Scattering Theory of Non-Equilibrium Noise and Delta $T$ current fluctuations through a quantum dot

Abstract

We consider the non-equilibrium zero frequency noise generated by a temperature gradient applied on a device composed of two normal leads separated by a quantum dot. We recall the derivation of the scattering theory for non-equilibrium noise for a general situation where both a bias voltage and a temperature gradient can coexist and put it in a historical perspective. We provide a microscopic derivation of zero frequency noise through a quantum dot based on a tight binding Hamiltonian, which constitutes a generalization of the pioneering work of Caroli et al. for the current obtained in the context of the Keldysh formalism. For a single level quantum dot, the obtained transmission coefficient entering the scattering formula for the non-equilibrium noise corresponds to a Breit-Wigner resonance. We compute the delta-$T$ noise as a function of the dot level position, and of the dot level width, in the Breit-Wigner case, for two relevant situations which were considered recently in two separate experiments. In the regime where the two reservoir temperatures are comparable, our gradient expansion shows that the delta-$T$ noise is dominated by its quadratic contribution, and is minimal close to resonance. In the opposite regime where one reservoir is much colder, the gradient expansion fails and we find the noise to be typically linear in temperature before saturating. In both situations, we conclude with a short discussion of the case where both a voltage bias and a temperature gradient are present, in order to address the potential competition with thermoelectric effects.

19 pages, 9 figures

References in corpus (4)

• Electronic heat flow and thermal shot noise in quantum circuits
• General bounds on electronic shot noise in the absence of currents
• Dynamical Coulomb blockade under a temperature bias
• Theory of non-equilibrium noise in general multi-terminal superconducting hydrid devices: application to multiple Cooper pair resonances

Cited by in corpus (14)

• Charge, spin, and heat shot noises in the absence of average currents: Conditions on bounds at zero and finite frequencies
• Does delta-$T$ noise probe quantum statistics?
• Absence and recovery of cost-precision tradeoff relations in quantum transport
• Delta-T noise for fractional quantum Hall states at different filling factor
• Role of scaling dimensions in generalized noises in fractional quantum Hall tunneling due to a temperature bias
• Universal relations between thermoelectrics and noise in mesoscopic transport across a tunnel junction
• $\Delta T$-noise in Multiterminal Hybrid Systems
• Probing the dichotomy between Yu-Shiba-Rusinov and Majorana bound states via conductance, quantum noise and ${\Delta }_T$ noise
• Machine learning delta-T noise for temperature bias estimation
• Finite-frequency noise, Fano factor, $\Delta T$-noise and cross-correlations in double quantum dots
• Effect of uniaxial magnetic anisotropy on charge transport in a junction with a precessing anisotropic molecular spin
• Colored ${\Delta }_T$ noise probes the topological character of edge modes
• ${\Delta }_T$ Noise in Mesoscopic Hybrid Junctions: Influence of Barrier Strength and Thermal Bias
• Noise signatures of a charged Sachdev-Ye-Kitaev dot in mesoscopic transport