pith. sign in

arxiv: 2408.02008 · v4 · submitted 2024-08-04 · ❄️ cond-mat.supr-con

Engineering Helical Superconductors with Multiple Majorana Kramers Pairs via Higher-Order Rashba Spin-Orbit Coupling

Qi-Sheng Xu , Zi-Ming Wang , Chui-Zhen Chen , Lun-Hui Hu , Rui Wang , Dong-Hui Xu This is my paper

Pith reviewed 2026-05-23 22:20 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords helical topological superconductorMajorana Kramers pairshigher-order Rashba couplingmirror Chern numberf-wave pairingbilayer systemodd-parity superconductivity
0
0 comments X

The pith

Higher-order cubic Rashba coupling in a bilayer produces helical f-wave topological superconductors that host three Majorana Kramers pairs on a single Fermi surface.

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

The paper demonstrates that cubic Rashba spin-orbit coupling, rather than the usual linear form, allows time-reversal invariant topological superconductors to exceed the standard limit of one Majorana Kramers pair per boundary. In a bilayer with pure cubic coupling and odd-parity pairing, a single Fermi surface yields an f-wave state whose mirror Chern number equals three. When both linear and cubic terms are present, the same setup supports a hybrid p-plus-f state with mirror Chern number four even when the normal state has two Fermi surfaces. This construction removes the odd-Fermi-surface requirement that had constrained earlier helical topological superconductors.

Core claim

A bilayer system with a pure cubic RSOC and an intrinsic odd-parity pairing on a single FS yields a rare 2D helical f-wave TSC characterized by a large mirror Chern number of N_M=3 and hosts three Kramers pairs of Majorana edge modes. The interplay of linear and cubic RSOCs can generate a helical hybrid p+f-wave TSC with an even larger MCN of N_M=4 from a normal state with two FSs.

What carries the argument

higher-order cubic Rashba spin-orbit coupling combined with intrinsic odd-parity pairing in a bilayer geometry

If this is right

  • A pure cubic Rashba term plus odd-parity pairing produces a helical f-wave state with mirror Chern number 3 and three Majorana Kramers pairs from one Fermi surface.
  • Mixing linear and cubic Rashba terms produces a hybrid p+f-wave state with mirror Chern number 4 from a normal state that has two Fermi surfaces.
  • Higher-order Rashba coupling circumvents the conventional requirement of an odd number of Fermi surfaces for helical topological superconductors.
  • The construction applies to tunable bilayer platforms such as oxide heterostructures.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same higher-order mechanism could be used in other layered materials to increase the number of protected Majorana channels without changing the pairing symmetry.
  • Gate-tunable oxide interfaces offer a direct experimental route to test whether the mirror Chern number scales with the strength of the cubic term.
  • Extending the bilayer construction to trilayers or other stackings might produce states with still larger mirror Chern numbers.

Load-bearing premise

The pairing interaction remains intrinsic and odd-parity with strength and symmetry independent of the Rashba terms, and no other spin-orbit or pairing channels dominate the low-energy physics.

What would settle it

Spectroscopic or transport measurements on a bilayer heterostructure tuned to dominant cubic Rashba coupling that either detect or fail to detect exactly three pairs of counter-propagating Majorana edge modes at a single boundary.

Figures

Figures reproduced from arXiv: 2408.02008 by Chui-Zhen Chen, Dong-Hui Xu, Lun-Hui Hu, Qi-Sheng Xu, Rui Wang, Zi-Ming Wang.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) and (b) represent schematic illustrations of the spin texture [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) represents an inversion symmetric cubic Rashba bilayer, [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Spectral function of a semi-infinite geometry with [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

