In 1928, Dirac proposed a wave equation to describe relativistic electrons1. Shortly afterwards, Klein solved a simple potential step problem for the Dirac equation and encountered an apparent paradox: the potential barrier becomes transparent when its height is larger than the electron energy. For massless particles, backscattering is completely forbidden in Klein tunnelling, leading to perfect transmission through any potential barrier2,3. The recent advent of condensed-matter systems with Dirac-like excitations, such as graphene and topological insulators, has opened up the possibility of observing Klein tunnelling experimentally4,5,6. In the surface states of topological insulators, fermions are bound by spin–momentum locking and are thus immune from backscattering, which is prohibited by time-reversal symmetry. Here we report the observation of perfect Andreev reflection in point-contact spectroscopy—a clear signature of Klein tunnelling and a manifestation of the underlying ‘relativistic’ physics of a proximity-induced superconducting state in a topological Kondo insulator. Our findings shed light on a previously overlooked aspect of topological superconductivity and can serve as the basis for a unique family of spintronic and superconducting devices, the interface transport phenomena of which are completely governed by their helical topological states.
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The data that support the findings of this study are available within the paper. Additional data are available from the corresponding authors upon reasonable request.
Dirac, P. A. M. The quantum theory of the electron. Proc. R. Soc. Lond. A 117, 610–624 (1928).
Klein, O. Die reflexion von Elektronen an einem Potentialsprung nach der relativistischen Dynamik von Dirac. Z. Phys. 53, 157–165 (1929).
Calogeracos, A. & Dombey, N. History and physics of the Klein paradox. Contemp. Phys. 40, 313–321 (1999).
Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Beenakker, C. W. J. Colloquium: Andreev reflection and Klein tunneling in graphene. Rev. Mod. Phys. 80, 1337–1354 (2008).
Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).
Stander, N., Huard, B. & Goldhaber-Gordon, D. Evidence for Klein tunneling in graphene p–n junctions. Phys. Rev. Lett. 102, 026807 (2009).
Young, A. F. & Kim, P. Quantum interference and Klein tunneling in graphene heterojunctions. Nat. Phys. 5, 222–226 (2009).
Blonder, G. E., Tinkham, M. & Klapwijk, T. M. Transition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversion. Phys. Rev. B 25, 4515–4532 (1982).
Daghero, D. & Gonnelli, R. S. Probing multiband superconductivity by point-contact spectroscopy. Supercond. Sci. Technol. 23, 043001 (2010).
Lee, W.-C. & Greene, L. H. Recent progress of probing correlated electron states by point contact spectroscopy. Rep. Prog. Phys. 79, 094502 (2016).
Adroguer, P. et al. Probing the helical edge states of a topological insulator by Cooper-pair injection. Phys. Rev. B 82, 081303 (2010).
Dzero, M., Sun, K., Coleman, P. & Galitski, V. Theory of topological Kondo insulators. Phys. Rev. B 85, 045130 (2012).
Syers, P., Kim, D., Fuhrer, M. S. & Paglione, J. Tuning bulk and surface conduction in the proposed topological Kondo insulator SmB6. Phys. Rev. Lett. 114, 096601 (2015).
Eo, Y. S., Sun, K., Kurdak, Ç., Kim, D.-J. & Fisk, Z. Inverted resistance measurements as a method for characterizing the bulk and surface conductivities of three-dimensional topological insulators. Phys. Rev. Appl. 9, 044006 (2018).
Zhang, X. et al. Hybridization, inter-ion correlation, and surface states in the Kondo insulator SmB6. Phys. Rev. X 3, 011011 (2013).
Jiang, J. et al. Observation of possible topological in-gap surface states in the Kondo insulator SmB6 by photoemission. Nat. Commun. 4, 3010 (2013).
Neupane, M. et al. Surface electronic structure of the topological Kondo-insulator candidate correlated electron system SmB6. Nat. Commun. 4, 2991 (2013).
