic flux quanta to one electron.…”

“…We should note that there is a rising background in R xx with increasing B, which quickly turns the 2DES into an insulator at ν < 1/3, similar to previous observation [12]. The rising background could signal the onset of an insulating phase [21,22] and the coexistence of FQH…”

“…However, a well known counter example to this view is the 3 Activation Gap (K) ν = 8/5 ν = 4/3 ν = 2/3 ν = 4/7 ν = 4/9 ν = 2/5 ν = 1/3 Figure 1(b) shows R xx and R xy between ν = 1 and 2. The two strong minima are the FQH states at ν = 8/5 and 4/3, again consistent with previous studies [11,12]. Since the 2DES has a two-fold valley degeneracy, the states at ν = 8/5 and 4/3 can be viewed as the particle-hole conjugate of the states at ν = 2−8/5 = 2/5 and 2−4/3 = 2/3, respectively.…”

“…The two strong minima are the FQH states at ν = 8/5 and 4/3, again consistent with previous studies [11,12]. Since the 2DES has a two-fold valley degeneracy, the states at ν = 8/5 and 4/3 can be viewed as the particle-hole conjugate of the states at ν = 2−8/5 = 2/5 and 2−4/3 = 2/3, respectively.We should note that there is a rising background in R xx with increasing B, which quickly turns the 2DES into an insulator at ν < 1/3, similar to previous observation [12]. The rising background could signal the onset of an insulating phase [21,22] and the coexistence of FQH…”

“…Celebrated examples include Skyrmions in systems with small Zeeman splitting [6,7], even-denominator FQH states [8,9], and the excitonic superfluid in bilayer systems [10]. While much effort towards the understanding of the roles of spins, layers, and subbands in the FQH regime has been made using high-quality GaAs quantum wells, experimental studies on the effects of valleys have been relatively sparse, only a few reports on 2D electrons in Si [11,12] and AlAs [13][14][15][16] available, partly due to the less impressive material quality of multi-valley semiconductors.Indeed, the electron mobilities of the devices used in these studies were smaller than that of GaAs by almost two orders of magnitude [3,17]. Nevertheless, looking back at the history of discoveries of new states in GaAs, we may expect that more interesting physical phenomena in multi-valley systems will emerge, once materials with higher mobility are available.…”