On the microscopics of proximity effects in one-dimensional superconducting hybrid systems

Bhaskaran Muralidharan; Jonathan Baugh; Kaveh Gharavi; Roshni Singh; Siddhant Midha

REVIEW 3 major objections 6 minor 84 references

On the microscopics of proximity effects in one-dimensional superconducting hybrid systems

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A Keldysh non-equilibrium Green's function method computes the induced pair amplitude in one-dimensional superconductor-normal hybrids, yielding an algebraic decay law in clean wires, a disorder-driven crossover to exponential decay, and…

desk verdict A workmanlike NEGF framework for induced pair amplitudes; the spectral-resolution and device-application sections are the real contributions, while the self-consistency language and the disorder crossover need scaling back. read the letter →

arxiv 2411.12733 v2 pith:PMCNNRZC submitted 2024-11-19 cond-mat.mes-hall

Siddhant Midha , Roshni Singh , Kaveh Gharavi , Jonathan Baugh , Bhaskaran Muralidharan This is my paper · ORCID

classification cond-mat.mes-hall

keywords proximityeffectpairamplitudeKeldyshnon-equilibriumGreen'sfunctionssuperconductor-normalhybridAndreevapproximationdisorder-inducedcrossoverCooperinjectionone-dimensionalnanowire

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to show that the Keldysh non-equilibrium Green's function method, through the correlation Green's function $G^n(E)$, is a working microscope for proximity-induced superconductivity in one-dimensional superconductor-normal hybrids. In a clean wire the induced pair amplitude $F(x)=\langle c^\dagger_{\uparrow x}c^\dagger_{\downarrow x}\rangle$ decays algebraically, $F(x)=F_0\,\xi_{SN}/(x+\xi_{SN})$, rather than exponentially, and the extracted length $\xi_{SN}$ grows with $\mu/\Delta$ and shrinks as $1/\Delta$. The paper also finds that a localized disorder profile at the junction turns this algebraic tail into an exponential one, and that the spectral resolution of $F(x)$ explains why a resonant tunneling device injects Cooper pairs efficiently. If correct, the framework gives device designers a direct way to compute and engineer induced correlations in layered superconducting hybrids.

What carries the argument

The load-bearing object is the correlation Green's function $G^n(E)$ defined in Eq. (9), a Nambu-space two-point correlator whose energy integral gives $-i\langle\hat\psi^\dagger_i\hat\psi_j\rangle$ and hence the pair amplitude $F(x)$ at each site. It is built from the retarded Green's function and the contact in-scattering functions, so it connects the equilibrium many-body correlations to the same contact self-energies used in transport calculations. What it does for the argument is to decompose the induced pairing by energy and position: the interference of the spectrally resolved oscillating correlations is what produces the algebraic tail in clean wires, the exponential tail under disorder, and the resonant enhancement in the Cooper-pair injector.

What would settle it

A direct comparison calculation would settle it: solve the same one-dimensional SN junction with a self-consistent BdG scheme in which $\Delta(x)=g(x)F(x)$ is updated using the computed pair amplitude, at $\mu=10$ meV and $\Delta=1$ meV. If the self-consistent pair amplitude does not follow $F(x)=F_0\xi_{SN}/(x+\xi_{SN})$ with $\xi_{SN}\approx44$ nm, or if the disorder crossover line shifts, the rigid-order-parameter assumption is the reason.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central discovery is that the correlation Green's function $G^n(E)=G^r(E)[\Sigma^{in}_L(E)+\Sigma^{in}_R(E)]G^a(E)$ carries the full position- and energy-resolved information about induced pairing. Integrating it over energy recovers the pair amplitude $F(x)$, and resolving it by energy shows that sub-gap states ($|E|<\Delta$) are the carriers of proximity correlations, while energies far above the chemical potential contribute nothing. The same object yields the clean-wire algebraic decay law $F(x)=F_0\,\xi_{SN}/(x+\xi_{SN})$, with $\xi_{SN}$ behaving as $\sim\sqrt{\mu/\Delta}$ in the Andreev regime and $\sim 1/\Delta$ as the order parameter grows, and it produces the disorder-driven crossover from power-law to exponential decay. Applied to the resonant Cooper-pair injection device, the calculation shows that resonant tuning makes the in-gap spectral pair amplitude positive and resonantly enhanced inside the quantum well, which is the microscopic counterpart of the enhanced sub-gap conductance seen in transport.

Load-bearing premise

The load-bearing assumption is that the superconducting order parameter is a rigid step function $\Delta(x)=\Delta\Theta(-x)$ fixed before the calculation, so the computed pair amplitude is never fed back to suppress $\Delta$ near the interface; if the inverse proximity effect is strong, the extracted decay law and $\xi_{SN}$ would change.

