2025
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| 9. | Vrishali Sonar, Piotr Trocha Spin dependent thermoelectric transport in a multiterminal quantum dot hybrid including a superconductor and ferromagnets Scientific Reports, 15 (1), pp. 14509, 2025, ISSN: 2045-2322. Abstract | Links | BibTeX @article{sonar_spin_2025,
title = {Spin dependent thermoelectric transport in a multiterminal quantum dot hybrid including a superconductor and ferromagnets},
author = {Vrishali Sonar and Piotr Trocha},
url = {https://www.nature.com/articles/s41598-025-94991-2},
doi = {10.1038/s41598-025-94991-2},
issn = {2045-2322},
year = {2025},
date = {2025-04-25},
urldate = {2025-05-30},
journal = {Scientific Reports},
volume = {15},
number = {1},
pages = {14509},
abstract = {We investigate the thermoelectric response of a hybrid system consisting of two ferromagnetic electrodes and one superconducting lead coupled to a single-level quantum dot with finite Coulomb repulsion. Using the non-equilibrium Green’s function technique within the Hubbard-I approximation, local and non-local thermoelectric coefficients, along with their spin counterparts, such as electrical and thermal conductance, and the Seebeck coefficient are calculated up to linear order with respect to generalized forces. Here, we present a derivation of spin-dependent thermoelectric coefficients for a three-terminal system, extending the existing theory which allowed to describe only cases independent of spin-bias voltage, i.e. when spin accumulation is irrelevant. In the considered system, four competing processes- single particle tunneling, quasiparticle tunneling, direct and crossed Andreev reflection make the system highly adaptable for tuning charge and heat currents. A full analysis of their impact on thermoelectric effects is provided. Moreover, the output power and efficiency of the system operating as a heat engine are evaluated. The extensive goal of this work is to demonstrate how the presence of an additional terminal modifies the hybrid QD-based device’s performance and under which conditions non-local thermoelectric effects become significant.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We investigate the thermoelectric response of a hybrid system consisting of two ferromagnetic electrodes and one superconducting lead coupled to a single-level quantum dot with finite Coulomb repulsion. Using the non-equilibrium Green’s function technique within the Hubbard-I approximation, local and non-local thermoelectric coefficients, along with their spin counterparts, such as electrical and thermal conductance, and the Seebeck coefficient are calculated up to linear order with respect to generalized forces. Here, we present a derivation of spin-dependent thermoelectric coefficients for a three-terminal system, extending the existing theory which allowed to describe only cases independent of spin-bias voltage, i.e. when spin accumulation is irrelevant. In the considered system, four competing processes- single particle tunneling, quasiparticle tunneling, direct and crossed Andreev reflection make the system highly adaptable for tuning charge and heat currents. A full analysis of their impact on thermoelectric effects is provided. Moreover, the output power and efficiency of the system operating as a heat engine are evaluated. The extensive goal of this work is to demonstrate how the presence of an additional terminal modifies the hybrid QD-based device’s performance and under which conditions non-local thermoelectric effects become significant. |
| 8. | Piotr Trocha Spin-dependent thermoelectric properties of a hybrid ferromagnetic metal/quantum dot/topological insulator junction Scientific Reports, 15 (4904), 2025. Abstract | Links | BibTeX @article{Trocha2025,
title = {Spin-dependent thermoelectric properties of a hybrid ferromagnetic metal/quantum dot/topological insulator junction},
author = {Piotr Trocha},
url = {https://www.nature.com/articles/s41598-025-87931-7},
doi = {10.1038/s41598-025-87931-7},
year = {2025},
date = {2025-02-10},
journal = {Scientific Reports},
volume = {15},
number = {4904},
abstract = {The thermoelectric properties of hybrid system based on a single-level quantum dot coupled to a ferromagnetic metallic lead and attached to the surface states of a three-dimensional topological insulator are theoretically investigated. On the surface of a three-dimensional topological insulator, massless helical Dirac fermions emerge. We calculate the thermoelectric coefficients, including electrical conductance, Seebeck coefficient (thermopower), heat conductance, and the figure of merit, using the nonequilibrium Green’s function technique. The results are analyzed in terms of the emergence of new effects. The calculations are performed within the Hubbard I approximation concerning the dot’s Coulomb interactions. Additionally, the spin-dependent coupling of the quantum dot to the ferromagnetic lead lifts the spin degeneracy of the dot’s level, which influences the transport properties of the system. We incorporate this effect perturbatively to obtain the spin-dependent renormalization of the dot’s level. We also consider the case of finite spin accumulation in the ferromagnetic electrode, which leads to spin thermoelectric effects.