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Xue H, Qian R, Lu W, Gong X, Qin L, Zhong Z, An Z, Chen L, Lu W. Direct observation of hot-electron-enhanced thermoelectric effects in silicon nanodevices. Nat Commun 2023; 14:3731. [PMID: 37349328 DOI: 10.1038/s41467-023-39489-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Accepted: 06/14/2023] [Indexed: 06/24/2023] Open
Abstract
The study of thermoelectric behaviors in miniatured transistors is of fundamental importance for developing bottom-level thermal management. Recent experimental progress in nanothermetry has enabled studies of the microscopic temperature profiles of nanostructured metals, semiconductors, two-dimensional material, and molecular junctions. However, observations of thermoelectric (such as nonequilibrium Peltier and Thomson) effect in prevailing silicon (Si)-a critical step for on-chip refrigeration using Si itself-have not been addressed so far. Here, we carry out nanothermometric imaging of both electron temperature (Te) and lattice temperature (TL) of a Si nanoconstriction device and find obvious thermoelectric effect in the vicinity of the electron hotspots: When the electrical current passes through the nanoconstriction channel generating electron hotspots (with Te~1500 K being much higher than TL~320 K), prominent thermoelectric effect is directly visualized attributable to the extremely large electron temperature gradient (~1 K/nm). The quantitative measurement shows a distinctive third-power dependence of the observed thermoelectric on the electrical current, which is consistent with the theoretically predicted nonequilibrium thermoelectric effects. Our work suggests that the nonequilibrium hot carriers may be potentially utilized for enhancing the thermoelectric performance and therefore sheds new light on the nanoscale thermal management of post-Moore nanoelectronics.
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Affiliation(s)
- Huanyi Xue
- State Key Laboratory of Surface Physics and Department of Physics, Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, 200433, Shanghai, People's Republic of China
| | - Ruijie Qian
- State Key Laboratory of Surface Physics and Department of Physics, Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, 200433, Shanghai, People's Republic of China
- National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, 200083, Shanghai, China
| | - Weikang Lu
- State Key Laboratory of Surface Physics and Department of Physics, Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, 200433, Shanghai, People's Republic of China
- Shanghai Qi Zhi Institute, 41th Floor, AI Tower, No. 701 Yunjin Road, Xuhui District, 200232, Shanghai, China
| | - Xue Gong
- State Key Laboratory of Surface Physics and Department of Physics, Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, 200433, Shanghai, People's Republic of China
| | - Ludi Qin
- State Key Laboratory of Surface Physics and Department of Physics, Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, 200433, Shanghai, People's Republic of China
| | - Zhenyang Zhong
- State Key Laboratory of Surface Physics and Department of Physics, Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, 200433, Shanghai, People's Republic of China
| | - Zhenghua An
- State Key Laboratory of Surface Physics and Department of Physics, Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, 200433, Shanghai, People's Republic of China.
- Shanghai Qi Zhi Institute, 41th Floor, AI Tower, No. 701 Yunjin Road, Xuhui District, 200232, Shanghai, China.
- Yiwu Research Institute of Fudan University, Chengbei Road, 322000, Yiwu City, Zhejiang, China.
- Zhangjiang Fudan International Innovation Center, Fudan University, 201210, Shanghai, China.
| | - Lidong Chen
- State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Science, Shanghai, China
| | - Wei Lu
- National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, 200083, Shanghai, China.
- School of Physical Science and Technology, ShanghaiTech University, 201210, Shanghai, China.
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Riera-Campeny A, Sanpera A, Strasberg P. Open quantum systems coupled to finite baths: A hierarchy of master equations. Phys Rev E 2022; 105:054119. [PMID: 35706239 DOI: 10.1103/physreve.105.054119] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Accepted: 04/26/2022] [Indexed: 06/15/2023]
Abstract
An open quantum system in contact with an infinite bath approaches equilibrium, while the state of the bath remains unchanged. If the bath is finite, the open system still relaxes to equilibrium but it induces a dynamical evolution of the bath state. In this paper, we study the dynamics of open quantum systems in contact with finite baths. We obtain a hierarchy of master equations that improve their accuracy by including more dynamical information of the bath. For instance, as the least accurate but simplest description in the hierarchy, we obtain the conventional Born-Markov-secular master equation. Remarkably, our framework works even if the measurements of the bath energy are imperfect, which not only is more realistic but also unifies the theoretical description. Also, we discuss this formalism in detail for a particular noninteracting environment where the Boltzmann temperature and the Kubo-Martin-Schwinger relation naturally arise. Finally, we apply our hierarchy of master equations to study the central spin model.
