Low Frequency Admittance Measurements in the Quantum Hall Regime
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Low Frequency Admittance Measurements in the Quantum Hall Regime Carlos Hernández1 and Christophe Chaubet2 1 Departamento de Física, Universidad de los Andes, A.A. 4976, Bogotá D.C., Colombia. 2 Laboratoire Charles Coulomb L2C, Université Montpellier II, Pl. E. Bataillon, 34095 Montpellier Cedex 5, France. ABSTRACT In this paper we present an ac-magneto-transport study of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime, for frequencies in the range [100Hz, 1MHz]. We present an approach to understand admittance measurements based in the Landauer-Buttiker formalism for QHE edge channels and taking into account the capacitance and the topology of the cables connected to the contacts used in the measurements. Our model predicts an universal behavior with the a-dimensional parameter RHCω where RH is the 2 wires resistance of the 2DEG, C the capacitance cables and the angular frequency, in agreement with experiments. For a specific configuration, we measure the electrochemical capacitance of the quantum Hall edge channels as predicted by Christen and Büttiker. INTRODUCTION The quantum Hall effect (QHE) is widely used by national laboratories thanks to its great stability in dc [1,2]. The accuracy of measurements has allowed establishment of the international standard for the electrical resistance unit (Ohm). The QHE plateaus are perfectly quantized in dc (up to 10-9) but in ac the quantization has never been better that 10-7 [3]. The quantized Hall resistance of a QHE sample is usually found to be current and frequency dependent. That lack of precision in metrological studies, is caused by ac-losses [4,5]. One knows that these losses are linked to the charge distribution on the edges of the 2DEG, and that a good ac-quantization of the Hall resistance can be achieved in gated samples, by biasing a gate [6,7]. For ungated samples, ac-losses are explained by a “Polarization Model” and a “Capacitive Model” [4,5], however the origin of these ac-losses is not yet understood and other approaches have been explored. Desrat et al [8] have interpreted their measurements using the theory proposed by T. Christen and M. Büttiker [9, 10] based on the Büttiker, Prêtre and Thomas [11] theory of finite frequency transport that can be used to predict the frequency dependence of the conductor’s admittance. However this interpretation was very controversial because it did not take into account the parasitic capacitances of the experimental setup [12]. EXPERIMENTAL DETAILS We have performed a study of the longitudinal admittance of two-dimensional electron gases. The samples used for the experimental measures were GaAlAs/GaAs heterojonctions (Table 1), of metrological quality, obtained with the collaboration of the “Laboratoire National de Métrologie et d'Essais (LNE)”, french national laboratory of metrology. The samples were
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entirely processed in the Philips laboratory of Limeil Breivannes, as a Hall bar having six independent lateral voltage contacts in addition to the source and drain contacts (Fig. 1.
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