Abstract
Thermal transmission in a molecular transistor with fully spin-polarized electrodes subjected to a temperature gradient is considered. The problem has been solved using the density matrix method in perturbation approach over a small tunneling width. It has been found that due to the vibronic effects, a spintronic molecular transistor is characterized by negative differential thermoconductance. It has been demonstrated that in the dependence of thermopower S on the detuning energy, there is an increased number of points of change of the sign and magnitude of S comparing with that of a conventional molecular transistor. Optimal parameters, that provide the highest thermoelectric power at maximum efficiency \(P_\mathrm{me}\) for a spintronic molecular transistor, have been found. The dependences of the figure of merit ZT and \(P_\mathrm{me}\) on temperature and an external magnetic field have been calculated, and the influence of Coulomb interaction on the thermoelectric properties has been studied. It has been revealed that for nonzero Coulomb interaction, a more handy regime of thermoelectric device develops, characterized by a continuous region of external magnetic fields, which provide high values of thermoelectric power.
Similar content being viewed by others
References
G. Benenti, G. Casati, K. Saito, R.S. Whitney, Fundamental aspects of steady-state conversion of heat to work at the nanoscale. Phys. Rep. 694, 1 (2017)
Y. Dubi, M.D. Ventra, Colloquium: heat flow and thermoelectricity in atomic and molecular junctions. Rev. Mod. Phys. 83, 131 (2011)
L. Cui, R. Miao, C. Jiang, E. Meyhofer, P. Reddy, Perspective: thermal and thermoelectric transport in molecular junctions. J. Chem. Phys. 146, 092201 (2017)
C.M. Finch, V.M. Garcia-Suarez, C.J. Lambert, Giant thermopower and figure of merit in single-molecule devices. Phys. Rev. B 79, 033405 (2009)
M. Leijnse, M.R. Wegewijs, K. Flensberg, Nonlinear thermoelectric properties of molecular junctions with vibrational coupling. Phys. Rev. B 82, 045412 (2010)
P. Murphy, S. Mukerjee, J. Moore, Optimal thermoelectric figure of merit of a molecular junction. Phys. Rev. B 78, 161406(R) (2008)
C.W.J. Beenakker, A.A.M. Staring, Theory of the thermopower of a quantum dot. Phys. Rev. B 46, 9667 (1992)
D.M. Kennes, D. Schuricht, V. Meden, Effciency and power of a thermoelectric quantum dot device. Europhys. Lett. 102, 57003 (2013)
M. Sierra, D. Sánchez, Strongly nonlinear thermovoltage and heat dissipation in interacting quantum dots. Phys. Rev. B 90, 115313 (2014)
R. Swirkowicz, M. Wierzbicki, J. Barnaś, Thermoelectric effects in transport through quantum dots attached to ferromagnetic leads with noncollinear magnetic moments. Phys. Rev. B 80, 195409 (2009)
A. Parafilo, O.A. Ilinskaya, I. Krive, Y. Park, Thermoelectric effects in electron chiral tunneling in metallic carbon nanotubes. Superlattices Microstruct. 88, 72–79 (2015)
Y.D. Zubov, O.A. Ilinskaya, I.V. Krive, A.A. Krokhin, Transport properties and enhanced figure of merit of quantum dot-based spintronic thermoelectric device. J. Phys. Condens. Matter 30, 315303 (2018)
D. Segal, A. Nitzan, Spin-boson thermal rectifier. Phys. Rev. Lett. 94, 034301 (2005)
M. Sierra, D. Sánchez, Nonlinear heat conduction in coulomb-blockaded quantum dots. Mater. Today Proc. 2, 483–490 (2015)
M. Galperin, M.A. Ratner, A. Nitzan, Molecular transport junctions: vibrational effects. J. Phys.: Condens. Matter 19, 103201 (2007)
L. Gorelik, A. Isacsson, M. Voinova, B. Kasemo, R. Shekhter, M. Jonson, Shuttle mechanism for charge transfer in coulomb blockade nanostructures. Phys. Rev. Lett. 80, 4526 (1998)