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Affiliation(s)
- Andreu Riera-Campeny
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
| | - Anna Sanpera
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
- ICREA, Psg. Lluís Companys 23, 08001 Barcelona, Spain
| | - Philipp Strasberg
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
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Yazdani-Kachoei M, Rahimi S, Ebrahimi-Jaberi R, Nematollahi J, Jalali-Asadabadi S. Thermoelectric properties plus phonon and de Haas-van Alphen frequencies of hole/electron-doped [Formula: see text]. Sci Rep 2022; 12:663. [PMID: 35027573 PMCID: PMC8758700 DOI: 10.1038/s41598-021-04058-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Accepted: 12/15/2021] [Indexed: 11/08/2022] Open
Abstract
We investigate temperature, pressure, and localization dependence of thermoelectric properties, phonon and de Haas-van Alphen (dHvA) frequencies of the anti-ferromagnetic (AFM) CeIn[Formula: see text] using density functional theory (DFT) and local, hybrid, and band correlated functionals. It is found that the maximum values of thermopower, power factor, and electronic figure of merit of this compound occur at low (high) temperatures provided that the 4f-Ce electrons are (not) localized enough. The maximum values of the thermopower, power factor, electronic figure of merit (conductivity parameters), and their related doping levels (do not) considerably depend on the localization degree and pressure. The effects of pressure on these parameters substantially depend on the degree of localization. The phonon frequencies are calculated to be real which shows that the crystal is dynamically stable. From the phonon band structure, the thermal conductivity is predicted to be homogeneous. This prediction is found consistent with the thermal conductivity components calculated along three Cartesian directions. In analogous to the thermoelectric properties, it is found that the dHvA frequencies also depend on both pressure and localization degree. To ensure that the phase transition at Néel temperature cannot remarkably affect the results, we verify the density of states (DOS) of the compound at the paramagnetic phase constructing a non-collinear magnetic structure where the angles of the spins are determined so that the resultant magnetic moment vanishes. The non-collinear results reveal that the DOS and whence the thermoelectric properties of the compound are not changed considerably by the phase transition. To validate the accuracy of the results, the total and partial DOSs are recalculated using DFT plus dynamical mean-field theory (DFT+DMFT). The DFT+DMFT DOSs, in agreement with the hybrid DOSs, predict the Kondo effect in this compound.
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Affiliation(s)
- M. Yazdani-Kachoei
- Department of Physics, Faculty of Physics, University of Isfahan (UI), Hezar Jerib Avenue, Isfahan, 81746-73441 Iran
| | - S. Rahimi
- Department of Physics, Faculty of Physics, University of Isfahan (UI), Hezar Jerib Avenue, Isfahan, 81746-73441 Iran
| | - R. Ebrahimi-Jaberi
- Department of Physics, Faculty of Physics, University of Isfahan (UI), Hezar Jerib Avenue, Isfahan, 81746-73441 Iran
| | - J. Nematollahi
- Department of Physics, Faculty of Physics, University of Isfahan (UI), Hezar Jerib Avenue, Isfahan, 81746-73441 Iran
| | - S. Jalali-Asadabadi
- Department of Physics, Faculty of Physics, University of Isfahan (UI), Hezar Jerib Avenue, Isfahan, 81746-73441 Iran
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Strasberg P, Díaz MG, Riera-Campeny A. Clausius inequality for finite baths reveals universal efficiency improvements. Phys Rev E 2021; 104:L022103. [PMID: 34525673 DOI: 10.1103/physreve.104.l022103] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Accepted: 08/04/2021] [Indexed: 06/13/2023]
Abstract
We study entropy production in nanoscale devices, which are coupled to finite heat baths. This situation is of growing experimental relevance, but most theoretical approaches rely on a formulation of the second law valid only for infinite baths. We fix this problem by pointing out that Clausius' paper from 1865 already contains an adequate formulation of the second law for finite heat baths, which can be also rigorously derived from a microscopic quantum description. This Clausius inequality shows that nonequilibrium processes are less irreversible than previously thought. We use it to correctly extend Landauer's principle to finite baths and we demonstrate that any heat engine in contact with finite baths has a higher efficiency than previously thought. Importantly, our results are easy to study, requiring only the knowledge of the average bath energy.
