One-channel conductor coupled to a quantum of resistance: exact ac conductance and finite-frequency noise
arXiv:1202.0708 · doi:10.1103/PhysRevB.85.125421
Abstract
We consider a one-channel coherent conductor with a good transmission embedded into an ohmic environment whose impedance is equal to the quantum of resistance R_q=h/e^2 below the RC frequency. This choice is motivated by the mapping of this problem to a Tomonaga-Luttinger liquid with one impurity whose interaction parameter corresponds to the specific value K=1/2, allowing for a refermionization procedure. The "new" fermions have an energy-dependent transmission amplitude which incorporates the strong correlation effects and yields the exact dc current and zero-frequency noise through expressions similar to those of the scattering approach. We recall and discuss these results for our present purpose. Then we compute, for the first time, the finite-frequency differential conductance and the finite-frequency non-symmetrized noise. Contrary to intuitive expectation, both cannot be expressed within the scattering approach for the new fermions, even though they are still determined by the transmission amplitude. Even more, the finite-frequency conductance obeys an exact relation in terms of the dc current which is similar to that derived perturbatively with respect to weak tunneling within the Tien-Gordon theory, and extended recently to arbitrary strongly interacting systems coupled eventually to an environment or/and with a fractional charge. We also show that the emission excess noise vanishes exactly above eV, even though the underlying Tomonaga-Luttinger liquid model corresponds to a many-body correlated system. Our results apply for all ranges of temperature, voltages and frequencies below the RC frequency, and they allow to explore fully the quantum regime.
arXiv comment15 pages, 11 figures
References in corpus (39)
- Shot Noise in Mesoscopic Conductors
- Bosonization for Beginners --- Refermionization for Experts
- Coulomb blockade at almost perfect transmission
- Exact Conductance through Point Contacts in the Fractional Quantum Hall Effect
- Double Quantum Dots as Detectors of High-Frequency Quantum Noise in Mesoscopic Conductors
- Exact non-equilibrium transport through point contacts in quantum wires and fractional quantum Hall devices
- Detection of Quantum Noise from an Electrically-Driven Two-Level System
- Frequency-selective single photon detection using a double quantum dot
- Using a quantum dot as a high-frequency shot noise detector
- A one-channel conductor in an ohmic environment: mapping to a TLL and full counting statistics
- Experimental Test of the High-Frequency Quantum Shot Noise Theory in a Quantum Point Contact
- Coulomb Interaction and Quantum Transport through a Coherent Scatterer
- Transport properties of single channel quantum wires with an impurity: Influence of finite length and temperature on average current and noise
- Emission and Absorption quantum noise measurement with an on-chip resonant circuit
- Interaction effects on counting statistics and the transmission distribution
- Emission and absorption asymmetry in the quantum noise of a Josephson junction
- Tunneling through a barrier in Tomonaga-Luttinger liquid connected to reservoirs
- Energy relaxation at quantum Hall edge
- Applying voltage sources to a Luttinger liquid with arbitrary transmission
- Direct link between Coulomb blockade and shot noise in a quantum coherent structure
- Finite-Size Bosonization of 2-Channel Kondo Model: a Bridge between Numerical Renormalization Group and Conformal Field Theory
- Electron transport and current fluctuations in short coherent conductors
- Electron injection in a nanotube with leads: finite frequency noise-correlations and anomalous charges
- Strong back-action of a linear circuit on a single electronic quantum channel
- Conductance through a potential barrier embedded in a Luttinger liquid: nonuniversal scaling at strong coupling
- Local Perturbation in a Tomonaga-Luttinger Liquid at g=1/2
- Point contact tunneling in the fractional quantum Hall effect: an exact determination of the statistical fluctuations
- AC conductance and non-symmetrized noise at finite frequency in quantum wires and carbon nanotubes
- Anderson impurity model in nonequilibrium: analytical results versus quantum Monte Carlo data
- Experimental Test of the Dynamical Coulomb Blockade Theory for Short Coherent Conductors
- Emission and absorption noise in the fractional quantum Hall effect
- Non-equilibrium frequency-dependent noise through a quantum dot: A real time functional renormalization group approach
- Determination of tunneling charge via current measurements
- Correlations in one dimensional quantum impurity problems with an external field
- Current fluctuations of an interacting quantum dot
- Full counting statistics of chiral Luttinger liquids with impurities
- Finite size effects, super-and sub-poissonian noise in a nanotube connected to leads
- Transport properties of a molecular quantum dot coupled to one-dimensional correlated electrons
- Statistics of charge transfer through impurities in strongly correlated 1D metals
Cited by in corpus (20)
- Tomonaga-Luttinger physics in electronic quantum circuits
- Theory of light emission from quantum noise in plasmonic contacts: above-threshold emission from higher-order electron-plasmon scattering
- Energy and power fluctuations in ac-driven coherent conductors
- Mixed, charge and heat noises in thermoelectric nanosystems
- Perturbative fluctuation dissipation relation for non-equilibrium finite frequency noise in quantum circuits
- Waiting time distribution for trains of quantized electron pulses
- Dynamical Coulomb blockade under a temperature bias
- Nonsymmetrized noise in a quantum dot: Interpretation in terms of energy transfer and coherent superposition of scattering paths
- Waiting times of entangled electrons in normal-superconducting junctions
- Fluctuation dissipation relations for strongly correlated out-of-equilibrium circuits
- Unified time-dependent perturbative relations applied to spectroscopy through photo-drag current
- Strongly-Correlated Thermoelectric Transport beyond Linear Response
- Dynamical Coulomb Blockade in an interacting 1D system coupled to an arbitrary environment
- Interacting electrodynamics of short coherent conductors in quantum circuits
- Non-equilibrium quantum transport through a dissipative resonant level
- Series expansion of the quantum admittance in mesoscopic systems
- Finite-frequency noise in a non-interacting quantum dot
- Tunneling current and current correlations for anyonic quasiparticles of ν = 1/2 chiral Luttinger liquid in multi-edge geometries
- Exact calculation of current correlations and admittance in the fractional quantum Hall regime
- Renormalization of the Coulomb blockade gap due to extended tunneling in nanoscopic junctions