Dynamic nonlinear behavior is reported at high currents in the quantum Hall regime of GaAs heterostructures, resulting from breakdown of the dissipationless current flow. It is demonstrated that this breakdown is spatially localized and transient switching is observed on microsecond time scales among a set of distinct dissipative states. A simple macroscopic picture is proposed to account for these novel phenomena.PACS numbers: 73.40.Lq, 72.20.Ht, 72.20.My, 72.70. + m The quantum Hall effect 1 ' 2 is of great import for both many-body physics and fundamental metrology. The extreme accuracy with which the Hall resistance is quantized, despite the presence of disorder in the inversion-layer devices, is now fairly well understood as being due to the nearly complete freedom from dissipation in the quantized Hall regime. However, the nature of the localized states in a high magnetic field, the role of finite electric fields, and the nature of various dissipative effects remain poorly understood. Ebert etal. 3 have recently discovered that there is a critical current density above which the dissipation suddenly rises by several orders of magnitude. We report in this Letter unexpected new phenomena associated with this breakdown. We show that the breakdown is spatially localized and exhibits a rich time-dependent structure. In addition to a strong background of broadband noise we observe transient switching on a microsecond time scale among a discrete set of distinct dissipative states. Our observations demonstrate the significance of this breakdown phenomenon and provide a deeper understanding of the novel transport properties associated with the quantum Hall effect.Two high-quality GaAs-Ga^Al^As (# = 0.29) heterojunction devices [hereafter referred to as GaAs(7) and GaAs (8)] were used in this study. Both devices have zero-magnetic-field mobilities in excess of 10 5 cm 2 /(V s) at 4.2 K, and at 1.1 K yield excellent 6453.2-£2 (i =4) Hall steps that are flat and reproducible to at least 0.02 ppm. Figure 1 gives the sample geometry and displays the current dependence of the Hall resistance R H = (V 3 -V 4 )// SD and the dissipative voltage V x = V 2 -V 4 (at its minimum) for GaAs (7). Table I shows that V x changes by 7 orders of magnitude between / SD =25 and 370 juA and becomes as large as one-tenth of the Hall voltage V H while (as shown in Fig. 1) the value of JR H decreases by only 0.1 ppm! Similarly the other Hall-probe resistance R H f = (^I-^ASD decreases by only 0.6 ppm. These changes in R u are -0.01% of what is expected from the mixing of V x into V H due to the known misalignment of the Hall probes (3 rel-1374

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This paper describes a recent determination of the von Klitzing constant and the fine-structure constant by comparisons of values of the ohm as defined in the International System of Units (SI), derived from the National Institute of Standards and Technology (NIST) calculable cross-capacitor, and values of the international practical unit of resistance derived from the integral quantum Hall effect. In this determination, the comparisons were made in a series of measurements lasting three years. A small difference is observed between this determination and an earlier comparison carried out in this laboratory and reported in 1988. The most recent value of the fine-structure constant based on the experimental value and theoretical expression for the magnetic moment anomaly of the electron, which has the smallest uncertainty of any value currently available, is consistent with both of these results. The new value exceeds the 1990 conventional value of the von Klitzing constant by slightly more than twice the relative standard uncertainty of the present measurement, which is 2.4 10 -8 .

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