Coherent transport in disordered metals out of equilibrium

Schwab, Peter; Raimondi, Roberto

doi:10.1007/s10051-001-8706-1

Cited by 4 publications

(22 citation statements)

References 25 publications

(64 reference statements)

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“…ρ and Φ depend on the details of the device under consideration and we will come back to them below. The expression for the correction to the current in the wire has been obtained diagrammatically in [14] and is given by…”

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confidence: 99%

Coherent transport in disordered metals: zero dimensional limit

Schwab

Raimondi

2002

Eur. Phys. J. B

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We consider non-equilibrium transport in disordered conductors. We calculate the interaction correction to the current for a short wire connected to electron reservoirs by resistive interfaces. In the absence of charging effects we find a universal current-voltage-characteristics. The relevance of our calculation for existing experiments is discussed as well as the connection with alternative theoretical approaches. In recent years considerable attention has been devoted to the effects of the Coulomb interaction on the transport properties of small structures, like thin diffusive films and wires [1,2,3,4], tunnel junctions [5,6,7], and quantum dots [8]. One interesting issue concerns the way an applied bias voltage affects the interaction corrections to the electrical conductivity. In diffusive metals these corrections arise from the combination of the electron-electron and impurity scattering and yield well known singularities at low temperature [9]. It has been shown that a finite voltage or, more in general, a non-equilibrium situation leads to a suppression of these singularities [10,11,12,13,14]. In particular, in [10,14] non-equilibrium transport in a short wire connected to electrical reservoirs by ideal interfaces has been considered. However, in actual experiments the interfaces need not be ideal. Recently Weber et al. [15] investigated experimentally the non-equilibrium transport through a metallic nano-scale bridge. Both in [15] and in [16] it has been suggested that the Coulomb interaction effects are responsible for the observed temperature dependence of the conductance and the current-voltage-characteristics. Whereas [15] found an agreement between theory and experiment starting from a tunneling Hamiltonian, [16] pointed out that the experimental data agree with what they expect for a diffusive conductor. In this paper we develop a formalism in which both the resistive behavior due to the interfaces and due to the diffusive wire region are treated on the same footing. From our results we conclude that the main resistive behavior in [15] occurs at the interfaces.To begin with we recall the classical description of electrical transport through structures consisting of both interface barriers and diffusive regions. To be definite we consider a system made by a diffusive wire of length L which is attached to the reservoirs by two interface barriers. We study the system in a non-equilibrium situation with an applied voltage V l − V r = V where the subscripts l and r indicate the left and right reservoirs, respectively. The classical resistance of the structure is the sum of the wire resistance and the interface resistances R tot = R wire + R l + R r , so that the current as a function of voltage is

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Coherent transport in disordered metals: zero dimensional limit

Schwab

Raimondi

2002

Eur. Phys. J. B

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“…We now consider the other two limits, b) and c). We found that in both limits the current can be written as [54] δI…”

Section: Non-linear Conductivity In Wiresmentioning

confidence: 96%

“…The expression for the current density (113) has been derived first in [54], both using diagrammatic techniques as well as with the Keldysh version [51,52,125] of the non-linear sigma model [46]. Eq.…”

Section: Interaction Correction To Diffusive Transportmentioning

confidence: 99%

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Quasiclassical theory of charge transport in disordered interacting electron systems

Schwab

Raimondi

2003

Ann. Phys.

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We consider the corrections to the Boltzmann theory of electrical transport arising from the Coulomb interaction in disordered conductors. In this article the theory is formulated in terms of quasiclassical Green's functions. We demonstrate that the formalism is equivalent to the conventional diagrammatic technique by deriving the well-known Altshuler-Aronov corrections to the conductivity. Compared to the conventional approach, the quasiclassical theory has the advantage of being closer to the Boltzmann theory, and also allows description of interaction effects in the transport across interfaces, as well as non-equilibrium phenomena in the same theoretical framework. As an example, by applying the Zaitsev boundary conditions which were originally developed for superconductors, we obtain the P (E)-theory of the Coulomb blockade in tunnel junctions. Furthermore we summarize recent results obtained for the non-equilibrium transport in thin films, wires and fully coherent conductors.

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“…To be specific, we consider a weakly disordered quasi-1D metallic wire of length L in the out-ofequilibrium situation. At small voltage V , the quantum interaction correction to the classical result I class = (2 s e 2 V /h) g is 22,23 : ∆I(V ) (2 s e 2 V /h) (L T /L) − 1.57 + 0.067 (eV ) 2 E Th /(k B T ) 3 , where E Th = D/L 2 is the Thouless energy of the wire. The first term is the well-known Altshuler-Aronov correction [19][20][21]24,25 , dominated by exchange (Fock contribution) for weak screening.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

Texier

Mitscherling

2018

Phys. Rev. B

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We study the non-linear conductance G ∼ ∂ 2 I/∂V 2 |V =0 in coherent quasi-one-dimensional weakly disordered metallic wires. Our analysis is based on the scattering approach and includes the effect of Coulomb interaction. The non-linear conductance correlations can be related to integrals of two fundamental correlation functions : the correlator of functional derivatives of the conductance and the correlator of injectivities (the injectivity is the contribution to the local density of states of eigenstates incoming from one contact). These correlators are obtained explicitly by using diagrammatic techniques for weakly disordered metals. In a coherent wire of length L, we obtain rms G 0.006 E −1 Th (and G = 0), where E Th = D/L 2 is the Thouless energy of the wire and D the diffusion constant ; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal : the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, rms Ga 0.001 (gE Th ) −1 , where g 1 is the dimensionless (linear) conductance of the wire. In a weakly coherent wire (i.e. Lϕ L, where Lϕ is the phase coherence length), the non-linear conductance is of the same order than the result G0 of a free electron calculation (although screening again strongly reduces the dimensionless prefactor) : we get G ∼ G0 ∼ (Lϕ/L) 7/2 E −1 Th , while the antisymmetric part (at high magnetic field) now behaves as Ga ∼ (Lϕ/L) 11/2 (gE Th ) −1 G. The effect of thermal fluctuations is studied : when the thermal length LT = D/kBT is the smallest length scale, LT Lϕ L, the free electron result G0 ∼ (LT /L) 3 (Lϕ/L) 1/2 E −1 Th is negligible and the dominant contribution is provided by screening, G ∼ (LT /L)(Lϕ/L) 7/2 E −1 Th ; in this regime, the antisymmetric part is Ga ∼ (LT /L) 2 (Lϕ/L) 7/2 (gE Th ) −1 . All the precise dimensionless prefactors are obtained. Crossovers from zero to strong magnetic field regimes are also analysed.

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Coherent transport in disordered metals out of equilibrium

Cited by 4 publications

References 25 publications

Coherent transport in disordered metals: zero dimensional limit

Coherent transport in disordered metals: zero dimensional limit

Quasiclassical theory of charge transport in disordered interacting electron systems

Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

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