Keldysh technique and non-linear σ-model: basic principles and applications

Kamenev, Alex; Levchenko, Alex

doi:10.1080/00018730902850504

Cited by 368 publications

(456 citation statements)

References 130 publications

Supporting

Mentioning

449

Contrasting

Order By: Relevance

“…The proximity effect is a central feature of superconducting junctions that plays a key role in many devices and can be exploited in the design of new systems with quantum functionality [1][2][3][4][5][6][7][8][9][10][11][12] . Recently, exotic proximity effects have been observed in various systems, including superconductor-metallic nanowires [5][6][7] and graphenesuperconductor structures 4 .…”

mentioning

confidence: 99%

Visualization of geometric influences on proximity effects in heterogeneous superconductor thin films

et al. 2012

View full text Add to dashboard Cite

The proximity effect is a central feature of superconducting junctions that plays a key role in many devices and can be exploited in the design of new systems with quantum functionality [1][2][3][4][5][6][7][8][9][10][11][12] . Recently, exotic proximity effects have been observed in various systems, including superconductor-metallic nanowires 5-7 and graphenesuperconductor structures 4 . However, it is still not clear how superconducting order propagates spatially in a heterogeneous superconductor system. Here we report on intriguing junction geometry effects in a heterogeneous system consisting of electronically two-dimensional superconducting islands on a metallic substrate. Depending on the local geometry, the superconducting gap induced at the metallic surface sometimes decays within ∼20 nm of the superconductor, and sometimes survives at distances that are several coherence lengths from a superconductor. We show in particular that the curvature of the junction plays an essential role in the proximity effect.The sample system comprises superconducting two-dimensional (2D) Pb islands on top of a single-atomic-layer surface metal, the striped incommensurate (SIC) phase of the Pb overlayer on Si(111) (refs 13-16). The scanning tunnelling microscopy (STM) image shown in Fig. 1 captures a variety of junction configurations. Figure 1a shows an interesting 'π'-shaped Pb island five monolayers (ML) thick on top of the SIC surface. Previous scanning tunnelling spectroscopy (STS) studies have shown that the SIC phase is superconducting with T C_SIC = ∼1.8 K (ref. 17) and the 2D Pb islands have a T C around 6 K (ref. 18), although the actual T C value also depends on the lateral size as well as its thickness 19 . At 4.3 K, the SIC template is in the normal state. At locations far from the Pb islands, the tunnelling spectrum exhibits no gap (spectrum no. 2 in Fig. 1b), whereas the spectrum acquired at the 2D Pb island shows a clear superconducting gap (spectrum no. 3). In the SIC region near the 2D Pb island, a superconducting gap can also be observed (spectrum no. 1), indicative of a proximity effect. To address the spatial dependence, we performed spectroscopic mapping over the same area, whose differential conductance at zero bias (zero-bias conductance (ZBC)) is shown in Fig. 1c. As the ZBC directly correlates with the size of the tunnelling gap (the smaller the value of ZBC, the larger the tunnelling gap), the landscape of ZBC is a good representation of the landscape of the superconducting gap.The ZBC image reveals a rich landscape. In some regions (for example, region α), the induced superconducting gap decays very quickly within a very short distance from the SIC/superconductor (S) interface, whereas in region β where the SIC wetting layer is surrounded by Pb islands from both sides, the induced Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA. *e-mail: shih@physics.utexas.edu.superconducting gap is quite uniform. Similarly, in region γ where the SIC region is near the 'recess'...

show abstract

mentioning

confidence: 99%

Visualization of geometric influences on proximity effects in heterogeneous superconductor thin films

et al. 2012

View full text Add to dashboard Cite

show abstract

“…In this chapter we review the derivation of the fRG equation within the functional integral formulation. In the following we presume a detailed knowledge of functional integrals in the coherent state representation using Grassmann algebra, which is introduced in the book of Negele and Orland (1988) in the Matsubara formalism, and in the review of Kamenev and Levchenko (2009) in the Keldysh formalism. Both formalisms are introduced in the context of fRG in the thesis of Karrasch (2010).…”

Section: Functional Renormalization Groupmentioning

confidence: 99%

Microscopic origin of the ‘0.7-anomaly’ in quantum point contacts

Bauer

Heyder

Schubert

et al. 2013

Nature

100

184

View full text Add to dashboard Cite

“…The seminal papers by Schwinger and Keldysh are [66,67]. Our discussion will mainly follow the presentation in [65,68,69].…”

Section: F Brief Review Of Schwinger-keldysh Formalism For Hydrodynamicsmentioning

confidence: 99%

Effective actions for anomalous hydrodynamics

Haehl

Loganayagam

Rangamani

2014

J. High Energ. Phys.

111

View full text Add to dashboard Cite

Abstract:We argue that an effective field theory of local fluid elements captures the constraints on hydrodynamic transport stemming from the presence of quantum anomalies in the underlying microscopic theory. Focussing on global current anomalies for an arbitrary flavour group, we derive the anomalous constitutive relations in arbitrary even dimensions. We demonstrate that our results agree with the constraints on anomaly governed transport derived hitherto using a local version of the second law of thermodynamics. The construction crucially uses the anomaly inflow mechanism and involves a novel thermofield double construction. In particular, we show that the anomalous Ward identities necessitate non-trivial interaction between the two parts of the Schwinger-Keldysh contour.

show abstract

Keldysh technique and non-linear σ-model: basic principles and applications

Cited by 368 publications

References 130 publications

Visualization of geometric influences on proximity effects in heterogeneous superconductor thin films

Visualization of geometric influences on proximity effects in heterogeneous superconductor thin films

Microscopic origin of the ‘0.7-anomaly’ in quantum point contacts

Effective actions for anomalous hydrodynamics

Contact Info

Product

Resources

About