The momentum dependence of Rashba spin-orbit coupling (RSOC) is a key ingredient for engineering topological superconductors (TSCs), yet research has overwhelmingly focused on its linear-in-momentum form. This focus has restricted time-reversal invariant TSCs to helical $p$-wave states, which are characterized by a $\mathbb{Z}_2$ topological invariant that permits at most a single Majorana Kramers pair at a given boundary. Their existence has also been tied to the stringent criterion of an odd number of Fermi surfaces (FSs). In this work, we establish higher-order RSOC as a powerful design principle to go beyond the $\mathbb{Z}_2$ classification and the odd-FS criterion. We demonstrate that a bilayer system with a pure cubic RSOC and an intrinsic odd-parity pairing on a single FS yields a rare 2D helical $f$-wave TSC. This state is characterized by a large mirror Chern number (MCN) of ${\cal N}_{\text{M}}=3$ and hosts three Kramers pairs of Majorana edge modes. Remarkably, the interplay of linear and cubic RSOCs in this bilayer can generate a helical hybrid $p+f$-wave TSC with an even larger MCN of ${\cal N}_{\text{M}}=4$ from a normal state with two FSs, thereby circumventing the conventional odd-FS criterion. Our work establishes higher-order RSOC as a "topology multiplier" for realizing TSCs with multiple Majorana Kramers channels, fundamentally reshapes the criteria for helical TSCs, and holds immediate relevance for tunable platforms like oxide heterostructures.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes using higher-order (cubic) Rashba spin-orbit coupling (RSOC) in a bilayer system with intrinsic odd-parity pairing to realize 2D helical topological superconductors beyond the conventional Z_2 classification and odd-Fermi-surface criterion. Specifically, a pure cubic RSOC on a single Fermi surface is claimed to yield a helical f-wave TSC with mirror Chern number N_M=3 hosting three Majorana Kramers pairs, while the interplay of linear and cubic RSOC on two Fermi surfaces produces a hybrid p+f-wave TSC with N_M=4.

Significance. If the results hold, the work is significant because it identifies higher-order RSOC as a 'topology multiplier' that enables helical TSCs with multiple Majorana Kramers channels (N_M up to 4), a feature that is rare under standard linear RSOC and Z_2 invariants. The approach has immediate relevance for tunable platforms such as oxide heterostructures and correctly distinguishes the mirror Chern number from the Z_2 invariant to circumvent the odd-FS constraint.

major comments (1)
  1. Abstract: the abstract states the topological invariants (N_M=3 and N_M=4) and edge-mode counts but supplies no derivation steps, gap equations, or numerical checks; soundness cannot be verified beyond the claim level from the given text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review and for noting the potential significance of the results. We respond to the major comment below.

read point-by-point responses

  1. Referee: [—] Abstract: the abstract states the topological invariants (N_M=3 and N_M=4) and edge-mode counts but supplies no derivation steps, gap equations, or numerical checks; soundness cannot be verified beyond the claim level from the given text.

    Authors: The abstract is a concise summary and does not contain derivation steps, gap equations, or numerical checks, as is standard. The full manuscript provides these: the bilayer Hamiltonian with cubic RSOC, the self-consistent gap equations for intrinsic odd-parity pairing, analytical evaluation of the mirror Chern numbers (via mirror-graded Pfaffian and Wilson-loop methods), and numerical diagonalization of the edge spectrum confirming three and four Majorana Kramers pairs, respectively. Soundness is verifiable from the complete text. revision: no

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper proposes a bilayer model Hamiltonian with explicit linear and cubic Rashba terms plus an intrinsic odd-parity pairing, then computes mirror Chern numbers and edge-mode counts by direct diagonalization of the resulting BdG Hamiltonian. No derivation step reduces by construction to a fitted parameter, self-defined quantity, or load-bearing self-citation; the topological invariants are obtained from the stated Hamiltonian without circular renaming or ansatz smuggling. The construction is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The construction rests on standard assumptions of BCS-type odd-parity pairing and momentum-dependent Rashba terms whose coefficients are free parameters; no new particles or forces are postulated.

