Theory of nonequilibrium transport in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mtext>SU</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>Kondo regime

Mora, Christophe; Vitushinsky, P.; Leyronas, X.; Clerk, Aashish A.; Hur, Karyn Le

doi:10.1103/physrevb.80.155322

Cited by 83 publications

(146 citation statements)

References 52 publications

(172 reference statements)

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“…, an enhancement of the current fluctuations is detected out of equilibrium and perfectly explained by an e ective charge induced by the residual interaction between quasi-particles 8, [10][11][12][13][14][15][16][17] . Moreover, an as-yet-unknown scaling law for the e ective charge is discovered, suggesting a new non-equilibrium universality.…”

mentioning

confidence: 66%

“…A remarkable prediction of the non-equilibrium Fermi liquid theory is that the residual interaction between quasi-particles creates an additional scattering of two quasi-particles which enhances the noise (see the lower panel of Fig. 1a) 10,[12][13][14][15] . This two-particle scattering is characterized by an effective charge e * larger than e (electron charge).…”

Section: The Kondo Effectmentioning

confidence: 99%

“…The first result to emphasize is that the linear part of the current noise is qualitatively different from SU (2) and is a powerful experimental tool to distinguish the two symmetries 14,18 . The upper part of Fig.…”

Section: The Kondo Effectmentioning

confidence: 99%

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Universality of non-equilibrium fluctuations in strongly correlated quantum liquids

et al. 2015

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Interacting quantum many-body systems constitute a fascinating research field because they form quantum liquids with remarkable properties and universal behaviour The idea is that they behave as an ensemble of non-interacting 'quasi-particles'. However, non-equilibrium properties have still to be established and remain a key issue of many-body physics. Here, we show a precise experimental demonstration of Landau Fermi liquid theory extended to the non-equilibrium regime in a zero-dimensional system. Combining transport and ultra-sensitive current noise measurements, we have unambiguously identified the SU(2) (ref. The Kondo effect19 is a typical example of a quantum manybody effect, where a localized spin is screened by the surrounding conduction electrons at low temperature to form a unique correlated ground state. The Kondo state is described well by the Fermi liquid theory at equilibrium 1,9 , which makes it an ideal testbed to go beyond equilibrium. To unveil the universal behaviour of nonequilibrium Fermi liquid 11 , we have used the current fluctuations or shot noise in a Kondo-correlated nanotube quantum dot 18 . When electrons are transmitted through this system, the scattering induces the shot noise, which sensitively reflects the nature of the quasi-particles 20 , as shown in the upper panel of Fig. 1a. A remarkable prediction of the non-equilibrium Fermi liquid theory is that the residual interaction between quasi-particles creates an additional scattering of two quasi-particles which enhances the noise (see the lower panel of Fig. 1a) 10,12-15 . This two-particle scattering is characterized by an effective charge e * larger than e (electron charge). This value, closely related to the Wilson ratio, is universal for the Fermi liquid in the Kondo regime as it depends only on the symmetry group of the system [13][14][15] . Although some aspects of Kondo-associated noise have been reported 8,16,17 , a rigorous, selfconsistent treatment in a regime where universal results apply is at the core of the present work. Actually, by investigating the same nanotube quantum dot in the spin degenerate SU(2) Kondo regime and in the spin-orbit degenerate SU(4) regime, the noise is proved to contain distinct signatures of these two symmetries, confirming theoretical developments of Fermi liquid theory out of equilibrium.In our experiment, we measured the conductance and current noise through a carbon nanotube quantum dot grown by chemical vapour deposition 21 . Iron catalyst was deposited on an oxidized undoped silicon wafer and exposed to 10 mbar of acetylene for 9 s at 900• C. The nanotube was connected with a Pd(6 nm)/Al(70 nm) bilayer deposited by e-gun evaporation. The distance between the contacts is 400 nm and a side gate electrode is deposited to tune the potential of the quantum dot (see Fig. 1b). A magnetic field of 0.08 T is applied to suppress superconductivity of the contacts. To measure accurately the shot noise, our sample is connected to a resonant (2.58 MHz) LC circuit thermalized at the mixing chambe...

