Thermopower of single-channel disordered and chaotic conductors

Langen, S. A. van; Silvestrov, P. G.; Beenakker, C. W. J.

doi:10.1006/spmi.1997.0532

Cited by 29 publications

(61 citation statements)

References 8 publications

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“…The most immediate effect of this failure is that the thermopower coefficient, which gives the voltage induced by a temperature gradient when no electrical current flows, becomes random in sign and is enhanced by (E F /E c )g −1 , where g ≡ G/G 0 is the dimensionless conductance and G 0 = e 2 /h. This enhancement can be many orders of magnitude, has been discussed in a number of previous works 8,9,10,11,12 , and has been measured in at least one experiment on quantum dots 13 .…”

Section: Introductionmentioning

confidence: 68%

“…8,9 for the case of a disordered wire and in Ref. 11 for the case of a chaotic quantum dot. The thermopower Q = −B/G is the coefficient of the voltage induced by a temperature difference when no electrical current flows, I e = 0.…”

Section: Thermopowermentioning

confidence: 96%

“…Semiconducting quantum dots exhibit large aperiodic thermopower fluctuations as a function of magnetic field 13 ; these have been treated theoretically by Van Langen et al 11 . The behavior of the Lorenz number for this case was not studied either experimentally or theoretically.…”

Section: Open Quantum Dotsmentioning

confidence: 99%

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Failure of the Wiedemann-Franz law in mesoscopic conductors

Vavilov

Stone

2005

Phys. Rev. B

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We study the effect of mesoscopic fluctuations on the validity of the Wiedemann-Franz (WF) law for quasi-one-dimensional metal wires and open quantum dots. At temperatures much less than the generalized Thouless energy, Ec, the WF law is satisfied for each specific sample but as the temperature is raised through Ec a sample-specific correction to the WF law of order 1/g appears (g is the dimensionless conductance) and then tends to zero again at kBT ≫ Ec. The mesoscopic violation of the Weidemann-Franz law is even more pronounced in a ring geometry, for which Lorenz number exhibits h/e flux-periodic Aharonov-Bohm oscillations.

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Section: Introductionmentioning

confidence: 68%

Section: Thermopowermentioning

confidence: 96%

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Failure of the Wiedemann-Franz law in mesoscopic conductors

Vavilov

Stone

2005

Phys. Rev. B

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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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“…The charging effects are taken into account 2,27 by the function F (τ 1 ,τ 2 ): C being the capacitance of the cavity,…”

Section: Introductionmentioning

confidence: 99%

Delay-time and thermopower distributions at the spectrum edges of a chaotic scatterer

et al. 2013

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We study chaotic scattering outside the wide band limit, as the Fermi energy EF approaches the band edges EB of a one-dimensional lattice embedding a scattering region of M sites. We show that the delay-time and thermopower distributions differ near the edges from the universal expressions valid in the bulk. To obtain the asymptotic universal forms of these edge distributions, one must keep constant the energy distance EF − EB measured in units of the same energy scale proportional to ∝ M −1/3 which is used for rescaling the energy level spacings at the spectrum edges of large Gaussian matrices. In particular the delay-time and the thermopower have the same universal edge distributions for arbitrary M as those for an M = 2 scatterer, which we obtain analytically.

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Thermopower of single-channel disordered and chaotic conductors

Cited by 29 publications

References 8 publications

Failure of the Wiedemann-Franz law in mesoscopic conductors

Failure of the Wiedemann-Franz law in mesoscopic conductors

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

Delay-time and thermopower distributions at the spectrum edges of a chaotic scatterer

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