Heat-Driven Electron-Motion in a Nanoscale Electronic Circuit

Abstract

We study the interaction between two closely spaced but electrically isolated quasi-onedimensional electrical wires by a drag experiment. In this work we experimentally demonstrate the generation of current in an unbiased (drag) wire, which results from the interactions with a neighboring biased (drive) wire. The direction of the drag current depends on the length of the one-dimensional wire with respect to the position of the barrier in the drag wire. When we additionally form a potential barrier in the drive wire, the direction of the drag current is determined by the relative position of the two barriers. We interpret this behavior in terms of electron excitations by phonon-mediated interactions between the two wires in presence of the electron scattering inside the drive wire. Nanoscale electronic circuits lie at the heart of emerging quantum technologies. The miniaturisation poses however a challenge for electrical isolation owing to interaction effects at the level of elementary particles. The precise understanding of energy and momentum transfer between electrons and phonons is thus key for nanoscale electronic-circuit design. An original approach to study this aspect is the so-called drag experiment, where two close-by, but electrically isolated systems are considered. One of these parts – the drive system – introduces excitation via an injected electric current, whereas the other so-called drag system is sensitive to measurable responses owing to energy and momentum transfer from quantum interactions. Studying and understanding the nature of these fundamental interactions is of paramount importance for future quantum technologies. This is because coupled quantum systems have become essential building blocks for advanced quantum circuits employing solid-state flying qubits. In the past, drag experiments have been successfully performed to study electron-electron and electronphonon interactions. Various types of nanocircuits have been investigated, such as quantum wires, quantum dots or quantum point contacts. These experiments revealed physical phenomena ranging from Wigner crystallisation of electrons over high-frequency-noise detection to Tomonaga-Luttinger liquids. An interesting 1 ar X iv :2 10 7. 09 20 9v 2 [ co nd -m at .m es -h al l] 2 6 O ct 2 02 1 behaviour was observed in two adjacent but electrically isolated quantum point contacts (QPCs) that are nearly pinched. When one of the QPCs is biased with a voltage of about 1 mV or larger, a current with opposite direction is created in the other, unbiased QPC. It was suggested that this counterflow is a direct consequence of an augmented thermopower effect that manifests at half conductance plateau of a QPC as well as the asymmetric phonon-induced excitation of electrons between the two reservoirs of the drag QPC. However, a detailed understanding of the process has not been obtained yet. In this work, we study phonon-mediated interactions in a pair of neighboring quasi-one-dimensional (1D) wires, which are electrically isolated and equipped with potential barriers at different positions. The placement of potential barriers at different positions allows the systematic investigation of the phonon-induced electronmotion for different configurations. Our results corroborate the interpretation of previous experimental studies and highlight the importance of geometry for the direction of the phonon-induced current. Our measurement data furthermore indicate that heat-driven electron-motion is strongly affected by electron-scattering within the drive wire. The investigated sample is fabricated in a GaAs/AlGaAs heterostructure hosting a two-dimensional electron gas (2DEG) at a depth of 146 nm with electron density of 1.9× 10 cm−2 and mobility of 1.8× 10 cm/Vs at 4 K. We perform the measurement in a dilution refrigerator at a base temperature of ∼ 15 mK under zero magnetic field. Figure 1b shows a SEM image of the surface gates defining the investigated pair of quantum wires. Applying a set of negative voltages on these Schottky gates, we define the potential landscape within the 2DEG and thus the electronic nanocircuit. Surface gates that remain unused in the present experiment (gl, go) are darkened in the SEM image (Fig. 1b). All gates were polarised with 0.3 V during the cool down to reduce the operation voltage and improve the stability of the device. We electrostatically isolate the dragand drive-wire (illustrated by red; top and blue; bottom in Fig. 1a) by polarising the horizontal barrier gate (gc) and the upper entrance gate (gu) with a sufficiently negative voltage. In the following we investigate the currents along the drive Idrive and drag Idrag wires as function of the voltage bias Vsd applied on the drive wire for different arrangements of potential barrier. In these experimental scenarios, we control the presence of a potential barrier via a negative voltage applied on the corresponding Schottky gates g1 g3 in the (top) drag or g4 g6 in the (bottom) drive wire. For the measurements, the side gates of the two wires are tuned to host 4 ∼ 5 conduction modes in each wire in order to suppress significant electron-scattering due to disorders along the transport paths. To suppress the influence of thermal voltage variation between different measurement lines, all Ohmic contacts, except the injection contact on the left, are connected to ground at the base temperature through a 10 kΩ resistor. The currents flowing through the drive and drag wire are respectively obtained by measuring the voltages across the 10 kΩ resistor. If not indicated otherwise, the drag current is obtained by measuring the voltage Vdrag at the right-most Ohmic contact as shown in Fig 1b. To begin, we characterise the potential barriers. Figures 1c (1d) show conductance measurements as a function of the voltage applied on the barrier gates g1 – g3 (g4 – g6) along the drag (drive) wire. The data shows plateau-like features near the conductance pinch-off that are consistent for both drive and drag wires. By selectively polarising the barrier gates, we form a potential barrier at deliberately chosen positions along the drag and drive wires. The measurements are performed in the basic setup illustrated in Fig. 1a. Here we form a potential barrier only in the drag wire and the gates g4, g5, and g6 in the drive wire are not used. To measure the differential drag conductance Gdrag, we inject current into the drive wire by applying an AC voltage drive of V rms = 70.7 μV at