Dai, W. et al. Proximity-effect-induced superconducting gap in topological surface states – a point contact spectroscopy study of NbSe2/Bi2Se3 superconductor-topological insulator heterostructures. Sci. Rep. 7, 7631 (2017).
Xu, S.-Y. et al. Momentum-space imaging of Cooper pairing in a half-Dirac-gas topological superconductor. Nat. Phys. 10, 943–950 (2014).
Lee, S. et al. Observation of the superconducting proximity effect in the surface state of SmB6 thin films. Phys. Rev. X 6, 031031 (2016).
Borisov, K., Chang, C.-Z., Moodera, J. S. & Stamenov, P. High Fermi-level spin polarization in the (Bi1−xSbx)2Te3 family of topological insulators: a point contact Andreev reflection study. Phys. Rev. B 94, 094415 (2016).
Shoman, T. et al. Topological proximity effect in a topological insulator hybrid. Nat. Commun. 6, 6547 (2015).
Hutasoit, J. A. & Stanescu, T. D. Induced spin texture in semiconductor/topological insulator heterostructures. Phys. Rev. B 84, 085103 (2011).
Szabó, P. et al. Superconducting energy gap of YB6 studied by point-contact spectroscopy. Physica C 460–462, 626–627 (2007).
Alexandrov, V., Coleman, P. & Erten, O. Kondo breakdown in topological Kondo insulators. Phys. Rev. Lett. 114, 177202 (2015).
Wang, M.-X. et al. The coexistence of superconductivity and topological order in the Bi2Se3 thin films. Science 336, 52–55 (2012).
Soulen Jr, R. J. et al. Measuring the spin polarization of a metal with a superconducting point contact. Science 282, 85–88 (1998).
Strijkers, G. J., Ji, Y., Yang, F. Y., Chien, C. L. & Byers, J. M. Andreev reflections at metal/superconductor point contacts: Measurement and analysis. Phys. Rev. B 63, 104510 (2001).
Tkachov, G. & Hankiewicz, E. M. Helical Andreev bound states and superconducting Klein tunneling in topological insulator Josephson junctions. Phys. Rev. B 88, 075401 (2013).
Janvier, C. et al. Coherent manipulation of Andreev states in superconducting atomic contacts. Science 349, 1199–1202 (2015).
Kornev, V. K., Kolotinskiy, N. V., Levochkina, A. Y. & Mukhanov, O. A. Critical current spread and thermal noise in Bi-SQUID cells and arrays. IEEE Trans. Appl. Supercond. 27, 1601005 (2017).
Zhang, C., Lu, H.-Z., Shen, S.-Q., Chen, Y. P. & Xiu, F. Towards the manipulation of topological states of matter: a perspective from electron transport. Sci. Bull. (Beijing) 63, 580–594 (2018).
Yong, J. et al. Robust topological surface state in Kondo insulator SmB6 thin films. Appl. Phys. Lett. 105, 222403 (2014).
Li, Y., Ma, Q., Huang, S. X. & Chien, C. L. Thin films of topological Kondo insulator candidate SmB6: strong spin–orbit torque without exclusive surface conduction. Sci. Adv. 4, eaap8294 (2018).
Ohring, M. Materials science of thin films 2nd edn (Academic, 2001).
Schneider, R., Geerk, J. & Rietschel, H. Electron tunnelling into a superconducting cluster compound: YB6. Europhys. Lett. 4, 845–849 (1987).
Sluchanko, N. et al. Lattice instability and enhancement of superconductivity in YB6. Phys. Rev. B 96, 144501 (2017).
Dynes, R. C., Narayanamurti, V. & Garno, J. P. Direct measurement of quasiparticle-lifetime broadening in a strong-coupled superconductor. Phys. Rev. Lett. 41, 1509–1512 (1978).
Mazin, I. I., Golubov, A. A. & Nadgorny, B. Probing spin polarization with Andreev reflection: a theoretical basis. J. Appl. Phys. 89, 7576–7578 (2001).
Wolgast, S. et al. Low-temperature surface conduction in the Kondo insulator SmB6. Phys. Rev. B 88, 180405 (2013).