S. Braig, K. Flensberg, Vibrational sidebands and dissipative tunneling in molecular transistors. Phys. Rev. B 68, 205324 (2003)
J. Koch, F. von Oppen, Franck-Condon blockade and giant Fano factors in transport through single molecules. Phys. Rev. Lett. 94, 206804 (2005)
H. Park, J. Park, A.K.L. Lim, E.H. Anderson, A. Alivisatos, P.L. McEuen, Nanomechanical oscillations in a single-\(\text{ C}_{60}\) transistor. Nature 407, 57–60 (2000)
P. Utko, R. Ferone, I.V. Krive, R.I. Shekhter, M. Jonson, M. Monthioux, L. Noé, J. Nygård, Nanoelectromechanical coupling in fullerene peapods probed by resonant electrical transport experiments. Nat. Commun. 1, 37 (2010)
J. Martínez-Blanco, C. Nacci, S. Erwin, K. Kanisawa, E. Locane, M. Thomas, F. von Oppen, P. Brouwer, S. Fölsch, Gating a single-molecule transistor with individual atoms. Nat. Phys. 11, 640–644 (2015)
L. Glazman, R. Shekhter, Inelastic resonant tunneling of electrons through a potential barrier. Sov. Phys. JETP 67, 163 (1988)
A. Mitra, I. Aleiner, A. Millis, Phonon effects in molecular transistors: quantal and classical treatment. Phys. Rev. B 69, 245302 (2004)
I. Krive, R. Ferone, R.I. Shekhter, M. Jonson, P. Utko, J. Nygård, The influence of electro-mechanical effects on resonant electron tunneling through small carbon nano-peapods. New J. Phys. 10, 043043 (2008)
A. Khedri, T. Costi, V. Meden, Nonequilibrium thermoelectric transport through vibrating molecular quantum dots. Phys. Rev. B 98, 195138 (2018)
M.B. Tagani, H.R. Soleimani, Photon-phonon-assisted thermoelectric effects in the molecular devices. Physica E 48, 36–41 (2013)
D. Segal, Heat flow in nonlinear molecular junctions: master equation analysis. Phys. Rev. B 73, 205415 (2006)
J. Koch, F. von Oppen, Y. Oreg, E. Sela, Thermopower of single-molecule devices. Phys. Rev. B 70, 195107 (2004)
X. Zianni, Effect of electron–phonon coupling on the thermoelectric efficiency of single-quantum-dot devices. Phys. Rev. B 82, 165302 (2010)
P. Reddy, S.-Y. Jang, R.A. Segalman, A. Majumdar, Thermoelectricity in molecular junctions. Science 315, 1568 (2007)
L. Cui, S. Hur, Z.A. Akbar, J.C. Klöckner, W. Jeong, F. Pauly, S.-Y. Jang, P. Reddy, E. Meyhofer, Thermal conductance of single-molecule junctions. Nature 572, 628–633 (2019)
S.K. Yee, J.A. Malen, A. Majumdar, R.A. Segalman, Thermoelectricity in fullerene-metal heterojunctions. Nano Lett. 11, 4089 (2011)
G. Rastelli, M. Houzet, F. Pistolesi, Resonant magneto-conductance through a vibrating nanotube. Eur. Phys. Lett. 89, 57003 (2010)
G. Rastelli, M. Houzet, L. Glazman, F. Pistolesi, Interplay of magneto-elastic and polaronic effects in electronic transport through suspended carbon-nanotube quantum dots. C R Phys. 13, 410 (2012)
F. Pistolesi, R. Shekhter, Tunable spin-polaron state in a singly clamped semiconducting carbon nanotube. Phys. Rev. B 92, 035423 (2015)
G. Skorobagatko, S. Kulinich, I. Krive, R. Shekhter, M. Jonson, Magnetopolaronic effects in electron transport through a single-level vibrating quantum dot. Low Temp. Phys. 37, 1032 (2011)
P. Trocha, J. Barnaś, Large enhancement of thermoelectric effects in a double quantum dot system due to interference and coulomb correlation phenomena. Phys. Rev. B 85, 085408 (2012)
M.B. Tagani, H.R. Soleimani, Influence of electron–phonon interaction on the thermoelectric properties of a serially coupled double quantum dot system. J. Appl. Phys. 112, 103719 (2012)
F. Chi, J. Zheng, X.-D. Lu, K.-C. Zhang, Thermoelectric effect in a serial two-quantum-dot. Phys. Lett. A 375, 1352–1356 (2011)