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The thermoelectric properties of hybrid system based on a single-level quantum dot coupled to a ferromagnetic metallic lead and attached to the surface states of a three-dimensional topological insulator are theoretically investigated. On the surface of a three-dimensional topological insulator, massless helical Dirac fermions emerge. We calculate the thermoelectric coefficients, including electrical conductance, Seebeck coefficient (thermopower), heat conductance, and the figure of merit, using the nonequilibrium Green’s function technique. The results are analyzed in terms of the emergence of new effects. The calculations are performed within the Hubbard I approximation concerning the dot’s Coulomb interactions. Additionally, the spin-dependent coupling of the quantum dot to the ferromagnetic lead lifts the spin degeneracy of the dot’s level, which influences the transport properties of the system. We incorporate this effect perturbatively to obtain the spin-dependent renormalization of the dot’s level. We also consider the case of finite spin accumulation in the ferromagnetic electrode, which leads to spin thermoelectric effects. |
| 7. | Emil Siuda, Piotr Trocha Thermal Gradient Powering Spin Current in Quantum Dot-Magnetic Insulators Hybrid Journal of Superconductivity and Novel Magnetism, 38 (81), 2025. Abstract | Links | BibTeX @article{Siuda2025,
title = {Thermal Gradient Powering Spin Current in Quantum Dot-Magnetic Insulators Hybrid},
author = {Emil Siuda and Piotr Trocha },
url = {https://link.springer.com/article/10.1007/s10948-025-06921-y},
doi = {10.1007/s10948-025-06921-y},
year = {2025},
date = {2025-02-07},
journal = {Journal of Superconductivity and Novel Magnetism},
volume = {38},
number = {81},
abstract = {The growing energy consumption of the computational sector worldwide necessitates the search for sustainable methods of powering and performing calculations. The fast-emerging field of spin caloritronics offers a promising solution by combining the advantages of performing computations on spins instead of charges and driving these computations through temperature differences rather than voltage. Among the various approaches, spin waves and their quanta of excitations, known as magnons, are considered promising carriers of spin-encoded information. In this article, we examine the magnon current generated in a system composed of a magnetic insulator/quantum dot/magnetic insulator, driven by a small temperature difference applied between the two insulators. By expanding the magnon current in terms of the applied temperature bias, we analyze the contributions of successive terms up to the third order of the temperature difference. Each term exhibits a similar structure, consisting of a driving-like and a damping-like component. The driving-like term is dependent on the coupling strength between the quantum dot and the electrodes. We explicitly show that the second-order term of the magnon current vanishes when the couplings of the quantum dot to the magnetic insulators are equal. Overall, the first two terms are sufficient to capture the behavior of the magnon current across the full range of temperature differences. For extreme values of the temperature gradient, the approximate results align with the exact ones only when there is significant asymmetry in the coupling strengths. Finally, we demonstrate that the system can function as a spin diode, capable of rectifying the magnon current when the temperature bias is reversed.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The growing energy consumption of the computational sector worldwide necessitates the search for sustainable methods of powering and performing calculations. The fast-emerging field of spin caloritronics offers a promising solution by combining the advantages of performing computations on spins instead of charges and driving these computations through temperature differences rather than voltage. Among the various approaches, spin waves and their quanta of excitations, known as magnons, are considered promising carriers of spin-encoded information. In this article, we examine the magnon current generated in a system composed of a magnetic insulator/quantum dot/magnetic insulator, driven by a small temperature difference applied between the two insulators. By expanding the magnon current in terms of the applied temperature bias, we analyze the contributions of successive terms up to the third order of the temperature difference. Each term exhibits a similar structure, consisting of a driving-like and a damping-like component. The driving-like term is dependent on the coupling strength between the quantum dot and the electrodes. We explicitly show that the second-order term of the magnon current vanishes when the couplings of the quantum dot to the magnetic insulators are equal. Overall, the first two terms are sufficient to capture the behavior of the magnon current across the full range of temperature differences. For extreme values of the temperature gradient, the approximate results align with the exact ones only when there is significant asymmetry in the coupling strengths. Finally, we demonstrate that the system can function as a spin diode, capable of rectifying the magnon current when the temperature bias is reversed. |
