Macroscopic coherent rectification in Andreev interferometers

Meair, Jonathan; Jacquod, Philippe

doi:10.1088/0953-8984/24/27/272201

Cited by 6 publications

(9 citation statements)

References 31 publications

(93 reference statements)

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“…[18,34,35]). Rectification effects occur in that regime [36][37][38][39][40] , and their influence on thermoelectricity is not yet understood. There are only few works we know about which have discussed nonlinear thermoelec-tricity.…”

Section: Introductionmentioning

confidence: 99%

Scattering theory of nonlinear thermoelectricity in quantum coherent conductors

Meair¹,

Jacquod²

2013

J. Phys.: Condens. Matter

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110

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We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker [Europhys. Lett. 35, 523 (1996)] to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify in particular rectification effects that increase device performance.PACS numbers: 85.50.Fi

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Section: Introductionmentioning

confidence: 99%

Scattering theory of nonlinear thermoelectricity in quantum coherent conductors

Meair¹,

Jacquod²

2013

J. Phys.: Condens. Matter

Self Cite

110

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“…The Landauer-Büttiker scattering theory 33 is a widely used theory for modeling such electron flows through quantum systems; giving DC and AC conductances 34,35 , and nonlinear effects [36][37][38][39] . It has equally been used to get linear thermal and thermoelectric effects [40][41][42][43][44][45] .…”

Section: Introductionmentioning

confidence: 99%

“…[27] works equally well for a non-equilibrium scattering theory that includes Hartree-like electron-electron interactions (electrostatic charging effects) in a self-consistent and gaugeinvariant manner. This theory is the analogue for heatcurrents 13 of the nonlinear scattering theory for chargecurrents [36][37][38][39] ; although heat-currents are not conserved when charge-currents are. Such electrostatic interactions cannot be ignored for the nonlinear response [36][37][38][39] , and entropy production is a purely nonlinear effect (vanishing in the linear-response regime).…”

Section: Introductionmentioning

confidence: 99%

“…This theory is the analogue for heatcurrents 13 of the nonlinear scattering theory for chargecurrents [36][37][38][39] ; although heat-currents are not conserved when charge-currents are. Such electrostatic interactions cannot be ignored for the nonlinear response [36][37][38][39] , and entropy production is a purely nonlinear effect (vanishing in the linear-response regime). By keeping only electrostatic interaction effects, this approach is by no means exact, however it is a reasonable approximation for any system where the single-electron charging energy is small compared to temperature or broadening of the quantum system's levels due to the coupling to the reservoirs 36 .…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamic and quantum bounds on nonlinear dc thermoelectric transport

Whitney

2013

Phys. Rev. B

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I consider the non-equilibrium DC transport of electrons through a quantum system with a thermoelectric response. This system may be any nanostructure or molecule modeled by the nonlinear scattering theory which includes Hartree-like electrostatic interactions exactly, and certain dynamic interaction effects (decoherence and relaxation) phenomenologically. This theory is believed to be a reasonable model when single-electron charging effects are negligible. I derive three fundamental bounds for such quantum systems coupled to multiple macroscopic reservoirs, one of which may be superconducting. These bounds affect nonlinear heating (such as Joule heating), work and entropy production. Two bounds correspond to the first law and second law of thermodynamics in classical physics. The third bound is quantum (wavelength dependent), and is as important as the thermodynamic ones in limiting the capabilities of mesoscopic heat-engines and refrigerators. The quantum bound also leads to Nernst's unattainability principle that the quantum system cannot cool a reservoir to absolute zero in a finite time, although it can get exponentially close.

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“…Similarly, the correlation between the magnetic influence and the electrical transport may, in principle, lead to the asymmetry even for V → 0. Nevertheless, accessing the zero-voltage inequality remains a significant challenge despite numerous attempts [2][3][4][5][6][7][8][9][10][11][12]. A system with high intrinsic asymmetry could be far more advantageous in realizing the desired characteristics.…”

mentioning

confidence: 99%

Conductance Discontinuity on the Surface of a Topological Insulator with Magnetic Electrodes

Duan,

Li,

Semenov

et al. 2015

Preprint

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Asymmetric electrical conductance is theoretically demonstrated on the surface of a topological insulator (TI) in the limit of infinitesimally small forward and reverse biases between two spin selective electrodes. The discontinuous behavior relies on the spin-momentum interlocked nature of TI surface electrons together with the resulting imbalance in the coupling coefficients between the electrodes and TI surface states. The analysis is based on a transmission matrix model that, in combination with a phenomenological treatment for the diffusive limit, accounts for both ballistic and scattered paths simultaneously. With the estimated conductance asymmetry over a factor of 10, implementation in the ratchet-like applications and low-voltage rectification circuits appears practicable.

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Macroscopic coherent rectification in Andreev interferometers

Cited by 6 publications

References 31 publications

Scattering theory of nonlinear thermoelectricity in quantum coherent conductors

Scattering theory of nonlinear thermoelectricity in quantum coherent conductors

Thermodynamic and quantum bounds on nonlinear dc thermoelectric transport

Conductance Discontinuity on the Surface of a Topological Insulator with Magnetic Electrodes

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