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Anderson-Holstein model elucidates the most fundamental physics of cor- related quantum transport since it deals with the interaction between the electronic energy modes with strong Coulomb repulsion and a single phonon mode. From the practical stand-point, this model can be utilized to design a bias-driven heat engine to accomplish power generation or a refrigerator with substantial cooling efficiency [1]. In the first course of the presenta- tion, an in-depth 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 engine performs better than a p-type engine. In addition, with the aid of system temperature estimated by a thermometer bath, one can reveal the nature of optimum thermoelectric efficiency [2]. In the subsequent phase, it is demonstrated that, a phonon Peltier effect may arise in the non-linear ther- moelectric transport regime, leading to an electron induced phonon current in the absence of a thermal gradient. In further exploring possibilities that can arise from this effect, we propose a novel charge-induced phonon switching mechanism that may be incited via electrostatic gating [3]. Consequently, the observed cumulative effects of voltage and electronic temperature gradients on the non-linear phonon currents is explained by introducing a new trans- port coefficient, termed as the electron-induced phonon thermal conductivity [4]. Under suitable operating conditions, it can demonstrate two counter- intuitive situations: (a) the electronic system can pump in phonons into the hotter phonon reservoirs by exploiting voltage bias and (b) the electronic system can extract phonons out of the colder phonon reservoirs by utilizing voltage bias. For future analysis, this theoretical model can be implemented in designing hybrid refrigeration systems [5], light amplifying devices based on cavity-QED [6], thermal rectifiers[7] to name a few.

References

[1]  Muralidharan, B. and Grifoni, M., 2012. Performance analysis of an in- teracting quantum dot thermoelectric setup. Physical Review B, 85(15), p.155423.
[2]  De, B. and Muralidharan, B., 2016. Thermoelectric study of dissipative quantum-dot heat engines. Physical Review B, 94(16), p.165416.
[3]  De, B. and Muralidharan, B., 2018. Non-linear phonon Peltier effect in dissipative quantum dot systems. Scientific reports, 8(1), pp.1-9.
[4]  De, B. and Muralidharan, B., 2019. Manipulation of non-linear heat cur- rents in the dissipative Anderson–Holstein model. Journal of Physics: Condensed Matter, 32(3), p.035305.
[5]  Mukherjee, S., De, B. and Muralidharan, B., 2020. Three terminal vibron coupled hybrid quantum dot thermoelectric refrigeration. arXiv preprint arXiv:2004.12763.
[6]  Liu, Y.Y., Petersson, K.D., Stehlik, J., Taylor, J.M. and Petta, J.R., 2014. Photon emission from a cavity-coupled double quantum dot. Physical review letters, 113(3), p.036801.
[7]  Lu, J., Wang, R., Ren, J., Kulkarni, M. and Jiang, J.H., 2019. Quantum- dot circuit-QED thermoelectric diodes and transistors. Physical Review B, 99(3), p.035129.