| 6. | Piotr Trocha, Thibaut Jonckheere, Jérôme Rech, Thierry Martin Thermoelectric properties of a quantum dot attached to normal metal and topological superconductor Scientific Reports, 15 (3068), 2025. Abstract | Links | BibTeX @article{Trocha2025b,
title = {Thermoelectric properties of a quantum dot attached to normal metal and topological superconductor},
author = {Piotr Trocha and Thibaut Jonckheere and Jérôme Rech and Thierry Martin},
url = {https://www.nature.com/articles/s41598-024-84770-w},
doi = {10.1038/s41598-024-84770-w},
year = {2025},
date = {2025-01-24},
journal = {Scientific Reports},
volume = {15},
number = {3068},
abstract = {The thermoelectric properties of hybrid systems based on a single-level quantum dot coupled to a normal-metal/half-metallic lead and attached to a topological superconductor wire are investigated. The topological superconductor wire is modeled by a spinless p-wave superconductor which hosts both a Majorana bound state at its extremity and above gap quasiparticle excitations. The main interest of our investigation is to study the interplay of sub-gap and single-particle tunneling processes and their contributions to the thermoelectric response of the considered system. The above gap tunneling driven by a temperature gradient is responsible for relatively large thermopower, whereas sub-gap processes only indirectly influence the thermoelectric response. The thermoelectric coefficients, including electric conductance, Seebeck coefficient (thermopower), heat conductance, and figure of merit, are calculated by means of the non-equilibrium Green’s function technique and the temperature dependence of the superconducting gap is considered within the BCS theory. We also consider the system out of equilibrium working as a heat engine. The output power and the corresponding efficiency are presented. Interestingly, under certain conditions, it is possible to extract more power in the superconducting phase than in the normal phase, with comparable efficiency.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The thermoelectric properties of hybrid systems based on a single-level quantum dot coupled to a normal-metal/half-metallic lead and attached to a topological superconductor wire are investigated. The topological superconductor wire is modeled by a spinless p-wave superconductor which hosts both a Majorana bound state at its extremity and above gap quasiparticle excitations. The main interest of our investigation is to study the interplay of sub-gap and single-particle tunneling processes and their contributions to the thermoelectric response of the considered system. The above gap tunneling driven by a temperature gradient is responsible for relatively large thermopower, whereas sub-gap processes only indirectly influence the thermoelectric response. The thermoelectric coefficients, including electric conductance, Seebeck coefficient (thermopower), heat conductance, and figure of merit, are calculated by means of the non-equilibrium Green’s function technique and the temperature dependence of the superconducting gap is considered within the BCS theory. We also consider the system out of equilibrium working as a heat engine. The output power and the corresponding efficiency are presented. Interestingly, under certain conditions, it is possible to extract more power in the superconducting phase than in the normal phase, with comparable efficiency. |
2024
|
| 5. | Piotr Trocha, Thibaut Jonckheere, Jérôme Rech, Thierry Martin Out-of-equilibrium voltage and thermal bias response of a quantum dot hybrid system coupled to topological superconductor Journal of Magnetism and Magnetic Materials, 596 , pp. 171922, 2024. Abstract | Links | BibTeX @article{Trocha2024,
title = {Out-of-equilibrium voltage and thermal bias response of a quantum dot hybrid system coupled to topological superconductor},
author = {Piotr Trocha and Thibaut Jonckheere and Jérôme Rech and Thierry Martin},
url = {https://www.sciencedirect.com/science/article/pii/S0304885324002130?via%3Dihub},
doi = {/10.1016/j.jmmm.2024.171922},
year = {2024},
date = {2024-04-15},
journal = {Journal of Magnetism and Magnetic Materials},
volume = {596},
pages = {171922},
abstract = {We investigate theoretically the out-of-equilibrium transport properties of a single-level quantum dot coupled to a normal metal electrode and attached to a topological superconductor. Both voltage and thermal bias responses of the system in the nonequilibrium regime are studied. To obtain transport characteristics we used the nonequilibrium Green’s function approach. Particularly, we calculated the current and the corresponding differential conductance in two distinct cases. In the former situation, the charge current is induced by applying a bias voltage, whereas in the latter case it is generated by setting a temperature difference between the leads with no bias voltage. Moreover, strong diode effect in thermally generated current is found and non-equilibrium thermopower is analyzed.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We investigate theoretically the out-of-equilibrium transport properties of a single-level quantum dot coupled to a normal metal electrode and attached to a topological superconductor. Both voltage and thermal bias responses of the system in the nonequilibrium regime are studied. To obtain transport characteristics we used the nonequilibrium Green’s function approach. Particularly, we calculated the current and the corresponding differential conductance in two distinct cases. In the former situation, the charge current is induced by applying a bias voltage, whereas in the latter case it is generated by setting a temperature difference between the leads with no bias voltage. Moreover, strong diode effect in thermally generated current is found and non-equilibrium thermopower is analyzed. |
