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  1. We present the design and implementation of a measurement system that enables parallel drive and detection of small currents and voltages at numerous electrical contacts to a multi-terminal electrical device. This system, which we term a feedback lock-in, combines digital control-loop feedback with software-defined lock-in measurements to dynamically source currents and measure small, pre-amplified potentials. The effective input impedance of each current/voltage probe can be set via software, permitting any given contact to behave as an open-circuit voltage lead or as a virtually grounded current source/sink. This enables programmatic switching of measurement configurations and permits measurement of currents at multiple drain contacts without the use of current preamplifiers. Our 32-channel implementation relies on commercially available digital input/output boards, home-built voltage preamplifiers, and custom open-source software. With our feedback lock-in, we demonstrate differential measurement sensitivity comparable to a widely used commercially available lock-in amplifier and perform efficient multi-terminal electrical transport measurements on twisted bilayer graphene and SrTiO3 quantum point contacts. The feedback lock-in also enables a new style of measurement using multiple current probes, which we demonstrate on a ballistic graphene device.

     
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  2. Abstract

    A key feature of the topological surface state under a magnetic field is the presence of the zeroth Landau level at the zero energy. Nonetheless, it is challenging to probe the zeroth Landau level due to large electron–hole puddles smearing its energy landscape. Here, by developing ultra‐low‐carrier density topological insulator Sb2Te3films, an extreme quantum limit of the topological surface state is reached and a hidden phase at the zeroth Landau level is uncovered. First, an unexpected quantum‐Hall‐to‐insulator‐transition near the zeroth Landau level is discovered. Then, through a detailed scaling analysis, it is found that this quantum‐Hall‐to‐insulator‐transition belongs to a new universality class, implying that the insulating phase discovered here has a fundamentally different origin from those in nontopological systems.

     
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