The trade-off between large power output, high efficiency and small fluctuations in the operation of heat engines has recently received interest in the context of thermodynamic uncertainty relations (TURs). Here we provide a concrete illustration of this trade-off by theoretically investigating the operation of a quantum point contact (QPC) with an energy-dependent transmission function as a steady-state thermoelectric heat engine. As a starting point, we review and extend previous analysis of the power production and efficiency. Thereafter the power fluctuations and the bound jointly imposed on the power, efficiency and fluctuations by the TURs are analyzed as additional performance quantifiers. We allow for arbitrary smoothness of the transmission probability of the QPC, which exhibits a close to step-like dependence in energy, and consider both the linear and the non-linear regime of operation. It is found that for a broad range of parameters, the power production reaches nearly its theoretical maximum value, with efficiencies more than half of the Carnot efficiency and at the same time with rather small fluctuations. Moreover, we show that by demanding a non-zero power production, in the linear regime a stronger TUR can be formulated in terms of the thermoelectric figure of merit. Interestingly, this bound holds also in a wide parameter regime beyond linear response for our QPC device.

We investigate different types of time-dependently driven single-particle sources whose common feature is that they produce pulses of integer charge and minimally excite the Fermi sea. These sources are: a slowly driven mesoscopic capacitor, a Lorentzian-shaped time-dependent bias voltage, and a local gate-voltage modulation of a quantum Hall edge state. They differ by their specific driving protocols, e.g., they have a pure ac driving or a driving with a dc component. In addition, only in the first of these setups, strong confinement leading to a discrete energy spectrum of the conductor, is exploited for the single-particle emission. Here, we study if and how these basic differences impact transport properties. Specifically, we address time-and energy-resolved charge and energy currents, as well as their zero-frequency correlators (charge-, energy-and mixed noise), as they are frequently used to characterize experiments in quantum optics with electrons. Beyond disparities due to a different number and polarity of particles emitted per period, we in particular identify differences in the impact, which temperature has on the observables for sources with and without energy-dependent scattering properties. We trace back these characteristics to a small set of relevant parameter ratios. arXiv:1902.01209v1 [cond-mat.mes-hall]

The energetic properties of electron transport in mesoscopic and nanoscale conductors is of large current interest. Here we theoretically investigate the possibility of probing fluctuations of charge and heat currents as well as their mixed correlations via fluctuations of the temperature and electrochemical potential of a probe coupled to the conductor. Our particular interest is devoted to the charge and energy noise stemming from time-dependently driven nanoelectronic systems designed for the controlled emission of single electrons, even though our setup is appropriate for more general AC driving schemes. We employ a Boltzmann-Langevin approach in order to relate the frequencydependent electrochemical potential and temperature fluctuations in the probe to the bare charge and energy current fluctuations emitted from the electron source. We apply our findings to the prominent example of an on-demand single-electron source, realized by a driven mesoscopic capacitor in the quantum Hall regime. We show that neither the background fluctuations of the probe in the absence of the working source, nor the fluctuations induced by the probe hinder the access to the sought-for direct source noise for a large range of parameters. arXiv:1711.11523v1 [cond-mat.mes-hall]