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arXiv:2207.09494 · Physical review. B./Physical review. B

Andreev reflection spectroscopy in strongly paired superconductors

Cyprian Lewandowski, Étienne Lantagne-Hurtubise, Alex Thomson, Stevan Nadj-Perge, Jason Alicea

Published Jan 6, 2023• 14 citations
arXivHTMLPDF

Abstract

One of the challenges in the pursuit of solid state BEC superconductors is the need for unambiguous experimental signatures. Here, the authors propose a new signature, relying on Andreev reflection, which distinguishes BEC from BCS superconductors. They demonstrate that, in a standard tunneling spectroscopy setup, a BEC superconductor exhibits suppressed Andreev reflection; however, if the tunneling barrier becomes a potential well, then appreciable Andreev reflection can be revived. Their predictions can be probed in various architectures that are also discussed.

DOI
10.1103/physrevb.107.l020502

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One of the challenges in the pursuit of solid state BEC superconductors is the need for unambiguous experimental signatures. Here, the authors propose a new signature, relying on Andreev reflection, which distinguishes BEC from BCS superconductors. They demonstrate that, in a standard tunneling spectroscopy setup, a BEC superconductor exhibits suppressed Andreev reflection; however, if the tunneling barrier becomes a potential well, then appreciable Andreev reflection can be revived. Their predictions can be probed in various architectures that are also discussed.
Transport in Josephson junctions is commonly described using a simplifying assumption called the Andreev approximation, which assumes that excitations are fixed at the Fermi momentum and only Andreev reflections occur at interfaces (with no normal reflections). This approximation is appropriate for BCS-type superconductors, where the chemical potential vastly exceeds the pairing gap, but it breaks down for superconductors with low carrier density, such as topological superconductors, doped semiconductors, or superfluid quantum gases. Here, we present a generic analyticalanalyticalanalytical framework for calculating transport in Josephson junctions that lifts up the requirement of the Andreev approximation. Using this general framework, we study in detail transport in Josephson junctions across the BCS-BEC crossover, which describes the evolution from a BCS-type superconductor with loosely-paired Cooper pairs to a BEC of tighly-paired dimers. As the interaction is tuned from the BCS to the BEC regime, we find that the overall subgap current caused by multiple Andreev reflections decreases, but nonlinearities in the current-voltage characteristic called the subharmonic gap structure become more pronounced near the intermediate unitary limit, giving rise to sharp peaks and dips in the differential conductance with even negativenegativenegative conductance at specific voltages.
By developing a general framework for transport across superconducting junctions that goes beyond the standard Andreev approximation, two crucial transport signatures are proposed for sss-wave Josephson junctions along the BCS-BEC crossover: negative differential conductance as a signature of unitarity and a complete suppression of multiple-Andreev-reflection-induced current as a hallmark of the splitting point.
Generating non-locally entangled electron pairs via Cooper-pair splitting is vital for solid-state quantum information processing. However, isolating the underlying crossed Andreev reflection (CAR) is challenging due to competing transport processes like electron tunneling (ET) and local Andreev reflection (AR). Here, we propose a flux-tunable four-terminal normal metal-superconductor junction that achieves deterministic, 100\% efficient CAR. We demonstrate that at exactly half a magnetic flux quantum (φ=πφ=πφ=π), exact destructive Aharonov-Bohm and Peierls interferences structurally forbid ET and AR respectively. By tuning the central junction hopping, electron reflection is also suppressed to zero. Using the Cauchy argument principle, we prove that this suppression manifests as a quantized topological winding number, guaranteeing a topologically protected unit CAR probability. We establish that this regime is characterized by a strictly positive cross-correlation shot noise, providing an unambiguous experimental signature of Cooper-pair splitting. Furthermore, this perfect CAR is nearly broadband within the superconducting gap and remarkably robust against structural disorder, offering a highly resilient architecture for deterministic nonlocal entanglement generation.
Abstract The pioneering works by Eagles, Leggett, and Nozieres/Schmitt‐Rink [Eagles, Phys Rev, 1969, 186, 456; Leggett, In: Modern Trends in the Theory of Condensed Matter, Springer‐Verlag: Berlin, 1980; Nozieres and Schmitt‐Rink, Low Temp Phys, 1985, 59, 980] (reviewed and augmented by Randeria [Randeria, Bose‐Einstein Condensation, Cambridge University Press, Cambridge, 1995, p 255]) emphasize that in the limits of the models studied both at T = 0 and T ≠ 0, the “cross‐over” from a BCS‐type to a BEC‐type superconductor is continuous. The BCS and BEC “end points” seem to be well‐established. However, in the intermediate region—home to fulleride and high temperature superconductors—considerable extrapolation of the models must be done as there still is no exact theory. Yet, considerable current literature is devoted to what appears to be more “singular‐type phenomena” such as quantum critical points, “stripe” formation, insulator to superconductor phase transitions, loss of validity of the Fermi liquid theory, etc. Using a connection we have made with “cold” atom fermion‐boson crossover theory [Chen, Stajic, Levin, 2005, e‐print cond‐mat/0508603], we can establish that the resonance previously discussed [Squire and March, Int J Quant Chem, 2006, 106, 3343] is a result of the crossing of the fermion band by the boson band. While the ground state appears to remain continuous, the paired energy gap becomes transformed. We discuss features of the resonance and the experimentally observed pre‐formed “BEC Cooper pair” formation, essential to the boson‐fermion resonance theory. In addition some of the various singular phenomena discussed above can be put more into perspective. Finally, in both limits the relation of characteristic lengths to the inverse Fermi momentum is strongly emphasized, as is the role of the chemical potential near the pseudogap regime. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
We propose a source of purely electronic energy-entangled states implemented in a solid-state system with potential applications in quantum information protocols based on electron flying qubits. The proposed device relies on the standard tools of electron quantum optics and exploits entanglement of the Cooper pairs of a BCS superconductor. The latter is coupled via an adjustable quantum point contact to two opposite spin-polarized electron waveguides, which are driven by trains of Lorentzian pulses. This specific choice for the drive is crucial to inject purely electronic entangled states devoid of spurious electron-hole pairs. In the Andreev regime, a perturbative calculation in the tunnel coupling confirms that entangled electron states are generated at the output of the normal side. We introduce a quantity related to charge current cross correlations which allows one to experimentally verify the entangled nature of the emitted state.
The theory of unconventional superconductors continues to provide profound puzzles. The crossover between the weakly coupled Bardeen-Cooper-Schrieffer (BCS) state and the strong-pairing Bose-Einstein condensate (BEC) provides a useful perspective on how to address these questions. This paper describes a self-consistent framework for thinking about the crossover regime in between these two limits. The review discusses to what extent this BCS-BEC theory applies to a range of classes of superconducting materials including the cuprates, iron pnictides, twisted bilayer graphene, and interfacial superconductivity among others.