| 4. | Vrishali Sonar, Piotr Trocha Non-local thermoelectric transport in multi-terminal quantum dot hybrid system Journal of Magnetism and Magnetic Materials, 593 , pp. 171745, 2024. Abstract | Links | BibTeX @article{Sonar2024,
title = {Non-local thermoelectric transport in multi-terminal quantum dot hybrid system},
author = {Vrishali Sonar and Piotr Trocha},
url = {https://www.sciencedirect.com/science/article/pii/S0304885324000350?via%3Dihub},
doi = {10.1016/j.jmmm.2024.171745},
year = {2024},
date = {2024-03-01},
journal = {Journal of Magnetism and Magnetic Materials},
volume = {593},
pages = {171745},
abstract = {The heat and charge transport is studied in a hybrid multi-terminal device consisting of one metallic, one ferromagnetic and a superconducting lead coupled to quantum dot. The basic thermoelectric properties of the system are examined using non-equilibrium Green’s function method with finite on-dot Coulomb repulsion within Hubbard-I approximation. Local and non-local transport coefficients including electrical and thermal conductance, Seebeck coefficient calculated in the linear response regime. Main objective is to analyze effect of superconductor coupling and ferromagnet’s spin polarization on thermoelectric transport and how ferromagnetic lead modifies it. We also studied the role of different electron tunneling types, i. e. Andreev reflection, quasi-particle and normal single particle tunneling processes on thermoelectric properties of the considered system.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The heat and charge transport is studied in a hybrid multi-terminal device consisting of one metallic, one ferromagnetic and a superconducting lead coupled to quantum dot. The basic thermoelectric properties of the system are examined using non-equilibrium Green’s function method with finite on-dot Coulomb repulsion within Hubbard-I approximation. Local and non-local transport coefficients including electrical and thermal conductance, Seebeck coefficient calculated in the linear response regime. Main objective is to analyze effect of superconductor coupling and ferromagnet’s spin polarization on thermoelectric transport and how ferromagnetic lead modifies it. We also studied the role of different electron tunneling types, i. e. Andreev reflection, quasi-particle and normal single particle tunneling processes on thermoelectric properties of the considered system. |
| 3. | Emil Siuda, Piotr Trocha Thermal generation of spin current in a quantum dot coupled to magnetic insulators Journal of Magnetism and Magnetic Materials, 589 , pp. 171495, 2024. Abstract | Links | BibTeX @article{Siuda2024,
title = {Thermal generation of spin current in a quantum dot coupled to magnetic insulators},
author = {Emil Siuda and Piotr Trocha},
url = {https://www.sciencedirect.com/science/article/pii/S0304885323011459},
doi = {/10.1016/j.jmmm.2023.171495},
year = {2024},
date = {2024-01-01},
journal = {Journal of Magnetism and Magnetic Materials},
volume = {589},
pages = {171495},
abstract = {In this work, we study thermally-generated spin current in the system consisting of a quantum dot connected to two magnetic insulators. The external leads are kept at different temperatures which leads to an imbalance of magnon populations in two magnetic insulators resulting in the flow of the magnon (spin) current. We take into account many-body magnon interactions and incorporate energy-dependent density of states of the magnetic insulators. Both features can strongly affect magnon distribution in the magnetic insulators and the coupling strengths between the leads and the dot, and thus, the thermally generated spin current. All the calculations are carried out in the weak coupling regime. We show, that results obtained with a density of states being a function of energy differ significantly from the ones obtained with a density of states taken as a constant. In turn, magnon interactions in the leads proved to be important at high temperatures and large values of energy of transported spin waves.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this work, we study thermally-generated spin current in the system consisting of a quantum dot connected to two magnetic insulators. The external leads are kept at different temperatures which leads to an imbalance of magnon populations in two magnetic insulators resulting in the flow of the magnon (spin) current. We take into account many-body magnon interactions and incorporate energy-dependent density of states of the magnetic insulators. Both features can strongly affect magnon distribution in the magnetic insulators and the coupling strengths between the leads and the dot, and thus, the thermally generated spin current. All the calculations are carried out in the weak coupling regime. We show, that results obtained with a density of states being a function of energy differ significantly from the ones obtained with a density of states taken as a constant. In turn, magnon interactions in the leads proved to be important at high temperatures and large values of energy of transported spin waves. |
