Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions

Journal name:
Nature Physics
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Published online


Majorana fermions are the only fermionic particles that are expected to be their own antiparticles. Although elementary particles of the Majorana type have not been identified yet, quasi-particles with Majorana-like properties, born from interacting electrons in the solid, have been predicted to exist. Here, we present thorough experimental studies, backed by numerical simulations, of a system composed of an aluminium superconductor in proximity to an indium arsenide nanowire, with the latter possessing strong spin–orbit coupling and Zeeman splitting. An induced one-dimensional topological superconductor, supporting Majorana fermions at both ends, is expected to form. We concentrate on the characteristics of a distinct zero-bias conductance peak and its splitting in energy—both appearing only with a small magnetic field applied along the wire. The zero-bias conductance peak was found to be robustly tied to the Fermi energy over a wide range of system parameters. Although not providing definite proof of a Majorana state, the presented data and the simulations support its existence.

At a glance


  1. Energy dispersion of InAs nanowire excitations (Bogoliubov-de Gennes spectrum), in proximity to an Al superconductor.
    Figure 1: Energy dispersion of InAs nanowire excitations (Bogoliubov–de Gennes spectrum), in proximity to an Al superconductor.

    Heavy (light) lines show electron-like (hole-like) bands. Opposite spin directions are denoted in blue and magenta for the spin–orbit effective field direction; red and cyan for the spins in the perpendicular direction; relative mixture denotes intermediate spin directions. a, Split electronic spin bands due to spin–orbit coupling. The spin–orbit energy is denoted as Δso; the chemical potential is μ, with respect to spin bands crossing at p=0. b, With applied magnetic field , leading to a Zeeman gap EZ=1/2gμBB at p=0. c, Bringing a superconductor into close proximity opens a superconducting gap at the crossing of particle and hole curves (light lines). d, The same as in c but for a larger EZ with the gap at pF dominant. e, Field rotated to a direction of 30° with respect to Bso, leading to shifts of the original spin–orbit bands. f, The evolution of the energy gap at p=0 (dotted blue), at pF (dotted yellow), and the overall energy gap (dashed black) with Zeeman energy, EZ, for μ=0.

  2. A suspended Al-InAs nanowire on gold pedestals above p-type silicon.
    Figure 2: A suspended Al–InAs nanowire on gold pedestals above p-type silicon.

    The p-type silicon serves as a global gate (GG) coated with 150nm SiO2. a, A type I device with an additional gold pedestal at the centre, a gold normal contact at each end of the wire and an aluminium superconducting contact at the centre. Two narrow local gates (RG and LG), 50nm wide and 25nm high, displaced from the superconducting contact by 80nm, affect both the barrier height near the Al edge and the chemical potential in the wire. b, A type II device without the centre pedestal, thus allowing control of the chemical potential under the Al contact. c, Scanning electron micrograph of a type II device (scale bar, 300nm), with a 5 voltage source V SD and a cold-grounded drain. Inset: high-resolution TEM image (viewed from the left fence1120right fence zone axis) of a stacking-fault-free, wurtzite-structure, InAs nanowire, grown on (011) InAs in the left fence111right fence direction. The TEM image (scale bar, 10nm) is courtesy of R. Popovitz–Biro. A more detailed image can be found in the Supplementary Information. d, An estimated potential profile along the wire.

  3. Evolution of the ZBP with chemical potential and magnetic field, for the VRG range 1.17-1.24[thinsp]V at VGG[thinsp]=[thinsp]-18.3[thinsp]V for a type II device (D4).
    Figure 3: Evolution of the ZBP with chemical potential and magnetic field, for the VRG range 1.17–1.24V at VGG=−18.3V for a type II device (D4).

