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Register a new userThree Key Questions on Fractal Conductance Fluctuations: Dynamics, Quantization and Coherence
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Recent investigations of fractal conductance fluctuations (FCF) in electron billiards reveal crucial discrepancies between experimental behavior and the semiclassical Landauer-Buttiker (SLB) theory that predicted their existence. In particular, the roles played by the billiards geometry, potential profile and the resulting electron trajectory distribution are not well understood. We present measurements on two custom-made devices - a disrupted billiard device and a bilayer billiard device - designed to probe directly these three characteristics. Our results demonstrate that intricate processes beyond those proposed in the SLB theory are required to explain FCF.
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Conductance fluctuations have been studied in a soft wall stadium and a Sinai billiard defined by electrostatic gates on a high mobility semiconductor heterojunction. These reproducible magnetoconductance fluctuations are found to be fractal confirming recent theoretical predictions of quantum signatures in classically mixed (regular and chaotic) systems. The fractal character of the fluctuations provides direct evidence for a hierarchical phase space structure at the boundary between regular and chaotic motion.
We report the experimental observation of conductance quantization in graphene nanoribbons, where 1D transport subbands are formed due to the lateral quantum confinement. We show that this quantization in graphene nanoribbons can be observed at temperatures as high as 80 K and channel lengths as long as 1.7 $mu$m. The observed quantization is in agreement with that predicted by theoretical calculations.
Graphene provides a fascinating testbed for new physics and exciting opportunities for future applications based on quantum phenomena. To understand the coherent flow of electrons through a graphene device, we employ a nanoscale probe that can access the relevant length scales - the tip of a liquid-He-cooled scanning probe microscope (SPM) capacitively couples to the graphene device below, creating a movable scatterer for electron waves. At sufficiently low temperatures and small size scales, the diffusive transport of electrons through graphene becomes coherent, leading to universal conductance fluctuations (UCF). By scanning the tip over a device, we map these conductance fluctuations textit{vs.} scatterer position. We find that the conductance is highly sensitive to the tip position, producing $delta G sim e^2/h$ fluctuations when the tip is displaced by a distance comparable to half the Fermi wavelength. These measurements are in good agreement with detailed quantum simulations of the imaging experiment, and demonstrate the value of a cooled SPM for probing coherent transport in graphene.
The Josephson current flowing in a junction between two superconductors is a striking manifestation of macroscopic quantum coherence, with applications in metrology and quantum information. This equilibrium current is related with the formation of Andreev states localized in the junction, whose energy depends periodically on the superconducting phase difference. Topology emerged as a guide for predicting exotic properties of Andreev states. In particular, topological superconductors host Majorana modes at their ends. Then, in a junction with such leads, the hybridization of two Majorana modes results in an Andreev state with a period-doubling of its energy-phase dependence. Furthermore, topologically protected crossings between Andreev states in junctions with more than two leads may be revealed through a quantized transconductance. The prediction motivated recent efforts to fabricate multi-terminal junctions. Here we combine both topological effects to predict a robust non-vanishing quantized transconductance in trijunctions with topological leads. Such devices are envisioned to reveal the anyonic nature of Majorana states through their braiding. Our prediction can be used to assess that a given junction is indeed suitable to perform its braiding function.
In contrast to the case of ordinary quantum Hall effect, the resistance of ballistic helical edge channels in typical quantum spin-Hall experiments is non-vanishing, additive and poorly quantized. Here we present a simple argument connecting this qualitative difference with a spin relaxation in the current/voltage leads in an experimentally relevant multi-terminal bar geometry. Both the finite lead resistance and the spin relaxation contribute to a non-vanishing four-terminal edge resistance, explaining poor quantization quality. We show that corrections to the four-terminal and two-terminal resistances in the limit of strong spin relaxation are opposite in sign, making a measurement of the spin relaxation resistance feasible, and estimate the magnitude of the effect in HgTe-based quantum wells.
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