2022
|
| 2. | Piotr Trocha, Emil Siuda Spin-thermoelectric effects in a quantum dot hybrid system with magnetic insulator Scientific Reports, 12 (5348), 2022. Abstract | Links | BibTeX @article{Trocha2022c,
title = {Spin-thermoelectric effects in a quantum dot hybrid system with magnetic insulator},
author = {Piotr Trocha and Emil Siuda},
url = {https://www.nature.com/articles/s41598-022-09105-z},
doi = {10.1038/s41598-022-09105-z},
year = {2022},
date = {2022-03-30},
journal = {Scientific Reports},
volume = {12},
number = {5348},
abstract = {We investigate spin thermoelectric properties of a hybrid system consisting of a single-level quantum dot attached to magnetic insulator and metal electrodes. Magnetic insulator is assumed to be of ferromagnetic type and is a source of magnons, whereas metallic lead is reservoir of electrons. The temperature gradient set between the magnetic insulator and metallic electrodes induces the spin current flowing through the system. The generated spin current of magnonic (electric) type is converted to electric (magnonic) spin current by means of quantum dot. Expanding spin and heat currents flowing through the system, up to linear order, we introduce basic spin thermoelectric coefficients including spin conductance, spin Seebeck and spin Peltier coefficients and heat conductance. We analyse the spin thermoelectric properties of the system in two cases: in the large ondot Coulomb repulsion limit and when these interactions are finite.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We investigate spin thermoelectric properties of a hybrid system consisting of a single-level quantum dot attached to magnetic insulator and metal electrodes. Magnetic insulator is assumed to be of ferromagnetic type and is a source of magnons, whereas metallic lead is reservoir of electrons. The temperature gradient set between the magnetic insulator and metallic electrodes induces the spin current flowing through the system. The generated spin current of magnonic (electric) type is converted to electric (magnonic) spin current by means of quantum dot. Expanding spin and heat currents flowing through the system, up to linear order, we introduce basic spin thermoelectric coefficients including spin conductance, spin Seebeck and spin Peltier coefficients and heat conductance. We analyse the spin thermoelectric properties of the system in two cases: in the large ondot Coulomb repulsion limit and when these interactions are finite. |
| 1. | Piotr Trocha, Emil Siuda, Ireneusz Weymann Spin-polarized transport in quadruple quantum dots attached to ferromagnetic leads Journal of Magnetism and Magnetic Materials, 546 (168835), 2022. Abstract | Links | BibTeX @article{Trocha2022b,
title = {Spin-polarized transport in quadruple quantum dots attached to ferromagnetic leads},
author = {Piotr Trocha and Emil Siuda and Ireneusz Weymann},
url = {https://www.sciencedirect.com/science/article/pii/S0304885321010453},
doi = {10.1016/j.jmmm.2021.168835},
year = {2022},
date = {2022-03-15},
journal = {Journal of Magnetism and Magnetic Materials},
volume = {546},
number = {168835},
abstract = {Motivated by the experimental evidence of the Nagaoka ferromagnetism in quantum dot systems by Dehollain et al. (2020), we search for possible confirmation of such kind of ferromagnetism by analyzing the spin-resolved transport properties of a quadruple quantum dot system focusing on the linear response regime. In particular, we consider four quantum dots arranged in a two-by-two square lattice, coupled to external ferromagnetic source and drain electrodes. Turning on and off the specific conditions for the Nagaoka ferromagnetism to occur by changing the value of the intra-dot Coulomb interactions, we determine the transport coefficients, including the linear conductance, tunnel magnetoresistance and current spin polarization. We show that a sign change of the current spin polarization may be an indication of a ferromagnetic order of Nagaoka type which develops in the system.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Motivated by the experimental evidence of the Nagaoka ferromagnetism in quantum dot systems by Dehollain et al. (2020), we search for possible confirmation of such kind of ferromagnetism by analyzing the spin-resolved transport properties of a quadruple quantum dot system focusing on the linear response regime. In particular, we consider four quantum dots arranged in a two-by-two square lattice, coupled to external ferromagnetic source and drain electrodes. Turning on and off the specific conditions for the Nagaoka ferromagnetism to occur by changing the value of the intra-dot Coulomb interactions, we determine the transport coefficients, including the linear conductance, tunnel magnetoresistance and current spin polarization. We show that a sign change of the current spin polarization may be an indication of a ferromagnetic order of Nagaoka type which develops in the system. |
