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Register a new userInduced currents, frozen charges and the quantum Hall effect breakdown
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Puzzling results obtained from torque magnetometry in the quantum Hall effect (QHE) regime are presented, and a theory is proposed for their explanation. Magnetic moment saturation, which is usually attributed to the QHE breakdown, is shown to be related to the charge redistribution across the sample.
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The quantum anomalous Hall effect (QAHE) realizes dissipationless longitudinal resistivity and quantized Hall resistance without the need of an external magnetic field. However, when reducing the device dimensions or increasing the current density, an abrupt breakdown of the dissipationless state occurs with a relatively small critical current, limiting the applications of the QAHE. We investigate the mechanism of this breakdown by studying multi-terminal devices and identified that the electric field created between opposing chiral edge states lies at the origin. We propose that electric-field-driven percolation of two-dimensional charge puddles in the gapped surface states of compensated topological-insulator films is the most likely cause of the breakdown.
We report on the stability of the quantum Hall plateau in wide Hall bars made from a chemically gated graphene film grown on SiC. The $ u=2$ quantized plateau appears from fields $B simeq 5$ T and persists up to $B simeq 80$ T. At high current density, in the breakdown regime, the longitudinal resistance oscillates with a $1/B$ periodicity and an anomalous phase, which we relate to the presence of additional electron reservoirs. The high field experimental data suggest that these reservoirs induce a continuous increase of the carrier density up to the highest available magnetic field, thus enlarging the quantum plateaus. These in-plane inhomogeneities, in the form of high carrier density graphene pockets, modulate the quantum Hall effect breakdown and decrease the breakdown current.
In the quantum anomalous Hall effect, quantized Hall resistance and vanishing longitudinal resistivity are predicted to result from the presence of dissipationless, chiral edge states and an insulating 2D bulk, without requiring an external magnetic field. Here, we explore the potential of this effect in magnetic topological insulator thin films for metrological applications. Using a cryogenic current comparator system, we measure quantization of the Hall resistance to within one part per million and longitudinal resistivity under 10 m$Omega$ per square at zero magnetic field. Increasing the current density past a critical value leads to a breakdown of the quantized, low-dissipation state, which we attribute to electron heating in bulk current flow. We further investigate the pre-breakdown regime by measuring transport dependence on temperature, current, and geometry, and find evidence for bulk dissipation, including thermal activation and possible variable-range hopping.
We report an investigation of quantum Hall induced currents by simultaneous measurements of their magnetic moment and their effect on the conductance of a quantum point contact (QPC). Features in the magnetic moment and QPC resistance are correlated at Landau-level filling factors nu=1, 2 and 4, which demonstrates the common origin of the effects. Temperature and non-linear sweep rate dependences are observed to be similar for the two effects. Furthermore, features in the noise of the induced currents, caused by breakdown of the quantum Hall effect, are observed to have clear correlations between the two measurements. In contrast, there is a distinct difference in the way that the induced currents decay with time when the sweeping field halts at integer filling factor. We attribute this difference to the fact that, while both effects are sensitive to the magnitude of the induced current, the QPC resistance is also sensitive to the proximity of the current to the QPC split-gate. Although it is clearly demonstrated that induced currents affect the electrostatics of a QPC, the reverse effect, the QPC influencing the induced current, was not observed.
We review the construction of a low-energy effective field theory and its state space for abelian quantum Hall fluids. The scaling limit of the incompressible fluid is described by a Chern-Simons theory in 2+1 dimensions on a manifold with boundary. In such a field theory, gauge invariance implies the presence of anomalous chiral modes localized on the edge of the sample. We assume a simple boundary structure, i.e., the absence of a reconstructed edge. For the bulk, we consider a multiply connected planar geometry. We study tunneling processes between two boundary components of the fluid and calculate the tunneling current to lowest order in perturbation theory as a function of dc bias voltage. Particular attention is paid to the special cases when the edge modes propagate at the same speed, and when they exhibit two significantly distinct propagation speeds. We distinguish between two geometries of interference contours corresponding to the (electronic) Fabry-Perot and Mach-Zehnder interferometers, respectively. We find that the interference term in the current is absent when exactly one hole in the fluid corresponding to one of the two edge components involved in the tunneling processes lies inside the interference contour (i.e., in the case of a Mach-Zehnder interferometer). We analyze the dependence of the tunneling current on the state of the quantum Hall fluid and on the external magnetic flux through the sample.
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