    The cuts are taken at V RG=1.183, 1.205 and 1.228V. a, The main features at B=0are the Al superconducting gap ΔAl~±150μeV, and the induced gap Δind~±45μeV. At B=30mT the gap closes at V RG=1.205V and turns into a relatively wide, barely split, ZBP; to split at higher and lower gate voltages. At B=50mT, a sharper ZBP persists in a wide range of gate voltage, with marked splitting. At B=70mT, the ZBP peak splits in a wide range of gate voltage. b, Colour plot of the ZBP with equal height contours lines, from 0.106e2/h to 0.197e2/h. The arrows indicate the transition from a single ZBP to split peaks. c, Simulated behaviour using analytical expressions for the wire spectrum. Contours lines of constant-size Majorana wavefunction, ξ=planckvF/Eg~1.5L, 3L and 10L are blue, red and black, respectively. The simulation of ξ<3L (red line contour) is similar to the contours of the data b. Although the range of chemical potential for which the wire is topological increases as a function of B, at higher B the gap decreases, increasing the extent of the Majoranas. The sharp termination of each contour at some maximal value of B is due to the weak dependence of Δind on μ.

  4. Low-bias conductance as a function of applied magnetic field parallel to the wire axis (type II device, D4).
    Figure 4: Low-bias conductance as a function of applied magnetic field parallel to the wire axis (type II device, D4).

    a, Colour plot. b,c, Cuts in increments ΔB~2mT (each shifted by ~0.02e2/h). At B=0, there is a typical conductance dip at V SD=0, flanked by two shoulders at ±eV SD=Δind~45μV, and outer peaks at . At B~30mT, the two shoulders merge into a single ZBP, and remain robust until ~ 70mT. Beyond ~ 70mT the ZBP splits and the conductance features are weaker. c, Zoom in of cuts between ~ 65–120mT. The split peaks remain nearly parallel with increasing B. d, A simulation of the conductance with a topological segment length of 160nm and spin–orbit energy of Δso=70μeV. A second channel was added in parallel, which ends with a ΔAl superconductor, to account for the quasiparticles tunnelling into the aluminium at high energy (the contribution of this channel was ~ 75%, and that of the main channel was ~ 25%; see Supplementary Information). The measured dependence of ΔAl and Δind on the magnetic field was used. The data were convolved with a Fermi–Dirac kernel to simulate an electron temperature of 30mK.

  5. Low-bias conductance as a function of applied magnetic field parallel to the wire axis (type II device, D4), at a higher chemical potential.
    Figure 5: Low-bias conductance as a function of applied magnetic field parallel to the wire axis (type II device, D4), at a higher chemical potential.

    a, 2D colour plot. b, Cuts with bias and magnetic field for V RG=1.224V. The two shoulder peaks come closer with B but remain split and parallel to each other over a wide range of magnetic field (60–85mT). They disappear when the Al superconductivity is quenched. c, Zoom in of the cuts in the interval 65–120mT, allowing clear observation of the splitting.

  6. Temperature and magnetic field orientation dependence of the ZBP of device D3 at B[thinsp]=[thinsp]70[thinsp]mT.
    Figure 6: Temperature and magnetic field orientation dependence of the ZBP of device D3 at B=70mT.

    a, Cuts at 8mK intervals shifted by 0.05e2/h each. The peak vanishes before T~100mK. b, Summary of the data. The estimated electron temperature is ~ 30mK (dilution refrigerator temperature is 10mK), leading to the observed peak width and lower conductance. c, Energy dispersion for the external field perpendicular to the spin–orbit effective field and parallel to it. d, Dependence of the ZBP on rotation angle, from 0° to 75°, where the peak practically vanishes, and back to 0°.


