Performance analysis of nanostructured Peltier coolers

Employing non-equilibrium quantum transport models, we investigate the details and operating conditions of nano-structured Peltier coolers embedded with an energy filtering barrier. Our investigations point out non-trivial aspects of Peltier cooling which include an inevitable trade-off between the cooling power and the coefficient of performance, the coefficient of performance being high at a low voltage bias and subsequently deteriorating with increasing voltage bias. We point out that there is an optimum energy barrier height for nanowire Peltier coolers at which the cooling performance is optimized. However, for bulk Peltier coolers, the cooling performance is enhanced with the height of the energy filtering barrier. Exploring further, we point out that a degradation in cooling performance with respect to bulk is inevitable as a single moded nanowire transitions to a multi-moded one. The results discussed here can provide theoretical insights for optimal design of nano Peltier coolers

Quantum thermoelectrics based on 2-D Semi-Dirac materials

We show that a gap parameter can fully describe the merging of Dirac cones in semi-Dirac materials from $K$- and $K^\prime$-points into the common $M$-point in the Brillouin zone. We predict that the gap parameter manifests itself by enhancing the thermoelectric figure of merit $zT$ as the chemical potential crosses the gap followed by a sign change in the Seebeck coefficient around the same point. Subsequently, we show that there is also a trade-off feature between the maximum power delivered and the efficiency when the chemical potential crosses the gap parameter. An optimal operating point that minimizes the power-efficiency trade-off is consequently singled out for the best thermoelectric performance. Our work paves the way for the use of 2D semi-Dirac materials for thermoelectric applications.Comment: 5 pages, 5 figure

Thermoelectric study of dissipative quantum dot heat engines

This paper examines the thermoelectric response of a dissipative quantum dot heat engine based on the Anderson-Holstein model in two relevant operating limits: (i) when the dot phonon modes are out of equilibrium, and (ii) when the dot phonon modes are strongly coupled to a heat bath. In the first case, a detailed analysis of the physics related to the interplay between the quantum dot level quantization, the on-site Coulomb interaction and the electron-phonon coupling on the thermoelectric performance reveals that an n-type heat engine performs better than a p-type heat engine. In the second case, with the aid of the dot temperature estimated by incorporating a {\it{thermometer bath}}, it is shown that the dot temperature deviates from the bath temperature as electron-phonon interaction becomes stronger. Consequently, it is demonstrated that the dot temperature controls the direction of phonon heat currents, thereby influencing the thermoelectric performance. Finally, the conditions on the maximum efficiency with varying phonon couplings between the dot and all the other macroscopic bodies are analyzed in order to reveal the nature of the optimum junction.Comment: 10 pages, 9 figures, To be published in Phys Rev.

Incoherent scattering can favorably influence energy filtering in nanostructured thermoelectrics

Investigating in detail the physics of energy filtering through a single planar energy barrier in nanostructured thermoelectric generators, we reinforce the non-trivial result that the anticipated enhancement in generated power at a given efficiency via energy filtering is a characteristic of systems dominated by incoherent scattering and is absent in ballistic devices. In such cases, assuming an energy dependent relaxation time $\tau(E)=kE^r$, we show that there exists a minimum value $r_{min}$ beyond which generation can be enhanced by embedding nanobarriers. For bulk generators with embedded nanobarriers, we delve into the details of inter sub-band scattering and show that it has finite contribution to the enhancement in generation. We subsequently discuss the realistic aspects, such as the effect of smooth transmission cut-off and show that for $r>r_{min}$, the optimized energy barrier is just sufficiently wide enough to scatter off low energy electrons, a very wide barrier being detrimental to the performance. Analysis of the obtained results should provide general design guidelines for enhancement in thermoelectric generation via energy filtering. Our non-equilibrium approach is typically valid in the absence of local quasi-equilibrium and hence sets the stage for future advancements in thermoelectric device analysis, for example, Peltier cooling near a barrier interface.Comment: This article is related to our earlier submission arXiv:1609.07894 (Role of incoherent scattering on energy filtering in nanostructured thermoelectric generators