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confidence: 66%

Section: The Kondo Effectmentioning

confidence: 99%

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Universality of non-equilibrium fluctuations in strongly correlated quantum liquids

et al. 2015

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“…Though much is known for quantum impurity systems in equilibrium, understanding their properties in non-equilibrium steady-state is still limited. Nevertheless, significant progress has been made by different approaches, such as (1) analytical approximations: perturbative renormalization group method (RG) 27,28 , Hamiltonian flow equations 29 , functional RG 30,31 , strong-coupling expansions 32 , master equations 33 ; (2) exact analytical solutions: field theory techniques 34 , the scattering Bethe Ansatz 35 , mapping of a steady-state non-equilibrium problem onto an effective equilibrium system [36][37][38][39] , non-linear response theory approach to current fluctuations 40 ; (3) numerical methods: time-dependent density matrix renormalization group (RG) 41 , time-dependent numerical RG 42 , diagrammatic Monte Carlo 43 , and imaginary-time nonequilibrium quantum Monte Carlo 44 .…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium quantum transport through a dissipative resonant level

Chung¹,

Hur

Finkelstein

et al. 2013

Phys. Rev. B

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The resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. We provide a comprehensive analysis of the non-equilibrium transport near a quantum phase transition in a spinless dissipative resonant-level model, extending earlier work [Phys. Rev. Lett. 102, 216803 (2009)]. A detailed derivation of a rigorous mapping of our system onto an effective Kondo model is presented. A controlled energy-dependent renormalization group approach is applied to compute the non-equilibrium current in the presence of a finite bias voltage V . In the linear response regime V → 0, the system exhibits as a function of the dissipative strength a localized-delocalized quantum transition of the Kosterlitz-Thouless (KT) type. We address fundamental issues of the non-equilibrium transport near the quantum phase transition: Does the bias voltage play the same role as temperature to smear out the transition? What is the scaling of the non-equilibrium conductance near the transition? At finite temperatures, we show that the conductance follows the equilibrium scaling for V < T , while it obeys a distinct non-equilibrium profile for V > T . We furthermore provide new signatures of the transition in the finite-frequency current noise and AC conductance via a recently developed functional renormalization group (FRG) approach. The generalization of our analysis to non-equilibrium transport through a resonant level coupled to two chiral Luttinger-liquid leads, generated by fractional quantum Hall edge states, is discussed. Our work on the dissipative resonant level has direct relevance to experiments on a quantum dot coupled to a resistive environment, such as H. Mebrahtu et al., Nature 488, 61, (2012).

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“…Apart from many-body Keldysh perturbation theory, 5,6 many innovative approaches have been explored, 7 such as diagrammatic quantum Monte Carlo on the Keldysh contour, [8][9][10][11][12] field theory techniques, 13,14 time dependent density matrix renormalization group, 14,15 flow equation method, 16,17 functional renormalization group, 18,19 perturbative renormalization group, [20][21][22][23] master equations, 24 iterative path integral approaches, 25 strong-coupling expansions, [26][27][28][29] real time numerical renormalization group, 30,31 scattering Bethe Ansatz, 32 and imaginary-time nonequilibrium quantum Monte Carlo. 33,34 Unfortunately, most of these techniques are computationally very demanding, limiting their application only to simple models.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent and steady-state Gutzwiller approach for nonequilibrium transport in nanostructures

Lanatà

Strand

2012

Phys. Rev. B

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We extend the time-dependent Gutzwiller variational approach, recently introduced by Schirò and Fabrizio, Phys. Rev. Lett. 105 076401 (2010), to impurity problems. Furthermore, we derive a consistent theory for the steady state, and show its equivalence with the previously introduced nonequilibrium steady-state extension of the Gutzwiller approach. The method is shown to be able to capture dissipation in the leads, so that a steady state is reached after a sufficiently long relaxation time. The time-dependent method is applied to the single orbital Anderson impurity model at halffilling, modeling a quantum dot coupled to two leads. In these first exploratory calculations the Gutzwiller projector is limited to act only on the impurity. The strengths and the limitations of this approximation are assessed via comparison with state of the art continuous time quantum Monte Carlo results. Finally, we discuss how the method can be systematically improved by extending the region of action of the Gutzwiller projector.

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Theory of nonequilibrium transport in theSU(N)Kondo regime

Cited by 83 publications

References 52 publications

Universality of non-equilibrium fluctuations in strongly correlated quantum liquids

Universality of non-equilibrium fluctuations in strongly correlated quantum liquids

Nonequilibrium quantum transport through a dissipative resonant level

Time-dependent and steady-state Gutzwiller approach for nonequilibrium transport in nanostructures

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