Effect of Quantum Hall Edge Strips on Valley Splitting in Silicon Quantum Wells

Abstract

We determine the energy splitting of the conduction-band valleys in two-dimensional electrons confined to low-disorder Si quantum wells. We probe the valley splitting dependence on both perpendicular magnetic field B and Hall density by performing activation energy measurements in the quantum Hall regime over a large range of filling factors. The mobility gap of the valley-split levels increases linearly with B and is strikingly independent of Hall density. The data are consistent with a transport model in which valley splitting depends on the incremental changes in density eB=h across quantum Hall edge strips, rather than the bulk density. Based on these results, we estimate that the valley splitting increases with density at a rate of 116 μeV=10 11 cm −2 , which is consistent with theoretical predictions for near-perfect quantum well top interfaces.

Valley splitting in silicon from the interference pattern of quantum oscillations

“…In Si-MOS, we observe large valley splitting energies that increase in the range of 3.7 to 8.2 meV nearlinearly with density, regardless of the device location on the wafer, transport properties of the 2DEG, and temperature. Crucially, we see that the valley splitting densitydependence in Si-MOS extends to the high density regime the same trend that was observed in Si/SiGe at low density [17]. This trend is compatible [32] with the predicted density-dependent valley splitting calculated for a disorder-free Si/SiGe quantum well top-interface [23].…”

“…Due to the large magnetic field needed to overcome the Landau level broadening, enhancement of energy gaps is observed [16], making a direct comparison to the single-particle energy levels of QDs challenging. Furthermore, the complex electrostatics of quantum Hall edge states must be taken into account to correctly interpret the measurements [17].…”

“…Magenta diamonds are experimental valley splitting values from Si/SiGe heterostructure-FET from ref. [17] of two parallel channels with similar high mobility contributing to transport. We attribute the origin of these channels to the two low-lying conducting band valleys in Si, since the valley splitting energy should dominate at low fields over cyclotron and Zeeman energy [25,26].…”

“…We compare our results with the experimental results (magenta diamonds, from ref. [17]) and effective mass calculations (black line, from ref. [23]) for valleys splitting in 2DEGs obtained in Si/SiGe heterostructures.…”

“…Note that in the Si/SiGe heterostructures in ref. [17]) valley splitting was estimated by activation measurements in the quantum Hall regime. In Si-MOS, we observe large valley splitting energies that increase in the range of 3.7 to 8.2 meV nearlinearly with density, regardless of the device location on the wafer, transport properties of the 2DEG, and temperature.…”