Derivation of Oguri's linear conductance formula for interacting fermions within the Keldysh formalism

Heyder, Jan; Bauer, F.; Schimmel, Dennis; Delft, Jan von

doi:10.1103/physrevb.96.125141

Cited by 3 publications

(10 citation statements)

References 22 publications

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“…is consistent in the sense that we also already observed it in our static Matsubara implementation of the eCLA [1]. Together with the other inconsistencies, namely the violation of the Ward identity (37) and the associated issue that the two-particle contribution to the conductance is negative unless the Ward-correction (38) is used, this implies that in order to obtain quantitatively reliable results for the conductance one will have to go beyond the channel decomposition (10), and in general also beyond second-order truncated fRG. In particular, a more refined description and treatment of the vertex is required, using not only one but all three bosonic frequencies.…”

Section: Further Challengessupporting

confidence: 80%

“…In the second subsection III B, we describe the combination of Keldysh-and eCLA fRG in detail, give the resulting flow equations and comment on symmetries of the involved quantities. Finally, in subsection III C we discuss how to obtain the conductance from our fRG data, using the approach presented in [10].…”

Section: Methodsmentioning

confidence: 99%

“…∈ Θ A f . In the limit of large L and N L , we recover the full channel decomposed description of the vertex as given in (10).…”

Section: Dynamic Feedback Lengthmentioning

confidence: 99%

“…The main observable of interest for us is the linear conductance g. In order to compute it, we use a formula first derived by Oguri [13]. We employ its convenient Keldysh formulation developed in [10], whose notational conventions we have also adopted in this work. Within this formulation the conductance g can be expressed as…”

Section: Conductance Computationmentioning

confidence: 99%

“…where α, β, γ, δ ∈ {c, q} denote Keldysh indices. Furthermore, we use a channel decomposition, (10) with the bosonic frequencies given by Π =…”

Section: Propagatorsmentioning

confidence: 99%

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Functional renormalization group treatment of the 0.7 analog in quantum point contacts

et al. 2018

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We combine two recently established methods, the extended Coupled-Ladder Approximation (eCLA) [Phys. Rev. B 95, 035122 (2017)] and a dynamic Keldysh functional Renormalization Group (fRG) approach for inhomogeneous systems [Phys. Rev. Lett. 119, 196401 (2017)] to tackle the problem of finite-ranged interactions in quantum point contacts (QPCs) at finite temperature. Working in the Keldysh formalism, we develop an eCLA framework, proceeding from a static to a fully dynamic description. Finally, we apply our new Keldysh eCLA method to a QPC model with finite-ranged interactions and show evidence that an interaction range comparable to the length of the QPC might be an essential ingredient for the development of a pronounced 0.7-shoulder in the linear conductance. We also discuss problems arising from a violation of a Ward identity in second-order fRG.

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Section: Further Challengessupporting

confidence: 80%

Section: Methodsmentioning

confidence: 99%

“…∈ Θ A f . In the limit of large L and N L , we recover the full channel decomposed description of the vertex as given in (10).…”

Section: Dynamic Feedback Lengthmentioning

confidence: 99%

Section: Conductance Computationmentioning

confidence: 99%

“…where α, β, γ, δ ∈ {c, q} denote Keldysh indices. Furthermore, we use a channel decomposition, (10) with the bosonic frequencies given by Π =…”

Section: Propagatorsmentioning

confidence: 99%

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Functional renormalization group treatment of the 0.7 analog in quantum point contacts

et al. 2018

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Analytic Continuation of Multipoint Correlation Functions

Ge,

Halbinger,

Lee

et al. 2024

Annalen der Physik

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Conceptually, the Matsubara formalism (MF), using imaginary frequencies, and the Keldysh formalism (KF), formulated in real frequencies, give equivalent results for systems in thermal equilibrium. The MF has less complexity and is thus more convenient than the KF. However, computing dynamical observables in the MF requires the analytic continuation from imaginary to real frequencies. The analytic continuation is well‐known for two‐point correlation functions (having one frequency argument), but, for multipoint correlators, a straightforward recipe for deducing all Keldysh components from the MF correlator had not been formulated yet. Recently, a representation of MF and KF correlators in terms of formalism‐independent partial spectral functions and formalism‐specific kernels was introduced by Kugler, Lee, and von Delft [Phys. Rev. X 11, 041006 (2021)]. This representation is used to formally elucidate the connection between both formalisms. How a multipoint MF correlator can be analytically continued to recover all partial spectral functions and yield all Keldysh components of its KF counterpart is shown. The procedure is illustrated for various correlators of the Hubbard atom.

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Spin Fluctuations in the 0.7 Anomaly in Quantum Point Contacts

2017

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It has been argued that the 0.7 anomaly in quantum point contacts (QPCs) is due to an enhanced density of states at the top of the QPC-barrier (van Hove ridge), which strongly enhances the effects of interactions. Here, we analyze their effect on dynamical quantities. We find that they pin the van Hove ridge to the chemical potential when the QPC is subopen; cause a temperature dependence for the linear conductance that qualitatively agrees with experiment; strongly enhance the magnitude of the dynamical spin susceptibility; and significantly lengthen the QPC traversal time. We conclude that electrons traverse the QPC via a slowly fluctuating spin structure of finite spatial extent.Quantum point contacts are narrow, one-dimensional (1D) constrictions usually patterned in a two-dimensional electron system (2DES) by applying voltages to local gates. As QPCs are the ultimate building blocks for controlling nanoscale electron transport, much effort has been devoted to understand their behavior at a fundamental level. Nevertheless, in spite of a quarter of a century of intensive research into the subject, some aspects of their behavior still remain puzzling.When a QPC is opened up by sweeping the gate voltage, V g , that controls its width, its linear conductance famously rises in integer steps of the conductance quantum,. This conductance quantization is well understood [3] and constitutes one of the foundations of mesoscopic physics. However, during the first conductance step, where the dimensionless conductance g = G/G Q changes from 0 to 1 ("closed" to "open" QPC), an unexpected shoulder is generically observed near g 0.7. More generally, the conductance shows anomalous behavior as function of temperature (T ), magnetic field (B) and source-drain voltage (V sd ) throughout the regime 0.5 g 0.9, where the QPC is "subopen". The source of this behavior, collectively known as the "0.7-anomaly", has been controversially discussed [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] ever since it was first systematically described in 1996 [4]. Though no consensus has yet been reached regarding its detailed microscopic origin [10,22], general agreement exists that it involves electron spin dynamics and geometrically-enhanced interaction effects.In this paper we further explore the van Hove ridge scenario, proposed in [22]. It asserts that the 0.7 anomaly is a direct consequence of a "van Hove ridge", i. e. a smeared van Hove peak in the energy-resolved local density of states (LDOS) A i (ω) at the bottom of the lowest 1D subband of the QPC. Its shape follows that of the QPC barrier [22,23] and in the subopen regime, where the barrier top lies just below the chemical potential µ, it causes the LDOS at µ to be strongly enhanced. This reflects the fact that electrons slow down while crossing the QPC barrier (since the semiclassical velocity of an electron with energy ω at position i is inversely proportional to the LDOS, A i (ω) ∼ v −1 ). The slow electrons experience strongly enhanced mutual interactions...

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Derivation of Oguri's linear conductance formula for interacting fermions within the Keldysh formalism

Cited by 3 publications

References 22 publications

Functional renormalization group treatment of the 0.7 analog in quantum point contacts

Functional renormalization group treatment of the 0.7 analog in quantum point contacts

Analytic Continuation of Multipoint Correlation Functions

Spin Fluctuations in the 0.7 Anomaly in Quantum Point Contacts

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