Y. Dai, X.-F. Wang, P. Vasilopoulos, Y.-S. Liu, Tunable spin-polarized transport through a side-gated double quantum dot molecular junction in the coulomb blockade regime. Appl. Nanosci. 9, 1685–1693 (2019)
P. Stadler, W. Belzig, G. Rastelli, Ground-state cooling of a carbon nanomechanical resonator by spin-polarized current. Phys. Rev. Lett. 113, 047201 (2014)
P. Stadler, W. Belzig, G. Rastelli, Control of vibrational states by spin-polarized transport in a carbon nanotube resonator. Phys. Rev. B 91, 085432 (2015)
S. Weiss, J. Brüggemann, M. Thorwart, Spin-vibronics in interacting nonmagnetic molecular nanojunctions. Phys. Rev. B 92, 045431 (2015)
M. Krawiec, K.I. Wysokiński, Thermoelectric effects in strongly interacting quantum dot coupled to ferromagnetic leads. Phys. Rev. B 73, 075307 (2006)
O. Ilinskaya, S. Kulinich, I. Krive, R. Shekhter, M. Jonson, Magnetically controlled single-electron shuttle. Low Temp. Phys. 41, 70 (2015)
R. de Groot, F. Mueller, P. van Engen et al., New class of materials: half-metallic ferromagnets. Phys. Rev. Lett. 50, 2024–2027 (1983)
M.I. Katsnelson, V.Y. Irkhin, L. Chioncel, A.I. Lichtenstein, R.A. de Groot, Half-metallic ferromagnets: from band structure to many-body effects. Rev. Mod. Phys. 80, 315 (2008)
E. Wada, K. Watanabe, Y. Shirahata et al., Efficient spin injection into GaAs quantum well across \(\text{ Fe}_3\text{ O}_4\) spin filter. Appl. Phys. Lett. 96, 1025101–1025103 (2010)
Y. Ji, G.J. Strijkers, F.Y. Yang, C.L. Chien, J.M. Byers, A. Anguelouch, G. Xiao, A. Gupta, Determination of the spin polarization of half-metallic \(\text{ Cr }\text{ O}_2\) by point contact Andreev reflection. Phys. Rev. Lett. 86, 5585 (2001)
G. Banach, R. Tyer, W.M. Temmerman, Study of half-metallicity in LSMO. J. Magn. Magn. Mater. 272, 1963–1964 (2004)
L.Y.G.S.I. Kulinich, A.N. Kalinenko, I.V. Krive, R.I. Shekhter, Y.W. Park, M. Jonson, Single-electron shuttle based on electron spin. Phys. Rev. Lett. 112, 117206 (2014)
O. Ilinskaya, D. Radic, H. Park, I. Krive, R. Shekhter, M. Jonson, Coulomb-promoted spintromechanics in magnetic shuttle devices. Phys. Rev. B 100, 045408 (2019)
A. Shkop, O. Bahrova, S. Kulinich, I. Krive, Interplay of vibration and coulomb effects in transport of spin-polarized electrons in a single-molecule transistor. Superlattices Microstruct. 37, 106356 (2020)
O. Bahrova, S. Kulinich, I. Krive, Polaronic effects induced by non-equilibrium vibrons in a single-molecule transistor. Low Temp. Phys./Fizika Nizkikh Temperatur 46, 799–804 (2020)
L. Gorelik, S. Kulinich, R. Shekhter, M. Jonson, V. Vinokur, Coulomb promotion of spin-dependent tunnelling. Phys. Rev. Lett. 95, 116806 (2005)
C.A. Perroni, D. Ninno, V. Cataudella, Electron-vibration effects on the thermoelectric efficiency of molecular junctions. Phys. Rev. B 90, 125421 (2014)
M.B. Tagani, H.R. Soleimani, Thermoelectric effects in a double quantum dot system weakly coupled to ferromagnetic leads. Solid State Comm. 152, 914–918 (2012)
Acknowledgements
The author thanks I.V. Krive for conceptualization of the problem and useful advices and S.I. Kulinich, O.A. Ilinskaya and O.M. Bahrova for fruitful discussions. This work is supported by the National Academy of Sciences of Ukraine (Scientific Program 1.4.10.26.4).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
Rights and permissions
About this article
Cite this article
Shkop, A.D. Thermoelectric Effects in Tunneling of Spin-Polarized Electrons in a Molecular Transistor. J Low Temp Phys 208, 248–270 (2022). https://doi.org/10.1007/s10909-022-02758-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10909-022-02758-0