Charge-vibration interaction effects in normal-superconductor quantum dots

Abstract

We study the quantum transport and the nonequilibrium vibrational states of a quantum dot embedded between a normal and a superconducting lead with the charge on the quantum dot linearly coupled to a harmonic oscillator of frequency $\omega$. To the leading order in the charge-vibration interaction, we calculate the current and the nonequilibrium phonon occupation by the Keldsyh Green's function technique. We analyze the inelastic, vibration-assisted tunneling processes in the regime $\omega <\Delta$, with the superconducting energy gap $\Delta$, and for sharp resonant transmission through the dot. When the energy ${\epsilon }_0$ of the dot's level is close to the Fermi energy $\mu$, i.e. $|{\epsilon }_0-\mu |\ll \Delta$, inelastic Andreev reflections dominate up to voltage $eV\gtrsim \Delta$. The inelastic quasiparticle tunneling becomes the leading process when the dot's level is close to the gap $|{\epsilon }_0-\mu |\sim \Delta \pm \omega$. In both cases, the inelastic tunneling processes appear as sharp and prominent peaks - not broadened by temperature - in the $I$-$V$ characteristic and pave the way for inelastic spectroscopy of vibrational modes even at temperatures $T\gg \omega$. We also found that inelastic Andreev reflections as well as quasiparticle tunneling induce a strong nonequilibrium state of the oscillator. In different ranges on the dot's level, we found that the current produces: (i) ground-state cooling of the oscillator with phonon occupation $n\ll 1$, (ii) accumulation of energy in the oscillator with $n\gg 1$ and (iii) a mechanical instability which is a precursor of self-sustained oscillations. We show that ground-state cooling is achieved simultaneously for several modes of different frequencies. Finally, we discuss how the nonequilibrium vibrational state can be detected by the asymmetric behavior of the inelastic current peaks respect to the gate voltage.

References in corpus (75)

