We report here a systematic study of the energy gaps at the odd-integer quantum Hall states ν = 3 and 5 under tilted magnetic (B) fields in a high quality Si two-dimensional electron system. Out of the coincidence region, the valley splitting is independent of the in-plane B fields. However, the ν = 3 valley gap differs by about a factor of 3 (∆v ∼ 0.4K vs. 1.2K) at either side of the coincidence. More surprisingly, instead of reducing to zero, the energy gaps at ν = 3 and 5 rise rapidly when approaching the coincidence angles. We believe that such anomaly is related to strong coupling of the nearly degenerate Landau levels. There has been a revival of research interest in understanding the valley degree of freedom in silicon (Si) since the original proposal of utilizing spins in Si as quantum bits [1,2,3,4]. In bulk Si, electrons occupy six degenerate valleys in the Brillouin zone. For the two-dimensional electron system (2DES) confined in a (001) Si quantum well [5], this six-fold degeneracy is lifted, with the two outof-plane valleys (the ±k z valleys) lower in energy than the four in-plane valleys. Further lifting of the remaining two-fold degeneracy has long been noticed, while its physical origin remains controversial [6,7,8]. In light of the quantum computation, a better understanding of this valley splitting now becomes more important since the existence of these two nearly degenerate ±k z valleys has been considered a potential source of spin decoherence [2].Previous experimental investigations on the valley splitting were largely performed in Si metal-oxidesemiconductor field-effect transistors (MOSFETs), where the disorder effect is strong [9,10,11]. In the past decade, significant progress has been made on high quality modulation doped Si/SiGe heterostructures [5], and it has become possible to study the valley splitting with much reduced disorder [12,13,14,15,16,17]. In this letter, we report experimental results of the energy gap measurement under tilted magnetic (B) fields in a high mobility Si 2DES. Consistent with previous observations by Weitz et al [12], we observed that the valley splitting is independent of in-plane B field out of the so-called coincidence region where two Landau levels cross each other at the Fermi level. However, the ν = 3 valley gap differs by about a factor of 3 (∆ v ∼ 0.4K vs. 1.2K) at either side of the coincidence. Even more surprisingly, in the coincidence region the inter-valley gaps at ν = 3 and 5, instead of reducing to zero as expected in an independentelectron model, rise rapidly when approaching the coincidence angles. We believe that such anomaly is related to strong coupling of the Landau levels close in energy in the coincidence region.The specimen in our experiment is a modulation doped Si quantum well sandwiched between Si 0.75 Ge 0.25 barriers. Details on the sample structure and fabrication process can be found in Ref. [18]. When cooled down to T=50mK in dark, the sample has an electron density n=1.4×1011 cm −2 and mobility µ=1.9×10 5 cm 2 /Vs (labeled a...