  1. Dirac, P. A. M. Quantum mechanics of many-electron systems. Proc. R. Soc. Lond. Ser. A 123, 714733 (1929).
  2. Majorana, E. Teoria simmetrica dell elettronee del positrone. Il Nuovo Cimento (1924-1942) 14, 171184 (1937).
  3. Wilczek, F. Majorana returns. Nature Phys. 5, 614618 (2009).
  4. Kitaev, A. Y. Unpaired Majorana fermions in quantum wires. Phys.-Usp. 44, 131136 (2001).
  5. Kopnin, N. & Salomaa, M. Mutual friction in superfluid 3He: Effects of bound states in the vortex core. Phys. Rev. B 44, 96679677 (1991).
  6. Alicea, J. New directions in the pursuit of Majorana fermions in solid state systems. Rep. Prog. Phys. 75, 076501 (2012).
  7. Beenakker, C. Search for Majorana fermions in superconductors. Preprint at (2011).
  8. Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 230 (2003).
  9. Halperin, B. I. et al. Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires. Phys. Rev. B 85, 144501 (2012).
  10. Sau, J. D., Clarke, D. J. & Tewari, S. Controlling non-Abelian statistics of Majorana fermions in semiconductor nanowires. Phys. Rev. B 84, 094505 (2011).
  11. Read, N. & Green, D. Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect. Phys. Rev. B 61, 10267 (2000).
  12. Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2111 (2006).
  13. Alicea, J., Oreg, Y., Refael, G., Oppen, F. V. & Fisher, M. P. A. Non-Abelian statistics and topological quantum information processing in 1D wire networks. Nature Phys. 7, 412417 (2011).
  14. Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 96407 (2008).
  15. Sau, J. D., Lutchyn, R. M., Tewari, S. & Sarma, S. D. Generic new platform for topological quantum computation using semiconductor heterostructures. Phys. Rev. Lett. 104, 40502 (2010).
  16. Sau, J., Tewari, S., Lutchyn, R. & Stanescu, T. Non-Abelian quantum order in spin-orbit-coupled semiconductors: Search for topological Majorana particles in solid-state systems. Phys. Rev. B 82, 159 (2010).
  17. Alicea, J. Majorana fermions in a tunable semiconductor device. Phys. Rev. B 81, 125318 (2010).
  18. Lutchyn, R. M., Sau, J. D. & Sarma, S. D. Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures. Phys. Rev. Lett. 105, 77001 (2010).
  19. Oreg, Y., Refael, G. & Oppen, F. V. Helical liquids and Majorana bound states in quantum wires. Phys. Rev. Lett. 105, 177002 (2010).
  20. Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices. Science 336, 10031007 (2012).
  21. Deng, M. T. et al. Observation of majorana fermions in a Nb–InSb nanowire-Nb hybrid quantum device. Preprint at (2012).
  22. Potter, A. C. & Lee, P. A. Multichannel generalization of Kitaev’s Majorana end states and a practical route to realize them in thin films. Phys. Rev. Lett. 105, 227003 (2010).
  23. Pientka, F., Kells, G., Romito, A., Brouwer, P. W. & von Oppen, F. Enhanced zero-bias Majorana peak in disordered multi-subband quantum wires. Preprint at (2012).
  24. Rainis, D., Trifunovic, L., Klinovajo, J. & Loss, D. Realistic transport modeling for a superconducting nanowire with Majorana fermions. Preprint at (2012).
  25. Bychkov, Y. A. & Rashba, E. Oscillatory effects and the magnetic susceptibility of carriers in inversion layers. J. Phys. C 17, 60396045 (1984).
  26. Wimmer, M., Akhmerov, A., Dahlhaus, J. & Beenakker, C. Quantum point contact as a probe of a topological superconductor. New J. Phys. 13, 053016 (2011).
  27. Bolech, C. & Demler, E. Observing majorana bound states in p-wave superconductors using noise measurements in tunneling experiments. Phys. Rev. Lett. 98, 237002 (2007).
  28. Shtrikman, H., Popovitz-Biro, R., Kretinin, A. V. & Kacman, P. GaAs and InAs nanowires for ballistic transport. IEEE J. Selected Top. Quant. Electron. 17, 922934 (2011).
  29. Das, A. et al. Entangling electrons by splitting Cooper pairs: Two-particle conductance resonance and time coincidence measurements. Preprint at (2012).
  30. Blonder, G., Tinkham, M. & Klapwijk, T. Transition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversion. Phys. Rev. B 25, 45154532 (1982).
