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Register a new userImaging the Conductance of Integer and Fractional Quantum Hall Edge States
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We measure the conductance of a quantum point contact (QPC) while the biased tip of a scanning probe microscope induces a depleted region in the electron gas underneath. At finite magnetic field we find plateaus in the real-space maps of the conductance as a function of tip position at integer ( u=1,2,3,4,6,8) and fractional ( u=1/3,2/3,5/3,4/5) values of transmission. They resemble theoretically predicted compressible and incompressible stripes of quantum Hall edge states. The scanning tip allows us to shift the constriction limiting the conductance in real space over distances of many microns. The resulting stripes of integer and fractional filling factors are rugged on the micron scale, i.e. on a scale much smaller than the zero-field elastic mean free path of the electrons. Our experiments demonstrate that microscopic inhomogeneities are relevant even in high-quality samples and lead to locally strongly fluctuating widths of incompressible regions even down to their complete suppression for certain tip positions. The macroscopic quantization of the Hall resistance measured experimentally in a non-local contact configuration survives in the presence of these inhomogeneities, and the relevant local energy scale for the u=2 state turns out to be independent of tip position.
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We propose ways to create and detect fractionally charged excitations in emph{integer} quantum Hall edge states. The charge fractionalization occurs due to the Coulomb interaction between electrons propagating on different edge channels. The fractional charge of the soliton-like collective excitations can be observed in time resolved or frequency dependent shot noise measurements.
Protected edge modes are the cornerstone of topological states of matter. The simplest example is provided by the integer quantum Hall state at Landau level filling unity, which should feature a single chiral mode carrying electronic excitations. In the presence of a smooth confining potential it was hitherto believed that this picture may only be partially modified by the appearance of additional counterpropagating integer-charge modes. Here, we demonstrate the breakdown of this paradigm: The system favors the formation of edge modes supporting fractional excitations. This accounts for previous observations, and leads to additional predictions amenable to experimental tests.
This review presents experimental results on the inter-edge-state transport in the quantum Hall effect, mostly obtained in the regime of high imbalance. The application of a special geometry makes it possible to perform I-V spectroscopy between individual edge channels in both the integer and the fractional regime. This makes it possible to study in detail a number of physical effects such as the creation of topological defects in the integer quantum Hall effect and neutral collective modes excitation in fractional regime. The while many of the experimental findings are well explained within established theories of the quantum Hall effects, a number of observations give new insight into the local structure at the sample edge, which can serve as a starting point for further theoretical studies.
Indium Arsenide (InAs) near surface quantum wells (QWs) are ideal for the fabrication of semiconductor-superconductor heterostructures given that they allow for a strong hybridization between the two-dimensional states in the quantum well and the ones in the superconductor. In this work we present results for InAs QWs in the quantum Hall regime placed in proximity of superconducting NbTiN. We observe a negative downstream resistance with a corresponding reduction of Hall (upstream) resistance. We analyze the experimental data using the Landauer-B{u}ttiker formalism, generalized to allow for Andreev reflection processes. Our analysis is consistent with a lower-bound for the averaged Andreev conversion of about 15%. We attribute the high efficiency of Andreev conversion in our devices to the large transparency of the InAs/NbTiN interface and the consequent strong hybridization of the QH edge modes with the states in the superconductor.
Since the charged mode is much faster than the neutral modes on quantum Hall edges at large filling factors, the edge may remain out of equilibrium in thermal conductance experiments. This sheds light on the observed imperfect quantization of the thermal Hall conductance at $ u=8/3$ and can increase the observed thermal conductance by two quanta at $ u=8/5$. Under certain unlikely but not impossible assumptions, this might also reconcile the observed thermal conductance at $ u=5/2$ with not only the PH-Pfaffian order but also the anti-Pfaffian order.
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