Dissipation and Dynamic Nonlinear Behavior in the Quantum Hall Regime

Abstract

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

Spectroscopic study of quantized breakdown voltage states of the quantum Hall effect

“…This sample and the AT&T GaAs(7) sample used in the previous breakdown experiments [3,[5][6][7][8] have been used as the United States resistance standard. The inset of Fig.…”

“…The current flow within the 2DEG is nearly dissipationless in the Hall plateau regions of highquality devices, and the longitudinal voltage drop Vx along the sample is very small. At high currents, however, energy dissipation can suddenly appear in these devices [2,3], and Vx can become quite large. This is the breakdown regime of the quantum Hall effect.…”

Observation of finite excess noise in the voltage-biased quantum Hall regime as a precursor for breakdown

“…The quantized Hall resistance collapses at finite source drain voltage V sd and/or at a current larger than a certain value. 21,22 The QHE breakdown is, in other words, a transition from a topologically protected phase to a completely different one. For this reason, the importance of the QHE breakdown has invoked renewed interest as new types of topologically protected phases, 23 that is, topological insulators, have gathered much attention today.…”

Monitoring the U.S. legal unit of resistance via the quantum Hall effect

“…No current dependence nor current breakdown phenomena [12] were observed for the three GaAs devices for I :5 25.5 fJ-A, so no correction for finite current is required. Table I summarizes the assigned uncertainties; the total root sum square (rss) uncertainty for each measurement system is typically ±0.020 ppm.…”