Editorial extensions

If this is right

In clean one-dimensional superconductor-normal wires at zero temperature, induced correlations penetrate with an algebraic tail $F(x)=F_0\xi_{SN}/(x+\xi_{SN})$; the effective coherence length $\xi_{SN}$ grows roughly as $\sqrt{\mu/\Delta}$ and falls as $1/\Delta$.
Disorder localized near the interface, characterized by strength $10^{-\gamma}$ and spatial spread $\sigma_D$, drives a crossover from algebraic to exponential decay of $F(x)$, so the disorder profile must be controlled to engineer reproducible proximity devices.
The spectral resolution shows that only energies inside the gap $|E|<\Delta$ carry the proximity correlations; the integral over energy in Eq. (10) can be truncated in practice.
In the resonant Cooper-pair injection device, the enhanced sub-gap conductance has a microscopic counterpart: a resonantly enhanced, non-negative in-gap pair amplitude inside the quantum well, offering a correlation-based design target for injection efficiency.
Because the method is built on contact self-energies, it extends to transport setups, finite temperatures, and higher-dimensional lattices with other pairing symmetries.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The rigid step-function $\Delta$ means the calculation omits the inverse proximity effect; a natural extension is to update $\Delta(x)=g(x)F(x)$ self-consistently and check whether the algebraic exponent and $\xi_{SN}$ values survive.
The conjectured order-disorder crossover, with $f_c/f_d\sim\log L$ separating clean and disordered correlation patterns, could be tested by finite-size scaling of $F(x)$ on much longer wires, since the current evidence rests on four data points.
The non-negativity of the in-gap spectral pair amplitude in the resonant case suggests an energy-resolved experimental probe: tunneling spectroscopy into the quantum well might see the same resonance directly, without relying on integrated conductance.
If the method generalizes as claimed, it supplies a ready design loop for Majorana nanowires and other topological hybrids, where optimizing the induced pair amplitude and its decay length in the semiconductor is the central engineering problem.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: the paper gives a Keldysh-NEGF recipe for computing induced pair amplitudes in 1D SN hybrids and applies it in three places: clean-wire decay, spectral decomposition via the correlation Green's function, and a published resonant Cooper-pair injector. The clean-wire power law was already in Rai et al. (Ref. [63]), and the authors say so; the benchmark is qualitative (same functional form), not coefficient-level. The credible new material is Sec. III C and III E: resolving F(x) by energy shows which spectral window carries the proximity correlations and how interference among those windows produces the net decay; the injector analysis ties the enhanced sub-gap conductance to a resonant enhancement of the pair amplitude inside the quantum well. That is a useful way to think about transport in layered devices.

The soft spots are real but not fatal. The stress-test note is right: the word 'self-consistent' is doing too much work. Delta is a rigid step input; the NEGF bath self-energies are iterated, but F(x) is never fed back into Delta. The paper says the method 'takes this into account' and claims to capture backaction from the normal region on the superconductor. It does not, because Delta(x) is static. That claim should be dialed back. Second, the disorder crossover in Sec. III D rests on four (sigma_D, gamma) points and is explicitly conjectured to be a phase transition. Fine as a motivated guess, but it is not established, and the text should say so more plainly. Third, the xi_SN(mu/Delta) and xi_SN(Delta) scalings are fits with phenomenological coefficients; the authors admit this, which is good, but the results should not be read as derivations. The citation pattern is solid: Ref. [63] is correctly credited and benchmarked, and self-citation is not an issue here.

No code is provided, so the numerics are unverified, but the method description is detailed enough to attempt a reproduction. The central modeling assumption, rigid Delta, is the conventional first step in this literature, and the NEGF pipeline itself is sound. If inverse proximity effects are significant, the quantitative xi_SN values could shift, though the power-law form is not likely to change.

Who is this for? NEGF toolbuilders and experimental groups interpreting sub-gap conductance in superconductor-semiconductor heterostructures. It is not a breakthrough, but it is a competent methods paper with a credible new decomposition and a clear device application. A serious editor should send this to peer review rather than desk reject it; I would accept with revisions, mainly asking the authors to soften the self-consistency claim, reframe the disorder crossover as suggestive rather than established, and ideally release code or data.

Referee Report

3 major / 6 minor

Summary. The paper develops a Keldysh non-equilibrium Green's function (NEGF) framework to compute the induced pair amplitude F(x) in one-dimensional superconductor-normal hybrids with a rigid step-function pair potential Δ(x)=ΔΘ(-x). The central claims are: (i) F(x) decays algebraically, F(x)=F0 ξSN/(x+ξSN), in clean wires, with an effective coherence length ξSN that grows with μ/Δ and decreases with Δ; (ii) an experimentally motivated disorder profile produces a crossover from power-law to exponential decay of F(x); and (iii) the spectral decomposition of the induced pair amplitude explains the enhanced Cooper-pair injection in the resonant device of Ref. [75]. The paper also discusses the Andreev approximation, the local density of states, and the inverse proximity effect in a qualitative way.

Significance. If the framework is correct, it offers a useful and comparatively general NEGF-based tool for studying proximity-induced correlations in hybrid devices, going beyond the restricted geometries of typical self-consistent BdG calculations and connecting correlations to transport observables. The spectral-resolution analysis of the resonant Cooper-pair injector is a constructive, falsifiable application. The numerical method is based on standard NEGF equations, and the power-law decay of F(x) agrees qualitatively with the self-consistent BdG results of Ref. [63]. However, the paper's claims are partially stronger than its evidence: the pair potential is not computed self-consistently despite the text saying otherwise, the scaling laws in Fig. 2 are phenomenological fits rather than derivations, and the disorder crossover in Sec. III D rests on a small number of points and an explicit conjecture. These issues do not invalidate the method, but they require a clearly revised presentation of what is derived versus what is fitted or conjectured.

major comments (3)

