Strong enhancement of the valley splitting in a two-dimensional electron system in silicon

Abstract

Using magnetocapacitance data, we directly determine the chemical potential jump in a strongly correlated 2D electron system in silicon when the filling factor traverses the valley gap at ν = 1 and ν = 3. The data yield a valley gap that is strongly enhanced compared to the single-particle value and increases linearly with magnetic field. This result has not been explained by existing theories.PACS numbers: 71.30.+h, 73.40.Qv A two-dimensional (2D) electron gas in (100)-silicon metal-oxide-semiconductor field-effect transistors (MOSFETs) is a unique double-layer electron system with strong interlayer interactions. Indeed, the valley index is identical with the isospin quantum number, and one can therefore try to apply to this system a good deal of recent theoretical work on double-layer electron systems. In a double-layer system with small layer separation compared to the interelectron distance in either layer, strong interlayer correlations are predicted to give rise to the appearance of both novel ground states and novel excitations [1,2]. In quantizing magnetic fields strong enough to fully polarize real electron spins, two cases as determined by the isospin system symmetry are discussed: (i) at finite layer separation the symmetry is U(1) corresponding to an "easy-plane" anisotropy and (ii) at vanishing layer separation the symmetry transforms to SU(2) and the anisotropy disappears. In the first (second) case the lowest energy charge-carrying excitations are merons (skyrmions) that are isospin textures with the charge e/2 (e), where e is the electron charge [1, 2]. There is little doubt that the valley splitting in the 2D electron system in silicon MOSFETs should be of many-body origin at least for lowest odd filling factors because the electron-electron interactions (and correlations) in this system are strong; particularly, in accessible magnetic fields, the Coulomb energy exceeds significantly the cyclotron energy. However, this is the strongly interacting limit in which existing theories are not valid and, therefore, they cannot be directly applied to silicon MOSFETs. The origin of the excitations for the valley splitting is unknown so far.Experimental investigations of the valley splitting were performed largely [3] at high filling factor ν ≥ 9 based on analysis of the beating pattern of Shubnikov-de Haas oscillations in tilted magnetic fields [4,5,6,7]. The gap value, its linear dependence on substrate bias [5], and its insensitivity to parallel magnetic field [8] are consistent with single-particle theoretical considerations for an asymmetric potential well that contains a 2D electron gas [9,10].In this paper, we perform, for the first time, lowtemperature measurements of the chemical potential jump across the valley gap at the lowest filling factors ν = 1 and ν = 3 in a 2D electron system in silicon using a magnetocapacitance technique. The valley splitting is found to exceed strongly the single-particle value, decaying with filling factor. Unexpectedly, the data are best described by a linear inc...

Direct Measurements of Fractional Quantum Hall Effect Gaps

“…This linear behavior is concurrent with that of the interaction-enhanced gaps in the integer quantum Hall effect [15,16] and, therefore, the linear law seems robust being valid for different gaps of many-body origin in different 2D electron systems with different interaction and disorder strengths. This points to a failure of the straightforward way of treating electron-electron interactions in 2D which leads to a square-root dependence of the gap on magnetic field.…”

“…The linear dependence of the fractional gap on magnetic field as well as the electron-hole symmetry in the spin-split Landau level are the case in the completely spin-polarized regime. Since the interaction-enhanced gaps in the integer quantum Hall effect in different 2D electron systems also increase linearly with magnetic field [15,16], the linear law seems robust. This indicates that electron-electron interactions in 2D should be treated in a less straightforward way.…”

Valley splitting ofSi∕Si1−xGexheterostructures in tilted magnetic fields

“…The linear density dependence of the valley gaps and strong enhancement over the bare valley splitting were recently reported in a Si-MOSFET system using magnetocapacitance method [11]. The authors pointed out that the electron-electron (e-e) interaction, especially the exchange interaction, is likely to account for the observed large valley gaps.…”

“…More than a decade ago, the introduction of the graded buffer scheme significantly improved the sample quality of the Si/SiGe heterostructures [7]. To date, the valley splitting has been studied by various experimental techniques, including thermal activation [8], tilted field magnetotransport [9,10], magnetocapacitance [11], microwave photoconductivity [12] and magnetization [13]. However, as pointed out by Wilde et al in Ref.…”

Intervalley splittings of Si quantum wells

“…Intervalley splitting of Si quantum structures is of current technological interest for the potential applications to future silicon hetero-structure devices that involve quantum effects, especially for the scalable quantum computation [1][2][3][4][5][6][7][8][9][10][11]. The lowest conduction band of a silicon crystal is known to have six equivalent minima of ellipsoidal shape called valleys along the [001] direction [12].…”