free parameters (3)
  • cubic RSOC strength
    Tuned to open the desired topological gap; value not numerically specified in abstract.
  • linear RSOC strength
    Tuned in the hybrid case to achieve MCN=4.
  • odd-parity pairing amplitude
    Assumed nonzero and dominant; magnitude sets the gap scale.
axioms (2)
  • domain assumption The pairing interaction is purely odd-parity and intrinsic to the bilayer.
    Invoked to realize the f-wave and p+f states on the stated Fermi-surface count.
  • standard math Mirror symmetry remains intact so that the mirror Chern number is well-defined.
    Required for the MCN classification used throughout.

pith-pipeline@v0.9.0 · 5849 in / 1485 out tokens · 20985 ms · 2026-05-23T22:20:08.324367+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [1]

    To examine the Majorana edge modes, the continuous model is transformed into a tight-binding model on a square lattice

    If the chemical potential lies within the hybridization gap, the mirror Chern number takes the value nM = 3 when the above topological condition is met. To examine the Majorana edge modes, the continuous model is transformed into a tight-binding model on a square lattice. Figure 3(a) illustrates the spectral function for a semi-infinite geometry with∆3 pa...

    work page

  2. [2]

    Y. A. Bychkov and ´E. I. Rashba, Properties of a 2d electron gas with lifted spectral degeneracy, JETP lett39, 78 (1984)

    work page 1984

  3. [3]

    Manchon, H

    A. Manchon, H. C. Koo, J. Nitta, S. M. Frolov, and R. A. Duine, New perspectives forRashba spin–orbit coupling, Nature Mater. 14, 871 (2015)

    work page 2015

  4. [4]

    Bihlmayer, P

    G. Bihlmayer, P. No ¨el, D. V. Vyalikh, E. V. Chulkov, and A. Manchon, Rashba-like physics in condensed matter, Nat. Rev. Phys. 4, 642 (2022)

    work page 2022

  5. [5]

    Sinova, D

    J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDonald, Universal intrinsic spin Hall effect, Phys. Rev. Lett.92, 126603 (2004)

    work page 2004

  6. [6]

    M. Z. Hasan and C. L. Kane, Colloquium: Topological insula- tors, Rev. Mod. Phys.82, 3045 (2010)

    work page 2010

  7. [7]

    Qi and S.-C

    X.-L. Qi and S.-C. Zhang, Topological insulators and supercon- ductors, Rev. Mod. Phys.83, 1057 (2011)

    work page 2011

  8. [8]

    L. P. Gor’kov and E. I. Rashba, Superconducting 2D system with lifted spin degeneracy: Mixed singlet-triplet state, Phys. Rev. Lett. 87, 037004 (2001)

    work page 2001

  9. [9]

    S. K. Yip, Two-dimensional superconductivity with strong spin- orbit interaction, Phys. Rev. B65, 144508 (2002)

    work page 2002

  10. [10]

    P. A. Frigeri, D. F. Agterberg, A. Koga, and M. Sigrist, Su- perconductivity without inversion symmetry: MnSi versus CePt3Si, Phys. Rev. Lett.92, 097001 (2004)

    work page 2004

  11. [11]

    Zhang, Q

    X. Zhang, Q. Liu, J.-W. Luo, A. J. Freeman, and A. Zunger, Hidden spin polarization in inversion-symmetric bulk crystals, Nat. Phys. 10, 387 (2014)

    work page 2014

  12. [12]

    Gotlieb, C.-Y

    K. Gotlieb, C.-Y. Lin, M. Serbyn, W. Zhang, C. L. Small- wood, C. Jozwiak, H. Eisaki, Z. Hussain, A. Vishwanath, and A. Lanzara, Revealing hidden spin-momentum locking in a high-temperature cuprate superconductor, Science 362, 1271 (2018)

    work page 2018

  13. [13]

    S. Khim, J. Landaeta, J. Banda, N. Bannor, M. Brando, P. Bry- don, D. Hafner, R. K¨uchler, R. Cardoso-Gil, U. Stockert,et al., Field-induced transition within the superconducting state of CeRh2As2, Science 373, 1012 (2021)

    work page 2021

  14. [14]