[Sec. III A, Eq. (1)] The text states that 'The NEGF method implicitly takes this into account through the self-consistent calculation of the Green's functions of the bath and subsequently of the system,' but this is not order-parameter self-consistency. Eq. (1) fixes Δ(x)=ΔΘ(-x) as an input, and the computed pair amplitude F(x) is never fed back to update Δ(x). The inverse proximity effect, i.e., suppression of the superconducting order parameter near the interface and its backaction on Andreev reflection, is therefore not captured. Since F0, ξSN, and the scalings in Fig. 2 are all extracted within this fixed-Δ model, their quantitative values could change under a self-consistent treatment. Please either implement an order-parameter self-consistency loop (or a controlled estimate of its effect) or revise the language in Sec. III A to state clearly that all results are obtained with a rigid, non-self-consistent pair potential.
[Eq. (11), Fig. 2] The decay form F(x)=F0 ξSN/(x+ξSN) is assumed a priori, and ξSN is obtained by fitting to this form rather than derived from the model. The reported ξSN(μ/Δ)=6.8√(μ/Δ)+28.7 nm and ξSN(Δ)=15.1+26.2/Δ-1.5/Δ² are phenomenological fits, as the authors note, but the surrounding discussion draws conclusions such as 'the growth of the effective coherence length is ∼√(μ/Δ)' as though this were a model prediction. The benchmark with Ref. [63] validates the power-law functional form qualitatively, but it does not validate these specific coefficients or the μ/Δ dependence. Please state explicitly which results are analytic or structural and which are numerical fits, and provide fit-quality measures or uncertainties for the extracted ξSN values.
[Sec. III D, Fig. 5] The claimed disorder-induced crossover from power-law to exponential decay is supported by only four (σD,γ) data points in Fig. 5(b), and the text itself labels the associated order-disorder transition a conjecture. No error bars, confidence intervals for the fitted decay forms, statistical comparison between power-law and exponential fits, or finite-size scaling are given, although the text acknowledges that finite-size scaling is difficult. As presented, the crossover is a suggestive model prediction rather than an established result. Please add quantitative evidence for the crossover, such as fit residuals, multiple system sizes, or a well-defined observable that sharply identifies the transition, or explicitly present this part as a preliminary finding that requires further numerical study.

minor comments (6)

[Fig. 2] The caption labels the top row (a-b) and bottom row (c-d), but the text refers to Fig. 2(d) for ξSN versus Δ, which appears to be panel (e) in the caption. Please harmonize the panel labels.
[Sec. III B, Fig. 2] The text lists μ/Δ ∈ {1.2,3,5,10,25}, while the Fig. 2 caption lists {1.2,3,5,10,15}. Please correct the discrepancy.
[Sec. III A] The phrase 'self-consistent calculation of the Green's functions' is misleading and should be replaced with 'iteratively converged Green's functions' or similar, reserving 'self-consistent' for treatments in which Δ is updated using F(x).
[Sec. III D, Eq. (13)] The vertical dotted line in Fig. 5(c) is described as denoting 'the variance of the disorder profile aσD,' but Eq. (13) defines σ(x) through a standard deviation aσD; please clarify whether the line marks the standard deviation or the variance and use consistent notation.
[Sec. III B] The sentence 'instead goes to zero in the opposite µ/∆ → 0 limit [77]' has a dangling bracket; the citation should be placed after the full clause.
[General] The manuscript does not include a data or code availability statement. Given that the fitting coefficients in Fig. 2 and the disorder averages in Fig. 5 are central quantitative outputs, a reproducibility statement would strengthen the paper.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the NEGF pair-amplitude results follow from the stated Hamiltonian, and the fitted decay parameters are explicitly phenomenological.

full rationale

The derivation is self-contained: the pair amplitude F(x) is computed from the Keldysh-NEGF correlation Green's function Gn(E)=Gr[Σin_L+Σin_R]Ga (Eq. 9) using the tight-binding Hamiltonian of Eq. 1 with Δ(x)=ΔΘ(−x), and no quantity derived from F(x) is fed back into the input Hamiltonian. The algebraic decay form Eq. 11 and the ξSN(μ/Δ, Δ) curves in Fig. 2 are explicitly presented as fits to the computed data; the paper states the coefficients are 'phenomenological, and expected to change with the microscopic parameters,' so they are not dressed as parameter-free predictions. The disorder crossover in Sec. III D is a direct comparison of computed pair amplitudes under different disorder profiles; the evidence is limited to four points, but that is an evidentiary weakness, not circularity. The comparison with Ref. [63] is an external benchmark for the same power-law form, not a self-citation. The only self-citations, Refs. [74] and [82], are methodological extensions and are not load-bearing premises for the central results. The remark in Sec. III A that the NEGF calculation is 'self-consistent' overstates the role of the fixed step-function Δ, since the computed F is not used to update Δ; this is an accuracy and interpretation concern about the inverse proximity effect, not a circular dependence of the results on their inputs. No load-bearing step reduces by construction to its own output, so no circularity is found.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The ledger shows that the paper's quantitative statements (decay law, coherence length scalings, disorder crossover) rest on two families of free choices: the fitting form Eq. (11) with its xi_SN, and the disorder profile Eqs. (12)-(13) with hand-picked gamma and sigma_D. There are no new physical entities, but the model-level assumptions (rigid Delta, zero temperature, Gaussian disorder) are substantial.

free parameters (5)