• Molecular Transport Junctions: Vibrational Effects
• Cooling a nanomechanical resonator with quantum back-action
• Franck-Condon blockade and giant Fano factors in transport through single molecules
• Strong coupling between single-electron tunneling and nano-mechanical motion
• Real-time path integral approach to nonequilibrium many-body quantum system
• Electrical generation and absorption of phonons in carbon nanotubes
• Inelastic electron tunneling via molecular vibrations in single-molecule transistors
• Franck-Condon blockade in suspended carbon nanotube quantum dots
• Vibrational sidebands and dissipative tunneling in molecular transistors
• Theory of the Franck-Condon blockade regime
• Tunneling in suspended carbon nanotubes assisted by longitudinal phonons
• Conserving GW scheme for nonequilibrium quantum transport in molecular contacts
• Modeling inelastic phonon scattering in atomic- and molecular-wire junctions
• Hierarchical Quantum Master Equation Approach to Electronic-Vibrational Coupling in Nonequilibrium Transport through Nanosystems
• Current-induced nonequilibrium vibrations in single-molecule devices
• Quantum-Limited Position Detection and Amplification: A Linear Response Perspective
• Quantum nano-electromechanics with electrons, quasiparticles and Cooper pairs: effective bath descriptions and strong feedback effects
• Phonon-assisted current noise in molecular junctions
• Vibrationally Induced Two-Level Systems in Single-Molecule Junctions
• Cooling carbon nanotubes to the phononic ground state with constant electron current
• Vibration-induced correction to the current through a single molecule
• Single-electron Tunneling with Strong Mechanical Feedback
• Numerical Renormalization Group Approach to a Quantum Dot Coupled to Normal and Superconducting Leads
• Pumping of vibrational excitations in a Coulomb blockaded suspended carbon nanotube
• Self-consistent theory of molecular switching
• Dynamics of a nanomechanical resonator coupled to a superconducting single-electron transistor
• Normal metal - superconductor tunnel junction as a Brownian refrigerator
• Strongly-coupled nanotube electromechanical resonators
• Probing the charge of a quantum dot with a nanomechanical resonator
• Strong feedback and current noise in nanoelectromechanical systems
• Superconducting proximity effect in interacting quantum dots revealed by shot noise
• Ground-state cooling of a carbon nanomechanical resonator by spin-polarized current
• Current noise in molecular junctions: effects of the electron-phonon interaction
• Phonon cooling of nanomechanical beams with tunnel junctions
• Effects of charge-dependent vibrational frequencies and anharmonicities in transport through molecules
• The Anderson--Holstein Model in Two Flavors of the Non--Crossing Approximation
• Vibrational cooling and thermoelectric response of nanoelectromechanical systems
• Josephson current through interacting double quantum dots with spin-orbit coupling
• Three-terminal scanning tunneling spectroscopy of suspended carbon nanotubes
• Josephson current through a molecular transistor in a dissipative environment
• Distortion blockade in classical nano-electromechanical resonator
• Dynamics and Dissipation induced by Single-Electron Tunneling in Carbon Nanotube Nanoelectromechanical Systems
• Vibrationally Induced Decoherence in Single-Molecule Junctions
• Electrical transport through a single-electron transistor strongly coupled to an oscillator
• Vibrational absorption sidebands in the Coulomb blockade regime of single-molecule transistors
• Superconducting transport through a vibrating molecule
• Few-hundred GHz Carbon Nanotube NEMS
• Cooling of a suspended nanowire by an AC Josephson current flow
• Ground-State Cooling of a Mechanical Oscillator by Interference in Andreev Reflection
• Crossover from adiabatic to antiadiabatic phonon-assisted tunneling in single-molecule transistors
• Magnetic damping of a carbon nanotube NEMS resonator
• Coherent properties of nano-electromechanical systems
• Nanoelectromechanical coupling in fullerene peapods probed via resonant electrical transport experiments
• Vibrational effects in charge transport through a molecular double quantum dot
• Low frequency current noise of the single-electron shuttle
• Transport through a molecular quantum dot in the polaron crossover regime
• Cooling a vibrational mode coupled to a molecular single-electron transistor
• Cooling of nanomechanical resonator by thermally activated single-electron transport
• Vibrationally-mediated molecular transistors
• Phonon Squeezing in a Superconducting Molecular Transistor
• Finite-frequency noise in a quantum dot with normal and superconducting leads
• Control of vibrational states by spin-polarized transport in a carbon nanotube resonator
• Quantum transport in a resonant tunnel junction coupled to a nanomechanical oscillator
• Electro-Mechanical Transition in Quantum dots
• Subgap resonant quasiparticle transport in normal-superconductor quantum dot devices
• Pair Tunneling and shot noise through a single molecule in a strong electron-phonon coupling
• Full counting statistics of phonon-assisted Andreev tunneling through a quantum dot coupled to normal and superconducting leads
• Polaron effects on the dc- and ac-tunneling characteristics of molecular Josephson junctions
• Switchable Coupling of Vibrations to Two-Electron Carbon-Nanotube Quantum Dot States
• Suspended single-electron transistors: fabrication and measurement
• Transport properties of a superconducting single-electron transistor coupled to a nanomechanical oscillator
• Interplay of magneto-elastic and polaronic effects in electronic transport through suspended carbon-nanotube quantum dots
• Nanomechanical effects in an Andreev quantum dot
• Resonant polaron-assisted tunneling of strongly interacting electrons through a single-level vibrating quantum dot
• Voltage-driven superconducting weak link as a refrigerator for cooling of nanomechanical vibrations

Cited by in corpus (8)

• Cooling by heating in nonequilibrium nanosystems
• Single atom laser in normal-superconductor quantum dots
• Quantum transport through a quantum dot side-coupled to a Majorana bound state pair in the presence of electron-phonon interaction
• Stabilizing quantum coherence against pure dephasing in the presence of quantum feedback at finite temperature
• Phonon-Assisted Andreev Reflection at Majorana Zero Mode
• Influences of electron-phonon interaction on quantum transport through one quantum-dot system with side-coupled Majorana zero mode
• Single-photon pump by Cooper-pair splitting
• Ground state cooling of nanomechanical resonators by electron transport