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Affiliation(s)
- Philipp Strasberg
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - María García Díaz
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - Andreu Riera-Campeny
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
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Yazdani-Kachoei M, Jalali-Asadabadi S. Thermoelectric properties of heavy fermion CeRhIn 5 using density functional theory combined with semiclassical Boltzmann theory. RSC Adv 2019; 9:36182-36197. [PMID: 35540618 PMCID: PMC9074952 DOI: 10.1039/c9ra07859b] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2019] [Accepted: 10/18/2019] [Indexed: 11/21/2022] Open
Abstract
Experimental evidences show that Ce-based compounds can be good candidates for thermoelectric applications due to their high thermoelectric efficiencies at low temperatures. However, thermoelectric properties have been studied less than the other properties for CeRhIn5, a technologically and fundamentally important compound. Thus, we comprehensively investigate the thermoelectric properties, including the Seebeck coefficient, electrical conductivity, electronic part of thermal conductivity, power factor and electronic figure of merit, by a combination of quantum mechanical density functional and semiclassical Boltzmann theories, including relativistic spin–orbit interactions using different exchange–correlation functionals at temperatures T ≤ 300 K for CeRhIn5 along its a and c crystalline axes. The temperature dependences of the thermoelectric quantities are investigated. Our results reveal a better Seebeck coefficient, electrical conductivity, power factor and thermoelectric efficiency at T ≪ 300, in agreement with various other Ce-based compounds, when a high degree of localization is considered for the 4f-Ce electrons. The Seebeck coefficient, power factor and thermoelectric efficiency are made more efficient near room temperature by decreasing the degree of localization for 4f-Ce electrons. Our results also show that the thermoelectric efficiency along the a crystalline axis is slightly better than that of the c axis. We also investigate the effects of hydrostatic pressure on the thermoelectric properties of the compound at low and high temperatures. The results show that the effects of imposing pressure strongly depend on the degree of localization considered for 4f-Ce electrons. Consistent with experimental data, theoretical thermoelectric results calculated by our developed strategy show that CeRhIn5 is a good candidate for thermoelectric cooling applications due to its high thermoelectric efficiency at low temperatures.![]()
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Affiliation(s)
- M Yazdani-Kachoei
- Department of Physics, Faculty of Sciences, University of Isfahan (UI) Hezar Gerib Avenue Isfahan 81746-73441 Iran +98 31 37934800 +98 31 37932435
| | - S Jalali-Asadabadi
- Department of Physics, Faculty of Sciences, University of Isfahan (UI) Hezar Gerib Avenue Isfahan 81746-73441 Iran +98 31 37934800 +98 31 37932435
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Abstract
We report on coupled heat and particle transport measurements through a quantum point contact (QPC) connecting two reservoirs of resonantly interacting, finite temperature Fermi gases. After heating one of them, we observe a particle current flowing from cold to hot. We monitor the temperature evolution of the reservoirs and find that the system evolves after an initial response into a nonequilibrium steady state with finite temperature and chemical potential differences across the QPC. In this state any relaxation in the form of heat and particle currents vanishes. From our measurements we extract the transport coefficients of the QPC and deduce a Lorenz number violating the Wiedemann-Franz law by one order of magnitude, a characteristic persisting even for a wide contact. In contrast, the Seebeck coefficient takes a value close to that expected for a noninteracting Fermi gas and shows a smooth decrease as the atom density close to the QPC is increased beyond the superfluid transition. Our work represents a fermionic analog of the fountain effect observed with superfluid helium and poses challenges for microscopic modeling of the finite temperature dynamics of the unitary Fermi gas.
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Krinner S, Esslinger T, Brantut JP. Two-terminal transport measurements with cold atoms. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:343003. [PMID: 28749788 DOI: 10.1088/1361-648x/aa74a1] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In recent years, the ability of cold atom experiments to explore condensed-matter-related questions has dramatically progressed. Transport experiments, in particular, have expanded to the point in which conductance and other transport coefficients can now be measured in a way that is directly analogous to solid-state physics, extending cold-atom-based quantum simulations into the domain of quantum electronic devices. In this topical review, we describe the transport experiments performed with cold gases in the two-terminal configuration, with an emphasis on the specific features of cold atomic gases compared to solid-state physics. We present the experimental techniques and the main experimental findings, focusing on-but not restricted to-the recent experiments performed by our group. We finally discuss the perspectives opened up by this approach, the main technical and conceptual challenges for future developments, and potential applications in quantum simulation for transport phenomena and mesoscopic physics problems.
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Affiliation(s)
- Sebastian Krinner
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
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