Effective coherence length xi_SN = 44(1) nm for mu=10 meV, Delta=1 meV; varies in Fig. 2
Extracted by fitting F(x)=F0 xi/(x+xi) to the computed pair amplitude tail; it is the central quantity used to describe decay length.
Coefficients of xi_SN vs mu/Delta fit = 6.8 and 28.7 nm
Phenomenological fit xi_SN = 6.8 sqrt(mu/Delta) + 28.7 nm to five simulated points in Fig. 2(b); coefficients not derived.
Coefficients of xi_SN vs Delta fit = 15.1, 26.2, -1.5 nm
Phenomenological fit xi_SN = 15.1 + 26.2/Delta - 1.5/Delta^2 to seven simulated points in Fig. 2(d); the 1/Delta algebraic dependence is presented as a design insight.
Disorder scale parameter gamma = Values used: 1, 1.75, 2, 3
Exponent setting the disorder strength V/t0 ~ 10^{-gamma}; chosen by hand to sample the crossover; gamma -> infinity means clean.
Disorder spread parameter sigma_D = Values used: 5, 25, 50, 100
Spatial extent of the Gaussian variance profile sigma(x)=exp[-0.5(x/(a sigma_D))^2]; chosen by hand for the four crossover points in Fig. 5.

assumptions (5)

domain assumption Mean-field BCS description with a fixed, real pair potential Delta(x)=Delta Theta(-x); non-interacting quasiparticles.
This is the model Hamiltonian Eq. (1). The pair amplitude is computed from this input and is not used to update Delta, so the treatment is not order-parameter self-consistent.
domain assumption Equilibrium, zero-temperature, zero-bias conditions: the bath in-scattering functions are equilibrium Fermi functions with mu_L=mu_R and T=0.
Eq. (8) and all results are obtained without bias or temperature; claims about conductance and pair correlations are specific to this regime.
ad hoc to paper The pair amplitude decay form F(x)=F0 xi/(x+xi) is assumed a priori for clean wires.
Eq. (11) is a fitting form, not derived; xi_SN is defined through it. If the true decay were not of this form, the extracted coherence length would not have the stated meaning.
ad hoc to paper Gaussian uncorrelated onsite disorder with variance profile sigma(x) and scale 10^{-gamma} models experimental disorder.
Eqs. (12)-(13) introduce an ad hoc, experimentally motivated disorder profile; no microscopic derivation links it to real disorder sources.
standard math Standard Keldysh NEGF formalism and recursive surface Green's function evaluation.
Eqs. (2)-(9) rely on the standard transport formalism; the recursion algorithm for the superconducting bath is described only in words.

how reviews work

0 comments

Cite this review

Pith. "Pith review of On the microscopics of proximity effects in one-dimensional superconducting hybrid systems." pith.science (2026). https://pith.science/paper/PMCNNRZC

@misc{pith2026241112733,
  author       = {Pith},
  title        = {Pith review of: On the microscopics of proximity effects in one-dimensional superconducting hybrid systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PMCNNRZC}},
  note         = {Machine review of arXiv:2411.12733}
}

read the original abstract

Investigating the microscopic details of the proximity effect is crucial for both key experimental applications and fundamental inquiries into nanoscale devices featuring superconducting elements. In this work, we develop a framework motivated by experiments to study induced superconducting correlations in hybrid nanoscale devices featuring layered superconductor-normal heterostructures using the Keldysh non-equilibrium Green's functions. Following a detailed method for analyzing the induced pair amplitude in a prototypical one-dimensional hybrid, we provide insights into the proximity effect within and outside the Andreev approximation. Our analysis also uncovers a disorder-induced crossover in the correlation patterns of the system. By elucidating the spectral distribution of the induced pair amplitude, we investigate the pair correlations established in a recent experiment [Phys.Rev.Lett.128,127701], providing a theoretical basis for the enhanced Cooper pair injection demonstrated through the lens of the induced pair correlations, thereby establishing the promise of our methods in guiding new experiments in hybrid quantum devices.

Figures

Figures reproduced from arXiv: 2411.12733 by the authors.

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

84 extracted references · 66 canonical work pages

[63]

G. Rai, S. Haas, and A. Jagannathan, Superconducting proximity effect and order parameter fluctuations in dis- ordered and quasiperiodic systems, Physical Review B 102, 134211 (2020)

work page 2020
[75]

Bouscher, D

S. Bouscher, D. Panna, K. Balasubramanian, S. Cohen, D. Ritter, and A. Hayat, Enhanced Cooper-Pair Injection into a Semiconductor Structure by Resonant Tunneling, Physical Review Letters 128, 127701 (2022), publisher: American Physical Society

work page 2022
[1]

Kroger, C

H. Kroger, C. Hilbert, D. A. Gibson, U. Ghoshal, and L. N. Smith, Superconductor-semiconductor hybrid de- vices, circuits, and systems, Proceedings of the IEEE 77, 1287 (1989)

1989
[2]

Benito and G

M. Benito and G. Burkard, Hybrid superconductor- semiconductor systems for quantum technology, Applied Physics Letters 116 (2020)

2020
[3]

De Franceschi, L

S. De Franceschi, L. Kouwenhoven, C. Sch¨ onenberger, and W. Wernsdorfer, Hybrid superconductor–quantum dot devices, Nature nanotechnology 5, 703 (2010)

2010
[4]