Taskin, A. A. et al. Planar Hall effect from the surface of topological insulators. Nat. Commun. 8, 1340 (2017).
Wang, L.-X. et al. Zeeman effect on surface electron transport in topological insulator Bi2Se3 nanoribbons. Nanoscale 7, 16687–16694 (2015).
Chang, C.-Z., Wei, P. & Moodera, J. S. Breaking time reversal symmetry in topological insulators. MRS Bull. 39, 867–872 (2014).
Fu, Y.-S. et al. Observation of Zeeman effect in topological surface state with distinct material dependence. Nat. Commun. 7, 10829 (2016).
Erten, O., Ghaemi, P. & Coleman, P. Kondo breakdown and quantum oscillations in SmB6. Phys. Rev. Lett. 116, 046403 (2016).
Wolgast, S. et al. Reduction of the low-temperature bulk gap in samarium hexaboride under high magnetic fields. Phys. Rev. B 95, 245112 (2017).
Analytis, J. G. et al. Transport in the quantum limit by two-dimensional Dirac fermions in a topological insulator. Nat. Phys. 6, 960–964 (2010).
Thomas, S. et al. Weak antilocalization and linear magnetoresistance in the surface state of SmB6. Phys. Rev. B 94, 205114 (2016).
Biswas, S. et al. Robust local and nonlocal transport in the topological Kondo insulator SmB6 in the presence of a high magnetic field. Phys. Rev. B 92, 085103 (2015).
Gonnelli, R. S. et al. Temperature and junction-type dependency of Andreev reflection in MgB2. J. Phys. Chem. Solids 63, 2319–2323 (2002).
Li, Z.-Z. et al. Andreev reflection spectroscopy evidence for multiple gaps in MgB2. Phys. Rev. B 66, 064513 (2002).
Park, W. K., Greene, L. H., Sarrao, J. L. & Thompson, J. D. Andreev reflection at the normal-metal/heavy-fermion superconductor CeCoIn5 interface. Phys. Rev. B 72, 052509 (2005).
Zhang, X. et al. Evidence of a universal and isotropic 2Δ/k B T C ratio in 122-type iron pnictide superconductors over a wide doping range. Phys. Rev. B 82, 020515 (2010).
Sheet, G., Mukhopadhyay, S. & Raychaudhuri, P. Role of critical current on the point-contact Andreev reflection spectra between a normal metal and a superconductor. Phys. Rev. B 69, 134507 (2004).
We thank Y. S. Eo for discussions on the properties of SmB6, F. C. Wellstood for discussions on the possible applications of superconducting Klein tunnelling devices, and H. M. Iftekhar Jaim for assistance with X-ray measurements. This project was funded by ONR N00014-13-1-0635; ONR N00014-15-1-2222; AFOSR number FA9550-14-10332; NSF (DMR-1410665); and C-SPIN, one of six centers of STARnet, a Semiconductor Research Corporation (SRC) programme sponsored by MARCO and DARPA. We acknowledge support from the Maryland NanoCenter. J.P. acknowledges support from the Gordon and Betty Moore Foundation's EPiQS Initiative through grant number GBMF4419. V.G. was supported by DOE-BES (DESC0001911) and the Simons Foundation. This work was also supported in part by the Center for Spintronic Materials in Advanced infoRmation Technologies (SMART), one of the centers in nCORE, an SRC programme sponsored by NSF and NIST. The work at University of California, Irvine, was carried out using the electron microscopy facilities of the Irvine Materials Research Institute (IMRI) and was supported by the National Science Foundation through grant DMR-1506535 and by DOE-BES under grant DE-SC0014430. We acknowledge support from the National Institute of Standards and Technology Cooperative Agreement 70NANB17H301.
Nature thanks Ewelina Hankiewicz, David Goldhaber-Gordon and Jinfeng Jia for their contribution to the peer review of this work.
The authors declare no competing interests.