  31. Lin, C. H., Sau, J. D. & Sarma, S. D. Zero bias conductance peak in Majorana wires made of semiconductor-superconductor hybrid structures. Preprint at (2012).
  32. Qu, C., Zhang, Y., Mao, L. & Zhang, C. Signature of majorana fermions in charge transport in semiconductor nanowires. Preprint at (2011).
  33. Stanescu, T. D., Lutchyn, R. M. & Sarma, S. D. Majorana fermions in semiconductor nanowires. Phys. Rev. B 84, 144522 (2011).
  34. Prada, E., San-Jose, P. & Aguado, R. Transport spectroscopy of NS nanowire junctions with Majorana fermions. Preprint at (2012).
  35. Andreev, A. Thermal conductivity of superconductors intermediate state. Soviet Phys. ZhETP 46, 18231828 (1964).
  36. Marmorkos, I., Beenakker, C. & Jalabert, R. Three signatures of phase-coherent Andreev reflection. Phys. Rev. B 48, 28112814 (1993).
  37. Kastalsky, A. et al. Observation of pair currents in superconductor-semiconductor contacts. Phys. Rev. Lett. 67, 30263029 (1991).
  38. Pillet, J. et al. Andreev bound states in supercurrent-carrying carbon nanotubes revealed. Nature Phys. 6, 965969 (2010).
  39. Klapwijk, T., Blonder, G. & Tinkham, M. Explanation of subharmonic energy gap structure in superconducting contacts. Physica B + C 109, 16571664 (1982).
  40. Goldhaber-Gordon, D. et al. Kondo effect in a single-electron transistor. Nature 391, 156159 (1998).
  41. Kretinin, A. V. et al. Spin-1/2 Kondo effect in an InAs nanowire quantum dot: Unitary limit, conductance scaling, and Zeeman splitting. Phys. Rev. B 84, 245316 (2011).
  42. Pikulin, D., Dahlhaus, J., Wimmer, M. & Beenakker, C. Zero-voltage conductance peak from weak antilocalization in a Majorana nanowire. Preprint at (2012).
  43. Csonka, S. et al. Giant fluctuations and gate control of the g-factor in InAs nanowire quantum dots. Nano Lett. 8, 39323935 (2008).
  44. Kretinin, A. V., Popovitz-Biro, R., Mahalu, D. & Shtrikman, H. Multimode Fabry–Perot conductance oscillations in suspended stacking-faults-free InAs nanowires. Nano Lett. 10, 34393445 (2010).
  45. Fasth, C., Fuhrer, A., Samuelson, L., Golovach, V. N. & Loss, D. Direct measurement of the spin-orbit interaction in a two-electron InAs nanowire quantum dot. Phys. Rev. Lett. 98, 266801 (2007).
  46. Kanai, Y. et al. Electrically tuned spin-orbit interaction in an InAs self-assembled quantum dot. Nature Nanotech. 6, 511516 (2011).
  47. Fu, L. Electron teleportation via Majorana bound states in a mesoscopic superconductor. Phys. Rev. Lett. 104, 56402 (2010).
  48. Jiang, L. et al. Unconventional Josephson signatures of Majorana bound states. Phys. Rev. Lett. 107, 236401 (2011).
  49. Nilsson, J., Akhmerov, A. & Beenakker, C. Splitting of a Cooper pair by a pair of Majorana bound states. Phys. Rev. Lett. 101, 120403 (2008).
  50. Chevallier, D., Sticlet, D., Simon, P. & Bena, C. Mutation of Andreev into Majorana bound states in long superconductor- normal and superconductor-normal-superconductor junctions. Phys. Rev. B 85, 235307 (2012).

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Author information

  1. These authors contributed equally to this work

    • Anindya Das &
    • Yuval Ronen


  1. Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel

    • Anindya Das,
    • Yuval Ronen,
    • Yonatan Most,
    • Yuval Oreg,
    • Moty Heiblum &
    • Hadas Shtrikman


A.D. and Y.R. contributed to sample design, device fabrication, set-up, data acquisition, analysis and writing of the paper. M.H. contributed to design, data interpretation and writing of the paper. Y.M. contributed to theory, simulations and writing of the paper. Y.O. contributed to theory, simulations, experimental insight and writing of the paper. H.S contributed to the Au-assisted vapour-liquid–solid molecular beam epitaxy growth and structural study of InAs nanowires, discussions and editing of the manuscript.

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