N. S. Kirsanov, Z. B. Tan, D. S. Golubev, P. J. Hakonen, and G. B. Lesovik, Heat switch and thermoelectric effects based on cooper-pair splitting and elastic cotunneling, Phys. Rev. B 99, 115127 (2019)

2019
[5]

S´ anchez, P

R. S´ anchez, P. Burset, and A. L. Yeyati, Cooling by cooper pair splitting, Phys. Rev. B 98, 241414 (2018)

work page 2018
[6]

Falci, D

G. Falci, D. Feinberg, and F. W. J. Hekking, Correlated tunneling into a superconductor in a multiprobe hybrid structure, Europhysics Letters 54, 255 (2001)

work page 2001

Show all 84 references

[7]

Sauret, D

O. Sauret, D. Feinberg, and T. Martin, Quantum mas- ter equations for the superconductor–quantum dot en- tangler, Phys. Rev. B 70, 245313 (2004)

2004
[8]

K. Sato, D. Loss, and Y. Tserkovnyak, Cooper-pair injec- tion into quantum spin hall insulators, Phys. Rev. Lett. 105, 226401 (2010)

2010
[9]

Bordin, G

A. Bordin, G. Wang, C.-X. Liu, S. L. Ten Haaf, N. Van Loo, G. P. Mazur, D. Xu, D. Van Driel, F. Za- telli, S. Gazibegovic, G. Badawy, E. P. Bakkers, M. Wim- mer, L. P. Kouwenhoven, and T. Dvir, Tunable Crossed Andreev Reflection and Elastic Cotunneling in Hybrid Nanowires, Phy...

2023
[10]

Hussein, M

R. Hussein, M. Governale, S. Kohler, W. Belzig, F. Gi- azotto, and A. Braggio, Nonlocal thermoelectricity in a Cooper-pair splitter, Physical Review B 99, 075429 (2019), arXiv:1806.04569 [cond-mat]

2019 arXiv
[11]

Arora, S

A. Arora, S. Midha, A. Zyuzin, P. Hakonen, and B. Mu- ralidharan, Steady-state dynamics and non-local corre- lations in thermoelectric cooper pair splitters (2024), arXiv:2406.06053 [cond-mat.mes-hall]

2024 arXiv
[12]

N. M. Chtchelkatchev and Y. V. Nazarov, Andreev quan- tum dots for spin manipulation, Phys. Rev. Lett. 90, 226806 (2003)

2003
[13]

Hoffman, M

S. Hoffman, M. Hays, K. Serniak, T. Hazard, and C. Tahan, Decoherence in andreev spin qubits (2024), arXiv:2403.00710 [cond-mat.mes-hall]

2024 arXiv
[14]

M. Hays, V. Fatemi, D. Bouman, J. Cerrillo, S. Dia- mond, K. Serniak, T. Connolly, P. Krogstrup, J. Nyg ˚ ard, A. Levy Yeyati, et al., Coherent manipulation of an an- dreev spin qubit, Science 373, 430 (2021)

2021
[15]

Park and A

S. Park and A. L. Yeyati, Andreev spin qubits in multi- channel rashba nanowires, Physical Review B 96, 125416 (2017)

2017
[16]

Aguado, A perspective on semiconductor-based super- conducting qubits, Applied Physics Letters 117, 240501 (2020)

R. Aguado, A perspective on semiconductor-based super- conducting qubits, Applied Physics Letters 117, 240501 (2020)

2020
[17]

Aguado and L

R. Aguado and L. P. Kouwenhoven, Majorana qubits for topological quantum computing, Physics today 73, 44 (2020)

2020
[18]

Prada, P

E. Prada, P. San-Jose, M. W. de Moor, A. Geresdi, E. J. Lee, J. Klinovaja, D. Loss, J. Nyg ˚ ard, R. Aguado, and L. P. Kouwenhoven, From andreev to majorana bound states in hybrid superconductor–semiconductor nanowires, Nature Reviews Physics 2, 575 (2020)

2020
[19]

Stern and N

A. Stern and N. H. Lindner, Topological quantum compu- tation—from basic concepts to first experiments, Science 339, 1179 (2013)

2013
[20]

Aguado, Majorana quasiparticles in condensed mat- ter, La Rivista del Nuovo Cimento 40, 523 (2017), arXiv:1711.00011 [cond-mat]

R. Aguado, Majorana quasiparticles in condensed mat- ter, La Rivista del Nuovo Cimento 40, 523 (2017), arXiv:1711.00011 [cond-mat]

2017 arXiv
[21]

Baselmans, A

J. Baselmans, A. Morpurgo, B. Van Wees, and T. Klap- wijk, Reversing the direction of the supercurrent in a controllable josephson junction, Nature 397, 43 (1999)

1999
[22]

Huang, F

J. Huang, F. Pierre, T. T. Heikkil¨ a, F. K. Wilhelm, and N. O. Birge, Observation of a controllable π junction in a 3-terminal josephson device, Phys. Rev. B 66, 020507 (2002)

2002
[23]

J. A. Van Dam, Y. V. Nazarov, E. P. Bakkers, S. De Franceschi, and L. P. Kouwenhoven, Supercurrent reversal in quantum dots, Nature 442, 667 (2006)

2006
[24]

le Sueur, P

H. le Sueur, P. Joyez, H. Pothier, C. Urbina, and D. Es- teve, Phase controlled superconducting proximity effect probed by tunneling spectroscopy, Phys. Rev. Lett. 100, 197002 (2008). 12

