Liquid-induced damping of mechanical feedback effects in single electron tunneling through a suspended carbon nanotube

In single electron tunneling through clean, suspended carbon nanotube devices at low temperature, distinct switching phenomena have regularly been observed. These can be explained via strong interaction of single electron tunneling and vibrational motion of the nanotube. We present measurements on a highly stable nanotube device, subsequently recorded in the vacuum chamber of a dilution refrigerator and immersed in the 3He/4He mixture of a second dilution refrigerator. The switching phenomena are absent when the sample is kept in the viscous liquid, additionally supporting the interpretation of dc-driven vibration. Transport measurements in liquid helium can thus be used for finite bias spectroscopy where otherwise the mechanical effects would dominate the current.Comment: 4 pages, 3 figure

Sub-gap spectroscopy of thermally excited quasiparticles in a Nb contacted carbon nanotube quantum dot

We present electronic transport measurements of a single wall carbon nanotube quantum dot coupled to Nb superconducting contacts. For temperatures comparable to the superconducting gap peculiar transport features are observed inside the Coulomb blockade and superconducting energy gap regions. The observed temperature dependence can be explained in terms of sequential tunneling processes involving thermally excited quasiparticles. In particular, these new channels give rise to two unusual conductance peaks at zero bias in the vicinity of the charge degeneracy point and allow to determine the degeneracy of the ground states involved in transport. The measurements are in good agreement with model calculations.Comment: 5 pages, 4 figure

Thermally induced subgap features in the cotunneling spectroscopy of a carbon nanotube

We report on nonlinear cotunneling spectroscopy of a carbon nanotube quantum dot coupled to Nb superconducting contacts. Our measurements show rich subgap features in the stability diagram which become more pronounced as the temperature is increased. Applying a transport theory based on the Liouville-von Neumann equation for the density matrix, we show that the transport properties can be attributed to processes involving sequential as well as elastic and inelastic cotunneling of quasiparticles thermally excited across the gap. In particular, we predict thermal replicas of the elastic and inelastic cotunneling peaks, in agreement with our experimental results.Comment: 21 pages, 9 figures, submitted to New Journal of Physic

Magnetic damping of a carbon nanotube NEMS resonator

A suspended, doubly clamped single wall carbon nanotube is characterized at cryogenic temperatures. We observe specific switching effects in dc-current spectroscopy of the embedded quantum dot. These have been identified previously as nano-electromechanical self-excitation of the system, where positive feedback from single electron tunneling drives mechanical motion. A magnetic field suppresses this effect, by providing an additional damping mechanism. This is modeled by eddy current damping, and confirmed by measuring the resonance quality factor of the rf-driven nano-electromechanical resonator in an increasing magnetic field.Comment: 8 pages, 3 figure

Universality of the Kondo effect in quantum dots with ferromagnetic leads

We investigate quantum dots in clean single-wall carbon nanotubes with ferromagnetic PdNi-leads in the Kondo regime. In most odd Coulomb valleys the Kondo resonance exhibits a pronounced splitting, which depends on the tunnel coupling to the leads and an external magnetic field $B$, and only weakly on gate voltage. Using numerical renormalization group calculations, we demonstrate that all salient features of the data can be understood using a simple model for the magnetic properties of the leads. The magnetoconductance at zero bias and low temperature depends in a universal way on $g \mu_B (B-B_c) / k_B T_K$, where $T_K$ is the Kondo temperature and $B_c$ the external field compensating the splitting.Comment: 4 pages, 4 figure

Kondo effect in a one-electron double quantum dot: Oscillations of the Kondo current in a weak magnetic field

We present transport measurements of the Kondo effect in a double quantum dot charged with only one or two electrons, respectively. For the one electron case we observe a surprising quasi-periodic oscillation of the Kondo conductance as a function of a small perpendicular magnetic field |B| \lesssim 50mT. We discuss possible explanations of this effect and interpret it by means of a fine tuning of the energy mismatch of the single dot levels of the two quantum dots. The observed degree of control implies important consequences for applications in quantum information processing

Direct control of the tunnel splitting in a one-electron double quantum dot

Quasi-static transport measurements are employed on a laterally defined tunnel-coupled double quantum dot. A nearby quantum point contact allows us to track the charge as added to the device. If charged with only up to one electron, the low-energy spectrum of the double quantum dot is characterized by its quantum mechanical interdot tunnel splitting. We directly measure its magnitude by utilizing particular anticrossing features in the stability diagram at finite source-drain bias. By modification of gate voltages defining the confinement potential as well as by variation of a perpendicular magnetic field we demonstrate the tunability of the coherent tunnel coupling.Comment: High resolution pdf file available at http://www2.nano.physik.uni-muenchen.de/~huettel/research/anticrossing.pd

Stepwise fabrication and optimization of coplanar waveguide resonator hybrid devices

From the background of microwave-optomechanical experiments involving carbon nanotubes, the optimization of superconducting coplanar waveguide resonator devices is discussed. Two devices, one with unmodified geometry compared to previous work and one integrating several improvements, are lithographically built up step by step. After each step, the low temperature GHz transmission properties are retested. This allows to identify the impact of the fabrication and the geometry modification on the device properties. In addition, simplified circuit geometries are modeled numerically, confirming the experimental results and providing further insights for optimization.Comment: 4 figure, 5 page

Optomechanical coupling and damping of a carbon nanotube quantum dot

Carbon nanotubes are excellent nano-electromechanical systems, combining high resonance frequency, low mass, and large zero-point motion. At cryogenic temperatures they display high mechanical quality factors. Equally they are outstanding single electron devices with well-known quantum levels and have been proposed for the implementation of charge or spin qubits. The integration of these devices into microwave optomechanical circuits is however hindered by a mismatch of scales, between typical microwave wavelengths, nanotube segment lengths, and nanotube deflections. As experimentally demonstrated recently in [Blien et al., Nat. Comm. 11, 1363 (2020)], coupling enhancement via the quantum capacitance allows to circumvent this restriction. Here we extend the discussion of this experiment. We present the subsystems of the device and their interactions in detail. An alternative approach to the optomechanical coupling is presented, allowing to estimate the mechanical zero point motion scale. Further, the mechanical damping is discussed, hinting at hitherto unknown interaction mechanisms.Comment: 17 pages, 13 figures, 3 table

Co-sputtered MoRe thin films for carbon nanotube growth-compatible superconducting coplanar resonators

Molybdenum rhenium alloy thin films can exhibit superconductivity up to critical temperatures of $T_c=15\mathrm{K}$. At the same time, the films are highly stable in the high-temperature methane / hydrogen atmosphere typically required to grow single wall carbon nanotubes. We characterize molybdenum rhenium alloy films deposited via simultaneous sputtering from two sources, with respect to their composition as function of sputter parameters and their electronic dc as well as GHz properties at low temperature. Specific emphasis is placed on the effect of the carbon nanotube growth conditions on the film. Superconducting coplanar waveguide resonators are defined lithographically; we demonstrate that the resonators remain functional when undergoing nanotube growth conditions, and characterize their properties as function of temperature. This paves the way for ultra-clean nanotube devices grown in situ onto superconducting coplanar waveguide circuit elements.Comment: 8 pages, 6 figure