Fig. 2: Heat-engine characteristics for non-thermal (NT) and quasi-thermal (QT) states.
From: Efficient heat-energy conversion from a non-thermal Tomonaga-Luttinger liquid
a, b, Drain current ID as a function of the gate voltage VGD at various effective energy bias eVeff. Positive power generation is highlighted by red. The upper-right and lower-left insets in a show the energy diagrams for positive power generation at eVeff > 0 (ε > μD,↑ > μS,↑) and eVeff < 0 (ε < μD,↑ < μS,↑), respectively, where ε is the electrochemical potential of the quantum dot (QD), and μD,↑ and μS,↑ are the chemical potentials of the drain and source spin-up channels, respectively. c, d Color plot of electric power P = − IDVeff as a function of eVeff and \(\varepsilon -\bar{\mu }\), where \(\bar{\mu }=({\mu }_{{{\rm{D}}},\uparrow }+{\mu }_{{{\rm{S}}},\uparrow })/2\) is the average chemical potential. Comparable heat power JT ≃ 400 fW was used in a and c for the NT state, and b and d for the QT state. The NT state provides high electromotive force Vemf ≃ 130 μV and high efficiencies \({\bar{\eta }}_{{{\rm{Z}}}}\simeq\) 0.65 in the zero power limit and \({\bar{\eta }}_{{{\rm{M}}}}\simeq\) 0.45 at maximum power in c, as compared to the QT state (Vemf ≃ 50 μV, \({\bar{\eta }}_{{{\rm{Z}}}}\simeq\) 0.58 and \({\bar{\eta }}_{{{\rm{M}}}}\simeq\) 0.35) in (d). e, f Color plot of P calculated for an idealized QD by using the binary Fermi distribution function fbin with the fraction p = 0.12, the high thermal energy kBTS = 116 μeV, the low thermal energy kBTL = 5.2 μeV, and the heat transfer factor κ = 0.2 for the NT state in e and the thermalized Fermi distribution function fth with the thermal energies kBTth = 42.3 μeV in the source and \({k}_{{{\rm{B}}}}{T}_{{{\rm{th}}}}^{{\prime} }=\) 23.2 μeV in the drain for the thermalized state in f. The conditions for ε = μD,↑ and ε = μS,↑, and the idealized efficiency \(\bar{\eta }=\) 0.2, 0.4, and 0.6 are shown by the dashed and solid lines, respectively, in (c–f). The estimated \({\bar{\eta }}_{{{\rm{Z}}}}\) and \({\bar{\eta }}_{{{\rm{M}}}}\) are shown by red and blue dashed lines in (c–f), while those in f coincide with the Carnot efficiency ηC and the Curzon-Ahlborn efficiency ηCA, respectively.