2008
[25]

V. T. Petrashov, V. N. Antonov, P. Delsing, and T. Clae- son, Phase controlled conductance of mesoscopic struc- tures with superconducting “mirrors”, Phys. Rev. Lett. 74, 5268 (1995)

1995
[26]

Dimoulas, J

A. Dimoulas, J. P. Heida, B. J. v. Wees, T. M. Klap- wijk, W. v. d. Graaf, and G. Borghs, Phase-dependent resistance in a superconductor-two-dimensional-electron- gas quasiparticle interferometer, Phys. Rev. Lett.74, 602 (1995)

1995
[27]

Pothier, S

H. Pothier, S. Gu´ eron, D. Esteve, and M. H. Devoret, Flux-modulated andreev current caused by electronic in- terference, Phys. Rev. Lett. 73, 2488 (1994)

1994
[28]

Clarke, A

J. Clarke, A. N. Cleland, M. H. Devoret, D. Esteve, and J. M. Martinis, Quantum mechanics of a macroscopic variable: the phase difference of a josephson junction, Science 239, 992 (1988)

1988
[29]

Pannetier and H

B. Pannetier and H. Courtois, Andreev Reflection and Proximity effect (1999), arXiv:cond-mat/9912024

1999 arXiv
[30]

Beenakker, Colloquium: Andreev reflection and klein tunneling in graphene, Reviews of Modern Physics 80, 1337 (2008)

C. Beenakker, Colloquium: Andreev reflection and klein tunneling in graphene, Reviews of Modern Physics 80, 1337 (2008)

2008
[31]

Q.-f. Sun, J. Wang, and T.-h. Lin, Resonant andreev re- flection in a normal-metal–quantum-dot–superconductor system, Physical Review B 59, 3831 (1999)

1999
[32]

Beenakker, Specular andreev reflection in graphene, Physical review letters 97, 067007 (2006)

C. Beenakker, Specular andreev reflection in graphene, Physical review letters 97, 067007 (2006)

2006
[33]

Nagato, K

Y. Nagato, K. Nagai, and J. Hara, Theory of the andreev reflection and the density of states in proximity contact normal-superconducting infinite double-layer, Journal of low temperature physics 93, 33 (1993)

1993
[34]

De Jong and C

M. De Jong and C. Beenakker, Andreev reflection in ferromagnet-superconductor junctions, Physical review letters 74, 1657 (1995)

1995
[35]

T. D. Stanescu, J. D. Sau, R. M. Lutchyn, and S. Das Sarma, Proximity effect at the superconduc- tor–topological insulator interface, Physical Review B 81, 241310 (2010)

2010
[36]

Schneider, K

L. Schneider, K. T. Ton, I. Ioannidis, J. Neuhaus- Steinmetz, T. Posske, R. Wiesendanger, and J. Wiebe, Proximity superconductivity in atom-by-atom crafted quantum dots (2022), arXiv:2212.00657 [cond-mat]

2022 arXiv
[37]

E. A. Demler, G. B. Arnold, and M. R. Beasley, Super- conducting proximity effects in magnetic metals, Physical Review B 55, 15174 (1997)

1997
[38]

Khanna, A

U. Khanna, A. Kundu, S. Pradhan, and S. Rao, Proximity-induced superconductivity in Weyl semimet- als, Physical Review B 90, 195430 (2014)

2014
[39]

Lee and H.-J

G.-H. Lee and H.-J. Lee, Proximity coupling in superconductor-graphene heterostructures, Reports on Progress in Physics 81, 056502 (2018), publisher: IOP Publishing

2018
[40]

Yokoyama, Josephson and proximity effects on the surface of a topological insulator, Physical Review B 86, 075410 (2012), publisher: American Physical Society

T. Yokoyama, Josephson and proximity effects on the surface of a topological insulator, Physical Review B 86, 075410 (2012), publisher: American Physical Society

2012
[41]

C. X. Trang, N. Shimamura, K. Nakayama, S. Souma, K. Sugawara, I. Watanabe, K. Yamauchi, T. Oguchi, K. Segawa, T. Takahashi, Y. Ando, and T. Sato, Conver- sion of a conventional superconductor into a topological superconductor by topological proximity effect, Nature Communicat...

2020
[42]

Hofstetter, A

L. Hofstetter, A. Geresdi, M. Aagesen, J. Nyg ˚ ard, C. Sch¨ onenberger, and S. Csonka, Ferromagnetic Proximity Effect in a Ferromagnet–Quantum-Dot– Superconductor Device, Physical Review Letters 104, 246804 (2010), publisher: American Physical Society

2010
[43]

Nakamura, L

T. Nakamura, L. D. Anh, Y. Hashimoto, Y. Iwasaki, S. Ohya, M. Tanaka, and S. Katsumoto, Proximity- Induced Superconductivity in a Ferromagnetic Semicon- ductor (In,Fe)As, Journal of Physics: Conference Series 969, 012036 (2018), publisher: IOP Publishing

2018
[44]

Buzdin, Density of states oscillations in a ferromag- netic metal in contact with a superconductor, Physical Review B 62, 11377 (2000)

A. Buzdin, Density of states oscillations in a ferromag- netic metal in contact with a superconductor, Physical Review B 62, 11377 (2000)

