Temperature-dependent transport in a sixfold degenerate two-dimensional electron system on a H-Si(111) surface

Abstract

Low-field magnetotransport measurements on a high-mobility ͑ = 110, 000 cm 2 / Vs͒ two-dimensional electron system on a H-terminated Si͑111͒ surface reveal a sixfold valley degeneracy with a valley splitting Յ0.1 K. The zero-field resistivity xx displays strong temperature dependence for 0.07Յ T Յ 25 K as predicted for a system with high degeneracy and large mass. We present a method for using the low-field Hall coefficient to probe intervalley momentum transfer ͑valley drag͒. The relaxation rate is consistent with Fermiliquid theory but a small residual drag as T → 0 remains unexplained. Two-dimensional electron systems ͑2DESs͒ with additional discrete degrees of freedom ͑e.g., spin, valleys, subbands, and multiple charge layers͒ have attracted recent interest due to the role of such variables in transport and in the formation of novel ground states in the quantized Hall regime. In particular, systems with conduction-band valley degeneracy display a rich parameter space for observing and controlling 2DES behavior. 1 Among multivalley systems, electrons on the ͑111͒ surface of silicon are especially notable because effective-mass theory predicts the conduction band to be sixfold degenerate, yielding a total degeneracy ͑spinϫ valley͒ of 12 in the absence of a magnetic field ͑B͒. Previous investigations of Si͑111͒ transport using metaloxide-semiconductor field-effect transistor ͑MOSFETs͒ with peak mobilities Ϸ 4000 cm 2 / Vs observed a valley degeneracy g v of 2 or 6, with the reduced degeneracy attributed to oxide-induced surface strain. 2,3Here we report transport data on a hydrogen-terminated Si͑111͒ surface ͑H-Si͑111͒͒ with very high mobility ͑ = 110, 000 cm 2 / Vs at temperature T = 70 mK and carrier density n s = 6.7ϫ 10 11 cm −2 ͒ with clear sixfold valley degeneracy, indicated by the periodicity of Shubnikov-de Haas ͑SdH͒ oscillations, isotropic low-B transport, and strong T dependence of the longitudinal resistivity xx , consistent with a large g v . 4 In addition, we present a method for using the reduced Hall coefficient r H ϵ xy / ͑B / en s ͒ in the B → 0 limit as a probe of valley-valley interactions, using a drag model of intervalley momentum transfer in multivalley 2DESs. We find that the Hall coefficient ͑and thus, by our model, the intervalley drag͒ becomes strongly suppressed at low temperatures ͑T Շ 5 K͒; furthermore, although the T dependence of the drag is roughly quadratic as expected from Fermi-liquid theory, a small residual drag in the T → 0 limit remains unexplained.To create and probe a high-mobility electron system on a bare surface, we fabricate a device similar to a four wire MOSFET, with the critical difference that we replace the Si-SiO 2 interface with a H-Si͑111͒ surface adjacent to a vacuum cavity. 5 The main processing enhancements in the device discussed here relative to our prior samples are a higher resistivity Si͑111͒ substrate ͑ ϳ 10 k⍀-cm͒ and final H-termination and bonding performed in an oxygen-free ͑Ͻ1 ppm͒ environment. 6 The resulting device has a very high mobility wh...

Fractional quantum Hall effect in a dilute magnetic semiconductor

“…When the direction of the magnetic field B is tilted, the orbital LL splitting is given by the field component B ⊥ normal to the two-dimensional electron system (2DES) while the total field strength B determines the Zeeman splitting E Z . Early experiments on GaAs revealed that the ν = 4/3, 5/3, and 8/5 states behaved differently upon tilting the sample [4,5]: While the ν = 4/3 and 8/5 states were undergoing a transition from a spinunpolarized state to a polarized one, the ν = 5/3 state was always fully spin polarized.Although the FQHE has been reported in quite a number of different materials [6][7][8][9][10][11][12], the FQHE has never been observed in a diluted magnetic semiconductor in which atoms with magnetic moment (e.g., Mn 2+ ) are placed in a 2DES. Then, the localized spins in the magnetic impurities' d orbitals interact with the correlated electron system via the quantum mechanical s-d exchange interaction, causing giant Zeeman splitting [13] which is tunable in magnitude, sign, and field dependence [14].…”

“…Although the FQHE has been reported in quite a number of different materials [6][7][8][9][10][11][12], the FQHE has never been observed in a diluted magnetic semiconductor in which atoms with magnetic moment (e.g., Mn 2+ ) are placed in a 2DES. Then, the localized spins in the magnetic impurities' d orbitals interact with the correlated electron system via the quantum mechanical s-d exchange interaction, causing giant Zeeman splitting [13] which is tunable in magnitude, sign, and field dependence [14].…”

Photoexcitation of valley-orbit currents in (111)-oriented silicon metal-oxide-semiconductor field-effect transistors

“…A controllable way of occupying a particular spin state or filling a particular valley is a key ingredient, respectively, for spintronics 1 or valleytronics 2,3 aimed at the development of novel solid-state devices. The candidates appropriate for the realization of valleytronic concepts include multivalley semiconductors such as silicon, 2,4 graphene, 3,5,6 and carbon nanotubes. 2 A remarkable selective population of the electron states is achieved by optical pumping with polarized light: circularly for spin polarization 7 and linearly polarized for "valley polarization."…”

“…[9][10][11][12][13][14] Here we report on the vivid evidence of the existence of pure valley-orbit currents and demonstrate that the individual control of electron fluxes in valleys can be achieved by the excitation of (111)-oriented Si-metal-oxide-semiconductor (Si-MOS) structures with polarized light. Such two-dimensional systems contain six equivalent electron valleys 4,15 ( Fig. 1) and possess the overall point-group symmetry C 3v , that is, they are invariant with respect to the rotation by an angle of 120…”

Theory of transport properties of the sixfold-degenerate two-dimensional electron gas at the H-Si(111) surface

“…[5][6][7] For instance, at low temperature the magnetoresistance in a parallel magnetic field was measured for a low mobility sample. 3 A MIT at a critical density N MIT Ϸ 3 ϫ 10 11 cm −2 in a g v =2 Si͑111͒ was reported using a metaloxide-semiconductor field-effect transistor ͑MOSFET͒ for a sample with a peak mobility, at low temperatures, of peak Ϸ 2.5ϫ 10 3 cm 2 / Vs. 4 Recently grown samples, [5][6][7] made with hydrogen-passivated Si͑111͒/vacuum ͓H-Si͑111͔͒ structures, had higher mobility Ϸ 2.4ϫ 10 4 cm 2 / Vs with g v =2 at low electron density and with g v = 6 at high electron density. 6 Very recently a still higher mobility Ϸ 10 5 cm 2 / Vs together with a MIT at N MIT Ϸ 0.9 ϫ 10 11 cm −2 and a valley degeneracy g v = 6 was found with H-Si͑111͒ samples.…”