Mixed, charge and heat noises in thermoelectric nanosystems

Abstract

Mixed, charge and heat current fluctuations as well as thermoelectric differential conductances are considered for non-interacting nanosystems connected to reservoirs. Using the Landauer-Buttiker formalism, we derive general expressions for these quantities and consider their possible relationships in the entire ranges of temperature, voltage and coupling to the environment or reservoirs. We introduce a dimensionless quantity given by the ratio between the product of mixed noises and the product of charge and heat noises, distinguishing between the auto-ratio defined in the same reservoir and the cross-ratio between distinct reservoirs. From the linear response regime to the high-voltage regime, we further specify the analytical expressions of differential conductances, noises and ratios of noises, and examine their behavior in two concrete nanosystems: a quantum point contact in an ohmic environment and a single energy level quantum dot connected to reservoirs. In the linear response regime, we find that these ratios are equal to each other and are simply related to the figure of merit. They can be expressed in terms of differential conductances with the help of the fluctuation-dissipation theorem. In the non-linear regime, these ratios radically distinguish between themselves as the auto-ratio remains bounded by one, while the cross-ratio exhibits rich and complex behaviors. In the quantum dot nanosystem, we moreover demonstrate that the thermoelectric efficiency can be expressed as a ratio of noises in the non-linear Schottky regime. In the intermediate voltage regime, the cross-ratio changes sign and diverges, which evidences a change of sign in the heat cross-noise.

13 pages, 9 figures, 4 tables

References in corpus (6)

• Quantum limit of heat flow across a single electronic channel
• Thermopower of a Kondo-correlated quantum dot
• Quantum heat fluctuations of single particle sources
• Failure of the Wiedemann-Franz Law in Mesoscopic Conductors
• Kondo physics and orbital degeneracy interact to boost thermoelectrics on the nanoscale
• One-channel conductor coupled to a quantum of resistance: exact ac conductance and finite-frequency noise

Cited by in corpus (11)

• Finding the quantum thermoelectric with maximal efficiency and minimal entropy production at given power output
• Periodic energy transport and entropy production in quantum electronics
• General bounds on electronic shot noise in the absence of currents
• Charge, spin, and heat shot noises in the absence of average currents: Conditions on bounds at zero and finite frequencies
• Minimal-excitation single-particle emitters: A comparison of charge and energy transport properties
• Phase-coherent heat circulators with normal- or superconducting contacts
• Mixed electrical-heat noise spectrum in a quantum dot
• Coherent control of thermoelectric currents and noise in quantum thermocouples
• 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
• Noise signatures of a charged Sachdev-Ye-Kitaev dot in mesoscopic transport