2000
[45]

C. R. Reeg and D. L. Maslov, Proximity-induced triplet superconductivity in Rashba materials, Physical Review B 92, 134512 (2015)

2015
[46]

R. Cai, I. ˇZuti´ c, and W. Han, Superconduc- tor/Ferromagnet Heterostructures: A Platform for Superconducting Spintronics and Quantum Computa- tion (2022), arXiv:2211.08625 [cond-mat]

2022 arXiv
[47]

C. R. Reeg and D. L. Maslov, Hard gap in a normal layer coupled to a superconductor, Physical Review B 94, 020501 (2016)

2016
[48]

H. F. Legg, D. Loss, and J. Klinovaja, Metallization and proximity superconductivity in topological insulator nanowires, Physical Review B 105, 155413 (2022)

2022
[49]

Li, Y.-F

C. Li, Y.-F. Zhao, A. Vera, O. Lesser, H. Yi, S. Ku- mari, Z. Yan, C. Dong, T. Bowen, K. Wang, H. Wang, J. L. Thompson, K. Watanabe, T. Taniguchi, D. Reifs- nyder Hickey, Y. Oreg, J. A. Robinson, C.-Z. Chang, and J. Zhu, Proximity-induced superconductivity in epitaxial topolog...

2023
[50]

F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Long- range effects in superconductor-ferromagnet structures, Physical Review Letters 86, 4096 (2001), arXiv:cond- mat/0011425

2001
[51]

Cheng, Superconducting proximity effect on the edge of fractional topological insulators, Physical Review B 86, 195126 (2012)

M. Cheng, Superconducting proximity effect on the edge of fractional topological insulators, Physical Review B 86, 195126 (2012)

2012
[52]

Kontos, M

T. Kontos, M. Aprili, J. Lesueur, and X. Grison, Inhomo- geneous Superconductivity Induced in a Ferromagnet by Proximity Effect, Physical Review Letters86, 304 (2001)

2001
[53]

J.-P. Xu, C. Liu, M.-X. Wang, J. Ge, Z.-L. Liu, X. Yang, Y. Chen, Y. Liu, Z.-A. Xu, C.-L. Gao, D. Qian, F.-C. Zhang, and J.-F. Jia, Artificial Topological Superconduc- tor by the Proximity Effect, Physical Review Letters112, 217001 (2014), publisher: American Physical Society

2014
[54]

A. M. Black-Schaffer and A. V. Balatsky, Proximity- induced unconventional superconductivity in topological insulators, Physical Review B 87, 220506 (2013)

2013
[55]

Tanaka and A

Y. Tanaka and A. A. Golubov, Theory of the Proximity Effect in Junctions with Unconventional Superconduc- tors, Physical Review Letters 98, 037003 (2007)

2007
[56]

W. L. McMillan, Tunneling Model of the Superconduct- ing Proximity Effect, Physical Review 175, 537 (1968), publisher: American Physical Society

1968
[57]

A. I. Buzdin, Proximity effects in superconductor- ferromagnet heterostructures, Rev. Mod. Phys. 77, 935 (2005)

2005
[58]

Kiendl, F

T. Kiendl, F. von Oppen, and P. W. Brouwer, Proximity- induced gap in nanowires with a thin superconducting shell, Phys. Rev. B 100, 035426 (2019)

2019
[59]

Bhattacharyya, V

B. Bhattacharyya, V. P. S. Awana, T. D. Senguttuvan, V. N. Ojha, and S. Husale, Proximity-induced super- current through topological insulator based nanowires 13 for quantum computation studies, Scientific Reports 8, 17237 (2018), number: 1 Publisher: Nature Publishing Group

2018
[60]

A. I. Buzdin, Proximity effects in superconductor- ferromagnet heterostructures, Reviews of Modern Physics 77, 935 (2005)

2005
[61]

Bardeen, L

J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957)

1957
[62]

Heckschen and B

M. Heckschen and B. Sothmann, Pair-amplitude dynam- ics in strongly coupled superconductor–quantum dot hy- brids, Phys. Rev. B 105, 045420 (2022)

2022
[64]

L¨ othman, C

T. L¨ othman, C. Triola, J. Cayao, and A. M. Black- Schaffer, Disorder-robust p-wave pairing with odd- frequency dependence in normal metal–conventional su- perconductor junctions, Phys. Rev. B 104, 094503 (2021)

2021
[65]

T. D. Stanescu and S. Das Sarma, Proximity-induced su- perconductivity generated by thin films: Effects of Fermi surface mismatch and disorder in the superconductor, Physical Review B 106, 085429 (2022)

2022
[66]

Alidoust, K

M. Alidoust, K. Halterman, and O. T. Valls, Zero-energy peak and triplet correlations in nanoscale superconduc- tor/ferromagnet/ferromagnet spin valves, Phys. Rev. B 92, 014508 (2015)

2015
[67]

S. D. Sarma, M. Freedman, and C. Nayak, Majorana zero modes and topological quantum computation, npj Quantum Information 1, 1 (2015)

2015
[68]

Samuelson, V

W. Samuelson, V. Svensson, and M. Leijnse, Minimal quantum dot based kitaev chain with only local super- conducting proximity effect, Phys. Rev. B 109, 035415 (2024)

2024
[69]

