Phase Dependent Thermopower in Andreev Interferometers

Eom, Jonghwa; Chien, C. J.; Chandrasekhar, Venkat

doi:10.1103/physrevlett.81.437

Cited by 111 publications

(173 citation statements)

References 15 publications

(14 reference statements)

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“…However, there are some experimental results 8,14 where the latter symmetry does not hold. Such observations cannot be explained with the quasiclassical theory applied here.…”

Section: Figmentioning

confidence: 92%

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Peltier effects in Andreev interferometers

Virtanen¹,

Heikkilä²

2007

Phys. Rev. B

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The superconducting proximity effect is known to modify transport properties of hybrid normal--superconducting structures. In addition to changing electrical and thermal transport separately, it alters the thermoelectric effects. Changes to one off-diagonal element $L_{12}$ of the thermoelectric matrix $L$ have previously been studied via the thermopower, but the remaining coefficient $L_{21}$ which is responsible for the Peltier effect has received less attention. We discuss symmetry relations between $L_{21}$ and $L_{12}$ in addition to the Onsager reciprocity, and calculate Peltier coefficients for a specific structure. Similarly as for the thermopower, for finite phase differences of the superconducting order parameter, the proximity effect creates a Peltier effect significantly larger than the one present in purely normal-metal structures. This results from the fact that a nonequilibrium supercurrent carries energy.Comment: 5 pages, 4 figure

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“…However, there are some experimental results 8,14 where the latter symmetry does not hold. Such observations cannot be explained with the quasiclassical theory applied here.…”

Section: Figmentioning

confidence: 92%

“…in terms of the biases ∆V j = V j −V , ∆T j = T j −T and the modified response coefficients L. The proximityinduced changes in the conductance 8,9,10,11,12,13,14,15,16,17 have recently been investigated both experimentally and theoretically. Behavior of the remaining off-diagonal coefficient L ij 21 has previously been discussed in Ref.…”

mentioning

confidence: 99%

Peltier effects in Andreev interferometers

Virtanen¹,

Heikkilä²

2007

Phys. Rev. B

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“…4.6, this symmetry may be violated when electron-phonon or electron-electron interactions are taken into account. Non-symmetric thermopowers have been reported in measurements for certain orientations of a bismuth crystal [152] and in Andreev interferometer experiments [58] (for a theoretical analysis of these latter experiments see [74]). …”

Section: B)s(b B B)s(−b B B) κ(B B B) T = σ (B B B)s(b B B)π (B B B) mentioning

confidence: 99%

From Thermal Rectifiers to Thermoelectric Devices

Benenti

Casati

Mejía‐Monasterio

et al. 2016

Thermal Transport in Low Dimensions

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We discuss thermal rectification and thermoelectric energy conversion from the perspective of nonequilibrium statistical mechanics and dynamical systems theory. After preliminary considerations on the dynamical foundations of the phenomenological Fourier law in classical and quantum mechanics, we illustrate ways to control the phononic heat flow and design thermal diodes. Finally, we consider the coupled transport of heat and charge and discuss several general mechanisms for optimizing the figure of merit of thermoelectric efficiency.

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“…Therefore, this symmetry may be violated when electron-phonon and electron-electron interactions are taken into account. While the Seebeck coefficient has always been found to be an even function of the magnetic field in two-terminal purely metallic mesoscopic systems [20], Andreev interferometer experiments [21] and recent theoretical studies [22,23] have shown that systems in contact with a superconductor or with a heat bath can exhibit nonsymmetric thermopowers. It is a challenging problem to find realistic setups with x significantly different from unity, while approaching the Carnot efficiency.…”

Section: Reduces To Eq (5) While Thermodynamics Does Not Impose Anymentioning

confidence: 99%

Thermodynamic Bounds on Efficiency for Systems with Broken Time-Reversal Symmetry

Benenti¹,

Saito²,

Casati³

2011

Phys. Rev. Lett.

240

359

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We show that for systems with broken time-reversal symmetry the maximum efficiency and the efficiency at maximum power are both determined by two parameters: a "figure of merit" and an asymmetry parameter. In contrast to the time-symmetric case, the figure of merit is bounded from above; nevertheless the Carnot efficiency can be reached at lower and lower values of the figure of merit and far from the so-called strong coupling condition as the asymmetry parameter increases. Moreover, the Curzon-Ahlborn limit for efficiency at maximum power can be overcome within linear response. Finally, always within linear response, it is allowed to have simultaneously Carnot efficiency and non-zero power. The understanding of the fundamental limits that thermodynamics imposes on the efficiency of thermal machines is a central issue in physics and is becoming more and more practically relevant in the future society. In particular due to the need of providing a sustainable supply of energy and to strong concerns about the environmental impact of the combustion of fossil fuels, there is an increasing pressure to find best thermoelectric materials [1][2][3][4].A cornerstone result goes back to Carnot [5]. In a cycle between two reservoirs at temperatures T 1 and T 2 (T 1 > T 2 ), the efficiency η, defined as the ratio of the performed work W over the heat Q 1 extracted from the high temperature reservoir, is bounded by the so-called Carnot efficiency η C :The Carnot efficiency is obtained for a quasi static transformation which requires infinite time and therefore the extracted power, in this limit, reduces to zero. For this reason the notion of efficiency at maximum power has been introduced. An upper bound for the efficiency at maximum power has been proposed long ago by several authors [6][7][8][9] and is commonly referred to as Curzon-Ahlborn upper bound:The range of validity of this bound has been widely discussed in several interesting papers [10][11][12][13][14][15]. For the thermoelectric power generation and refrigeration, within linear response and for systems with time-reversal symmetry, both the maximum efficiency and the efficiency at maximum power, are governed by a single parameter, the dimensionless figure of meritwhere σ is the electric conductivity, S is the thermoelectric power (Seebeck coefficient), κ is the thermal conductivity, and T is the temperature. The maximum efficiency is given bywhere η C is the Carnot efficiency; the efficiency η(ω max ) at maximum power ω max reads [10]The only restriction imposed by thermodynamics is ZT ≥ 0, so that η max ≤ η C and η(ω max ) ≤ η (l) CA , where η (l) CA = η C /2 is the Curzon-Alhborn efficiency in the linear response regime. The upper bounds η C and η (l) CA are reached when the figure of merit ZT → ∞. This limit corresponds to the so-called strong coupling condition, for which the Onsager matrix L becomes singular (that is, det L = 0) and therefore the ratio J q /J ρ , with J q heat currrent and J ρ electric (particle) current, is independent of the applied temp...

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Phase Dependent Thermopower in Andreev Interferometers

Cited by 111 publications

References 15 publications

Peltier effects in Andreev interferometers

Peltier effects in Andreev interferometers

From Thermal Rectifiers to Thermoelectric Devices

Thermodynamic Bounds on Efficiency for Systems with Broken Time-Reversal Symmetry

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