Quantum resistance standard accuracy close to the zero-dissipation state

Abstract

We report on a comparison of four GaAs/AlGaAs-based quantum resistance standards using an original technique adapted from the well-known Wheatstone bridge. This work shows that the quantized Hall resistance at Landau level filling factor $\nu=2$ can be reproducible with a relative uncertainty of $32\times 10^{-12}$ in the dissipationless limit of the quantum Hall effect regime. In the presence of a very small dissipation characterized by a mean macroscopic longitudinal resistivity $\bar{R_{xx}(B)}$ of a few $\mu\Omega$, the discrepancy $\Delta R_{\mathrm{H}}(B)$ measured on the Hall plateau between quantum Hall resistors turns out to follow the so-called resistivity rule $\bar{R_{xx}(B)}=\alpha B\times d(\Delta R_{\mathrm{H}}(B))/dB$. While the dissipation increases with the measurement current value, the coefficient $\alpha$ stays constant in the range investigated ($40-120 \mathrm{\mu A}$). This result enlightens the impact of the dissipation emergence in the two-dimensional electron gas on the Hall resistance quantization, which is of major interest for the resistance metrology. The quantum Hall effect is used to realize a universal resistance standard only linked to the electron charge \emph{e} and the Planck's constant \emph{h} and it is known to play a central role in the upcoming revised \emph{Syst\`eme International} of units. There are therefore fundamental and practical benefits in testing the reproducibility property of the quantum Hall effect with better and better accuracy.Comment: 6 pages, 6 figure

Operation of graphene quantum Hall resistance standard in a cryogen-free table-top system

“…The maximum achievable sensitivity of the bridge depends for a large part on the signal-to-noise ratio in the voltmeter and therefore on the maximum current used to drive the resistors (the Johnson noise in the resistors is the other limiting factor) [23]. Under optimum conditions measurement accuracies in access of 1 part in 10 10 can be achieved [9,25]. However, for routine resistance metrology a few parts in 10 9 in a reasonable measurement time (∼ 15 min) is perfectly adequate.…”

Practical Quantum Realization of the Ampere from the Elementary Charge

“…This is a reasonable assumption since no measurable deviation has been predicted by quantum mechanics [26][27][28][29][30] and no significant deviation has been demonstrated experimentally, either by independent determinations of the constants in the relations [11,31,32] or by universality tests. Several experiments have indeed demonstrated the universality of the JE and the QHE with relative measurements uncertainties below 2 × 10 −16 [33][34][35] and 10 −10 [36][37][38] respectively. In the new SI, the Josephson voltage standard (JVS) and the quantum Hall resistance standard (QHRS) would therefore become realizations of the ohm and the volt with relative uncertainties below 10 −9 , only limited by their experimental implementation, and no longer by the uncertainties on K J and R K of 4 × 10 −7 [39] and 1 × 10 −7 [40] respectively, in the present SI (Appendix A).…”

Conductance oscillations in quantum point contacts of InAs/GaSb heterostructures

“…So far, QSHE has been predicted and observed for HgTe/(Hg,Cd)Te quantum wells (QWs) [4][5][6] and InAs/GaSb heterostructures [7][8][9][10]. However, the accuracy of the conductance quantization in these systems is substantially inferior compared to the case of the quantum Hall effect [11] and the quantum anomalous Hall effect [12]. For instance, in the case of HgTe/(Hg,Cd)Te QWs, while non-local transport studies clearly indicate the existence of the edge conducting channels [13,14], the magnitude of conductance approaches the theoretically expected quantized values only in micrometer-sized structures, i.e., when the distance between the probes is of the order of the mean free path [5,6,15].…”