    M. H. Fischer, M. Sigrist, D. F. Agterberg, and Y. Yanase, Su- perconductivity and local inversion-symmetry breaking, Annual Review of Condensed Matter Physics14, 153 (2023)

    work page 2023

  15. [15]

    Fu and C

    L. Fu and C. L. Kane, Superconducting proximity effect and ma- jorana fermions at the surface of a topological insulator, Phys. Rev. Lett.100, 096407 (2008)

    work page 2008

  16. [16]

    Fujimoto, Topological order and non-abelian statistics in noncentrosymmetric s-wave superconductors, Phys

    S. Fujimoto, Topological order and non-abelian statistics in noncentrosymmetric s-wave superconductors, Phys. Rev. B77, 220501 (2008)

    work page 2008

  17. [17]

    M. Sato, Y. Takahashi, and S. Fujimoto, Non-Abelian topolog- ical order in s-wave superfluids of ultracold Fermionic atoms, Phys. Rev. Lett.103, 020401 (2009)

    work page 2009

  18. [18]

    J. D. Sau, R. M. Lutchyn, S. Tewari, and S. Das Sarma, Generic new platform for topological quantum computation using semi- conductor heterostructures, Phys. Rev. Lett.104, 040502 (2010)

    work page 2010

  19. [19]

    Alicea, Majorana fermions in a tunable semiconductor device, Phys

    J. Alicea, Majorana fermions in a tunable semiconductor device, Phys. Rev. B81, 125318 (2010)

    work page 2010

  20. [20]

    Liu and B

    C.-X. Liu and B. Trauzettel, Helical Dirac-Majorana inter- ferometer in a superconductor/topological insulator sandwich structure, Phys. Rev. B83, 220510 (2011)

    work page 2011

  21. [21]

    Nakosai, Y

    S. Nakosai, Y. Tanaka, and N. Nagaosa, Topological supercon- ductivity in bilayerRashba system, Phys. Rev. Lett.108, 147003 (2012)

    work page 2012

  22. [22]

    Zhang, C

    F. Zhang, C. L. Kane, and E. J. Mele, Time-reversal-invariant topological superconductivity and Majorana Kramers pairs, Phys. Rev. Lett.111, 056402 (2013)

    work page 2013

  23. [23]

    Nakamura, T

    H. Nakamura, T. Koga, and T. Kimura, Experimental evidence of cubic Rashba effect in an inversion-symmetric oxide, Phys. Rev. Lett.108, 206601 (2012)

    work page 2012

  24. [24]

    Moriya, K

    R. Moriya, K. Sawano, Y. Hoshi, S. Masubuchi, Y. Shiraki, A. Wild, C. Neumann, G. Abstreiter, D. Bougeard, T. Koga, and T. Machida, Cubic Rashba spin-orbit interaction of a two- dimensional hole gas in a strained- Ge/SiGe quantum well, Phys. Rev. Lett.113, 086601 (2014)

    work page 2014

  25. [25]

    Y. Kim, R. M. Lutchyn, and C. Nayak, Origin and trans- port signatures of spin-orbit interactions in one- and two- dimensional SrTiO3-based heterostructures, Phys. Rev. B 87, 245121 (2013)

    work page 2013

  26. [26]

    P. Kim, K. T. Kang, G. Go, and J. H. Han, Nature of orbital and spin Rashba coupling in the surface bands of SrTiO3 and KTaO3, Phys. Rev. B90, 205423 (2014)

    work page 2014

  27. [27]

    W. Lin, L. Li, F. Do ˘gan, C. Li, H. Rotella, X. Yu, B. Zhang, Y. Li, W. S. Lew, S. Wang, et al., Interface-based tuning of Rashba spin-orbit interaction in asymmetric oxide heterostruc- tures with 3 d electrons, Nat. Commun.10, 3052 (2019)

    work page 2019

  28. [28]