Lee and A

S.-C. Lee and A. Wacker, Nonequilibrium green’s func- tion theory for transport and gain properties of quantum cascade structures, Physical Review B 66, 245314 (2002)

2002
[70]

J.-S. Wang, J. Wang, and N. Zeng, Nonequilibrium green’s function approach to mesoscopic thermal trans- port, Physical Review B—Condensed Matter and Mate- rials Physics 74, 033408 (2006)

2006
[71]

Datta, The non-equilibrium green’s function (negf) formalism: An elementary introduction, in Digest

S. Datta, The non-equilibrium green’s function (negf) formalism: An elementary introduction, in Digest. In- ternational Electron Devices Meeting,(IEEE, 2002) pp. 703–706

2002
[72]

Zhang, M

Q. Zhang, M. Tang, L. Wang, K. Xia, and Y. Ke, Random nonequilibrium green’s function method for large-scale quantum transport simulation, Phys. Rev. B110, 155430 (2024)

2024
[73]

Ozaki, K

T. Ozaki, K. Nishio, and H. Kino, Efficient imple- mentation of the nonequilibrium green function method for electronic transport calculations, Physical Review B—Condensed Matter and Materials Physics 81, 035116 (2010)

2010
[74]

Sriram, S

P. Sriram, S. S. Kalantre, K. Gharavi, J. Baugh, and B. Muralidharan, Supercurrent interference in semicon- ductor nanowire josephson junctions, Phys. Rev. B 100, 155431 (2019)

2019
[76]

Andreev, Thermal conductivity of the intermediate state in superconductors, Sov

A. Andreev, Thermal conductivity of the intermediate state in superconductors, Sov. Phys. JETP 46, 1823 (1964)

1964
[77]

Setiawan and J

F. Setiawan and J. Hofmann, Analytic approach to trans- port in superconducting junctions with arbitrary carrier density, Physical Review Research 4, 10.1103/physrevre- search.4.043087 (2022)

2022 doi
[78]

Ghosal, M

A. Ghosal, M. Randeria, and N. Trivedi, Inhomoge- neous pairing in highly disordered s-wave superconduc- tors, Phys. Rev. B 65, 014501 (2001)

2001
[79]

Sakai and R

S. Sakai and R. Arita, Exotic pairing state in quasicrys- talline superconductors under a magnetic field, Phys. Rev. Res. 1, 022002 (2019)

2019
[80]

P. W. Anderson, Theory of dirty superconductors, Jour- nal of Physics and Chemistry of Solids 11, 26 (1959)

1959
[81]

Golizadeh-Mojarad and S

R. Golizadeh-Mojarad and S. Datta, Nonequilibrium green’s function based models for dephasing in quantum transport, Phys. Rev. B 75, 081301 (2007)

2007
[82]

Midha, K

S. Midha, K. Jana, and B. Muralidharan, Are symme- try protected topological phases immune to dephasing?– a topological electronics perspective, Journal of Physics D: Applied Physics 57, 135308 (2024)

2024
[83]

G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Tran- sition from metallic to tunneling regimes in supercon- ducting microconstrictions: Excess current, charge im- balance, and supercurrent conversion, Phys. Rev. B 25, 4515 (1982)

1982
[84]

Bouscher, R

S. Bouscher, R. Winik, and A. Hayat, Andreev re- flection enhancement in semiconductor-superconductor structures, Phys. Rev. B 97, 054512 (2018)

2018

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [63]

G. Rai, S. Haas, and A. Jagannathan, Superconducting proximity effect and order parameter fluctuations in dis- ordered and quasiperiodic systems, Physical Review B 102, 134211 (2020)

work page 2020

[2] [75]

Bouscher, D

S. Bouscher, D. Panna, K. Balasubramanian, S. Cohen, D. Ritter, and A. Hayat, Enhanced Cooper-Pair Injection into a Semiconductor Structure by Resonant Tunneling, Physical Review Letters 128, 127701 (2022), publisher: American Physical Society

work page 2022

[3] [1]

Kroger, C

H. Kroger, C. Hilbert, D. A. Gibson, U. Ghoshal, and L. N. Smith, Superconductor-semiconductor hybrid de- vices, circuits, and systems, Proceedings of the IEEE 77, 1287 (1989)

1989

[4] [2]

Benito and G

M. Benito and G. Burkard, Hybrid superconductor- semiconductor systems for quantum technology, Applied Physics Letters 116 (2020)

2020

[5] [3]

De Franceschi, L

S. De Franceschi, L. Kouwenhoven, C. Sch¨ onenberger, and W. Wernsdorfer, Hybrid superconductor–quantum dot devices, Nature nanotechnology 5, 703 (2010)

2010

[6] [4]

N. S. Kirsanov, Z. B. Tan, D. S. Golubev, P. J. Hakonen, and G. B. Lesovik, Heat switch and thermoelectric effects based on cooper-pair splitting and elastic cotunneling, Phys. Rev. B 99, 115127 (2019)

2019

[7] [5]

S´ anchez, P

R. S´ anchez, P. Burset, and A. L. Yeyati, Cooling by cooper pair splitting, Phys. Rev. B 98, 241414 (2018)

work page 2018

[8] [6]

Falci, D

G. Falci, D. Feinberg, and F. W. J. Hekking, Correlated tunneling into a superconductor in a multiprobe hybrid structure, Europhysics Letters 54, 255 (2001)

work page 2001