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Extended data figures and tables
a, High-resolution cross-sectional transmission electron microscopy image of a SmB6 thin film. The yellow squares correspond to the regions of the SAED measurements shown in b–d. b–d, SAED measurements of SmB6 (b), Si substrate (c) and SmB6/Si interface regions (d). ZA, zone axis. e, Epitaxial relationship between the SmB6 and the Si substrate. f, Aberration-corrected scanning transmission electron microscopy cross-sectional image of a SmB6 thin film. g, θ−2θ X-ray diffraction pattern of a SmB6 thin film on a Si (001) substrate.
a, Temperature-dependent resistance curves of YBx thin films with different stoichiometric B/Y ratios. b, Change in Tc as a function of stoichiometric B/Y ratio (x).
a, Cross-sectional schematic of a Au-SmB6 (20 nm)/YB6 (100 nm) structure. b, Optical microscopy image of the device. c, Normalized dI/dV spectra of the Au-SmB6/YB6 structure at different temperatures. The red lines are fits using the Dirac–BTK model. The normalized dI/dV curves at 1.8 K are plotted using the obtained values, whereas the other curves are vertically shifted for clarity.
a, Comparison of logR against 1/T plots of SmB6, and 20% and 50% Y-substituted SmB6 (that is, Sm0.8Y0.2B6 and Sm0.5Y0.5B6, respectively). The resistance values are normalized by their values at 300 K. The positive linear slopes at in the relatively high-temperature regions are roughly proportional to the activation energy. b, G − Gsurface (logarithmic scale, normalized by the conductance at 300 K) plotted against 1/T for pure SmB6 (black squares) and Sm0.8Y0.2B6 (red circles). The slopes of the linear fits (black and red lines) correspond to the activation energies (Ea) of pure SmB6 and Sm0.8Y0.2B6, and are 3.0 meV and 2.2 meV, respectively.
Point-contact spectra obtained at different positions (1, 2 and 3, which are roughly 1 mm apart from each other) on SmB6/YB6 heterostructures with 20-nm-thick SmB6 (left) and 30-nm-thick SmB6 (right). Conductance doubling is consistently observed at all positions in the dI/dV spectra of the SmB6/YB6 heterostructures.
a, Comparison of calculated dI/dV spectra with the standard BTK and the Dirac–BTK models for Z = 0.2, 0.4 and 0.8 (∆ = 1 meV). b, Comparison of the Dirac–BTK and the standard BTK fits to the experimental dI/dV spectrum of a PtIr-SmB6 (20 nm)/YB6 contact (Fig. 1c). The red curve is the theoretical conductance curve in the Dirac–BTK model and the standard BTK model with Z = 0. Both appear identical, as expected, for the same ∆ (here 0.77). The blue curve is the theoretical standard BTK curve with ∆ = 0.77 and Z = 0.39, this Z value is assessed from contacts to other heterostructures in this study that do not exhibit perfect Andreev reflection (that is, those with thin SmB6 (10 nm) and Y-substituted SmB6). The effect of nullifying Z by incorporation of a Dirac material in the Andreev reflection process is clearly seen.
a, dI/dV spectra of Au-SmB6/YB6 device under a magnetic field applied along the in-plane and out-of-plane directions. b, Normalized dI/dV at zero bias as a function of magnetic field. The inset shows superconducting order parameter (∆) as a function of magnetic field normalized by ∆ at 0 T (∆(0)). ∆ was estimated as the bias voltage point at which the maximum first derivative of each dI/dV spectrum occurs under different magnetic fields.
Comparison of the normalized dI/dV spectrum obtained from the PtIr-SmB6 (20 nm)/YB6 junction in this work (red line, experimental data) with the reported point-contact spectra obtained from Nb-Cu junctions28,29. The arrows indicate conductance dips near the ∆. Such dips are not present in our spectrum.
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Lee, S., Stanev, V., Zhang, X. et al. Perfect Andreev reflection due to the Klein paradox in a topological superconducting state. Nature 570, 344–348 (2019). https://doi.org/10.1038/s41586-019-1305-1
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