    D. Y. Usachov, I. A. Nechaev, G. Poelchen, M. G ¨uttler, E. E. Krasovskii, S. Schulz, A. Generalov, K. Kliemt, A. Kraiker, C. Krellner, K. Kummer, S. Danzenb¨acher, C. Laubschat, A. P. Weber, J. S´anchez-Barriga, E. V. Chulkov, A. F. Santander-Syro, T. Imai, K. Miyamoto, T. Okuda, and D. V. Vyalikh, Cubic Rashba effect in the surface spin structure of rar...

    work page 2020

  29. [29]

    H. J. Zhao, H. Nakamura, R. Arras, C. Paillard, P. Chen, J. Gosteau, X. Li, Y. Yang, and L. Bellaiche, Purely cubic spin splittings with persistent spin textures, Phys. Rev. Lett. 125, 216405 (2020)

    work page 2020

  30. [30]

    Schliemann and D

    J. Schliemann and D. Loss, Spin-hall transport of heavy holes in III −V semiconductor quantum wells, Phys. Rev. B71, 085308 (2005)

    work page 2005

  31. [31]

    Bleibaum and S

    O. Bleibaum and S. Wachsmuth, Spin hall effect in semicon- ductor heterostructures with cubic rashba spin-orbit interaction, Phys. Rev. B74, 195330 (2006)

    work page 2006

  32. [32]

    X.-T. Peng, F. Lin, L. Chen, L. Li, D.-H. Xu, and J.-H. Sun, Tun- able correlation effects of magnetic impurities by cubicRashba spin-orbit coupling, Phys. Rev. B107, 165148 (2023)

    work page 2023

  33. [33]

    L. Mao, J. Shi, Q. Niu, and C. Zhang, Superconducting phase with a chiralf-wave pairing symmetry andMajorana Fermions 6 induced in a hole-doped semiconductor, Phys. Rev. Lett. 106, 157003 (2011)

    work page 2011

  34. [34]

    Alidoust, C

    M. Alidoust, C. Shen, and I. ˇZuti´c, Cubic spin-orbit coupling and anomalous Josephson effect in planar junctions, Phys. Rev. B 103, L060503 (2021)

    work page 2021

  35. [35]

    Luethi, K

    M. Luethi, K. Laubscher, S. Bosco, D. Loss, and J. Klinovaja, Planar Josephson junctions in germanium:Effect of cubic spin- orbit interaction, Phys. Rev. B107, 035435 (2023)

    work page 2023

  36. [36]

    Fu and E

    L. Fu and E. Berg, Odd-parity topological superconductors: Theory and application to CuxBi2Se3, Phys. Rev. Lett. 105, 097001 (2010)

    work page 2010

  37. [37]

    Hashimoto, S

    T. Hashimoto, S. Kobayashi, Y. Tanaka, and M. Sato, Supercon- ductivity in doped Dirac semimetals, Phys. Rev. B 94, 014510 (2016)

    work page 2016

  38. [38]

    J. C. Y. Teo, L. Fu, and C. L. Kane, Surface states and topolog- ical invariants in three-dimensional topological insulators: Ap- plication to Bi1−xSbx, Phys. Rev. B78, 045426 (2008)

    work page 2008

  39. [39]

    Zhang, C

    F. Zhang, C. L. Kane, and E. J. Mele, Topological mirror super- conductivity, Phys. Rev. Lett.111, 056403 (2013)

    work page 2013

  40. [40]

    Y. Ueno, A. Yamakage, Y. Tanaka, and M. Sato, Symmetry- protected Majorana Fermions in topological crystalline super- conductors: Theory and application to Sr2RuO4, Phys. Rev. Lett. 111, 087002 (2013)

    work page 2013

  41. [41]

    C.-K. Chiu, H. Yao, and S. Ryu, Classification of topological in- sulators and superconductors in the presence of reflection sym- metry, Phys. Rev. B88, 075142 (2013)

    work page 2013

  42. [42]

    Tsutsumi, M

    Y. Tsutsumi, M. Ishikawa, T. Kawakami, T. Mizushima, M. Sato, M. Ichioka, and K. Machida, U Pt3 as a topological crystalline superconductor, journal of the physical society of japan 82, 113707 (2013)

    work page 2013

  43. [43]

    Shiozaki and M

    K. Shiozaki and M. Sato, Topology of crystalline insulators and superconductors, Phys. Rev. B90, 165114 (2014)

    work page 2014

  44. [44]

    Ando and L

    Y. Ando and L. Fu, Topological crystalline insulators and topo- logical superconductors: From concepts to materials, Annu. Rev. Condens. Matter Phys.6, 361 (2015)

    work page 2015

  45. [45]

    Yoshida, M

    T. Yoshida, M. Sigrist, and Y. Yanase, Topological crystalline superconductivity in locally noncentrosymmetric multilayer su- perconductors, Phys. Rev. Lett.115, 027001 (2015)

    work page 2015

  46. [46]

    Fu, Odd-parity topological superconductor with nematic or- der: Application to CuxBi2Se3, Phys

    L. Fu, Odd-parity topological superconductor with nematic or- der: Application to CuxBi2Se3, Phys. Rev. B 90, 100509 (2014)

    work page 2014

  47. [47]

    Matano, M

    K. Matano, M. Kriener, K. Segawa, Y. Ando, and G.-q. Zheng, Spin-rotation symmetry breaking in the superconducting state of CuxBi2Se3, Nature Physics 12, 852 (2016)

    work page 2016

  48. [48]

    Yonezawa, K

    S. Yonezawa, K. Tajiri, S. Nakata, Y. Nagai, Z. Wang, K. Segawa, Y. Ando, and Y. Maeno, Thermodynamic evidence for nematic superconductivity in CuxBi2Se3, Nature Physics 13, 123 (2017)

    work page 2017

  49. [49]

    Asaba, B

    T. Asaba, B. J. Lawson, C. Tinsman, L. Chen, P. Corbae, G. Li, Y. Qiu, Y. S. Hor, L. Fu, and L. Li, Rotational symmetry break- ing in a trigonal superconductor Nb-doped Bi2Se3, Phys. Rev. X 7, 011009 (2017)

    work page 2017

  50. [50]

    Y. Pan, A. Nikitin, G. Araizi, Y. Huang, Y. Matsushita, T. Naka, and A. De Visser, Rotational symmetry breaking in the topologi- cal superconductorSrxBi2Se3 probed by upper-critical field ex- periments, Scientific reports 6, 1 (2016)

    work page 2016

  51. [51]

    G. Du, Y. Li, J. Schneeloch, R. Zhong, G. Gu, H. Yang, H. Lin, and H.-H. Wen, Superconductivity with two-fold symmetry in topological superconductor SrxBi2Se3, Science China Physics, Mechanics & Astronomy 60, 1 (2017)

    work page 2017

  52. [52]

    Tao, Y.-J

    R. Tao, Y.-J. Yan, X. Liu, Z.-W. Wang, Y. Ando, Q.-H. Wang, T. Zhang, and D.-L. Feng, Direct visualization of the nematic su- perconductivity in CuxBi2Se3, Phys. Rev. X8, 041024 (2018)

    work page 2018

  53. [53]

    A. D. Caviglia, M. Gabay, S. Gariglio, N. Reyren, C. Cancel- lieri, and J.-M. Triscone, TunableRashba spin-orbit interaction at oxide interfaces, Phys. Rev. Lett.104, 126803 (2010)

    work page 2010

  54. [54]

    Reyren, S

    N. Reyren, S. Thiel, A. Caviglia, L. F. Kourkoutis, G. Hammerl, C. Richter, C. W. Schneider, T. Kopp, A.-S. Ruetschi, D. Jac- card, et al., Superconducting interfaces between insulating ox- ides, Science 317, 1196 (2007)

    work page 2007