Evidence of Majorana States in an Al Superconductor – InAs Nanowire Device

[From left to right] Moty Heiblum, Yuval Oreg, Anindya Das, Yonathan Most, Hadas Shtrikman, Yuval Ronen

Authors: Yuval Ronen, Anindya Das, Yonatan Most, Yuval Oreg, Moty Heiblum, and Hadas Shtrikman

Affiliation: Dept. of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel

When a bridge between fields in physics is created, exciting physics can emerge. In 1962 Anderson walked on a bridge connecting condensed matter physics with particle physics, by introducing the Anderson mechanism in superconductivity to explain the Meissner effect. A similar idea was used on the other side of the bridge by Higgs in 1964, to explain the mechanism that generates the mass of elementary particles known as the Higgs mechanism. Nowadays, another bridge is formed between these two fields emanating from an idea first originated by Ettore Majorana in 1937 – where spin 1/2 particles can be their own anti-particles[1]. Back then, Majorana suggested the neutrino as a possible candidate for his prediction, and experiments such as double-beta decay are planned to test his prediction.

A link between Majorana’s prediction of new elementary particles and the field of condensed matter physics was formed already more than a decade ago. Quasi-particle excitations, which are equal to their anti-quasi-particle excitations, are predicted to be found in the solid. Specifically, in vortices that live in an esoteric two-dimensional P-wave spinless superconductor. Moreover, these excitations are expected to be inherently different from their cousins the elementary particles: they have non-abelian statistics. The non-abelian statistics is one of the beautiful triumphs of the physics of condensed matter.

This so far unobserved quasi-particle, that has non-abelian statistics, has for a while been a ‘holy grail’ in the fractional quantum Hall effect regime; with filling factor 5/2 being the most promising candidate for its observation. Lately, another realization of Majorana quasi-particles is pursued. It follows a 1D toy model presented by Kitaev in 2001, showing how one can isolate two Majorana states at two widely separated ends of a 1D P-wave spinless superconductor [2]. These two Majorana states are expected to sit in the gap of the superconductor (at the Fermi energy) for a wide range of system parameters. Seven years later, Fu and Kane [3] found that a P-wave spinless superconductor can be induced by an S-wave superconductor in proximity to a topological insulator, occurring in a semiconductor with an inversion gap. It was thus not long before two theoretical groups [4,5] provided a prescription for how to turn a 1D semiconductor nanowire into an effective Kitaev 1D spinless P-wave superconductor.

The prescribed system is a semiconductor nanowire, with strong spin-orbit coupling, coupled to an S-wave superconductor (a trivial superconductor, with Cooper pairs in a singlet state). Electrons from the semiconductor undergo Andreev reflections, a process which induces S-wave superconductivity in the nanowire. The induced superconductivity opens gaps in the nanowire spectrum around the Fermi energy, at momentums k=0 and k=k_F (the Fermi momentum), due to the two spin bands being separated by spin-orbit coupling. An applied magnetic field quenches the gap at k=0 while hardly affecting the gap at k_F (the Zeeman splitting competes with superconductivity at k=0, where spin-orbit coupling, being proportional to k, plays no role), creating an effective gap different from the one induced by superconductivity. A gate voltage is used to tune the chemical potential into the effective gap. When the Zeeman energy is equal to the induced superconducting gap, the effective gap at k=0 closes; it then reopens upon further increase of the magnetic field, bringing the nanowire into a so called ‘topological phase’. Kitaev’s original toy model of a 1D P-wave superconductor is then implemented (Fig. 1).

Figure 1: Energy dispersion of the InAs nanowire excitations (Bogoliubov-de Gennes spectrum), in proximity to the Al superconductor. Heavy lines show electron-like bands and light lines show hole-like bands. Opposite spin directions are denoted in blue and magenta (red and cyan) for the spin-orbit effective field direction (perpendicular direction), where a relative mixture denotes intermediate spin directions. (a) Split electronic spin bands due to spin-orbit coupling in the InAs wire. Spin-orbit energy defined as Δ_so, with the chemical potential μ measured with respect to the spin bands crossing at p=0. (b) With the application of magnetic field, B, perpendicular to the spin-orbit effective magnetic field, B_so a Zeeman gap, E_z= gμ_BB/2, opens at p=0. (c) Light curves for the hole excitations are added, and bringing into close proximity a superconductor opens up superconducting gaps at the crossing of particle and hole curves. The overall gap is determined by the minimum between the gap at p=0 and the gap at p_F, while for μ=0 and E_z close to Δ_ind the gap at p=0 is dominant. (d) As in (c) but E_z is increased so that the gap at p_F is dominant. (e) B is rotated to a direction of 30^o with respect to B_so. The original spin-orbit bands are shifted in opposite vertical directions, and the B component, which is perpendicular to B_so is diminished. (f) The evolution of the energy gap at p=0 (dotted blue), at p_F (dotted yellow), and the overall energy gap (dashed black) with Zeeman energy, E_z, for μ=0. The overall gap is determined by the minimum of the other two, where the p=0 gap is dominant around the phase transition, which occurs at E_z=Δ_ind. At high E_z the p_F gap, which is decreasing with E_z, becomes dominant.

Seventy five years after Majorana’s monumental paper, we may be close to a realization of a quasi-particle that is identical to its anti-quasi-particle, possessing non-abelian statistics. Several experimental groups [6,7,8] follow the prescribed recipe for a 1D P-wave spinless superconductor[4,5], with our group being one of them. A zero energy conductance peak, at a finite Zeeman field, had been seen now in InSb and InAs nanowires in proximity to Nb and Al superconductors, respectively. This peak is considered a signature for the existence of a Majorana quasi-particle, since the Majorana resides at the Fermi energy.

Figure 2: Structure of the Al-InAs structures suspended above p-type silicon covered with 150nm SiO₂. (a) Type I device, the nanowire is supported by three gold pedestals, with a gold ‘normal’ contact at one edge and an aluminum superconducting contact at the center. The conductive Si substrate serves as a global gate (GG), controlling barrier as well as the chemical potential of the nanowire. Two narrow local gates (RG and LG), 50nm wide and 25nm thick, displaced from the superconducting contact by 80nm, also strongly influence the barrier height as well as the chemical potential in the wire. (b) Type II device, similar to type I device, but without the pedestal under the Al superconducting contact. This structure allows control of the chemical potential under the Al contact. (c) SEM micrograph of type II device. A voltage source, with 5 Ohm resistance, provides V_SD, and closes the circuit through the ‘cold ground’ (cold finger) in the dilution refrigerator. Gates are tuned by V_GG and V_RG to the desired conditions. Inset: High resolution TEM image (viewed from the <1120> zone axis) of a stacking faults free, wurtzite structure, InAs nanowire, grown on (011) InAs in the <111> direction. TEM image is courtesy of Ronit Popovitz-Biro. (d) An estimated potential profile along the wire. The two local gates (LG and RG) and global gate (GG) determine the shape of the potential barriers; probably affect the distance between the Majoranas.

Our work, with MBE grown InAs nanowire in proximity to an Al superconductor [8] (Fig 2), demonstrated a zero bias peak and several more interesting features in the parameters' space. First, the closing of the gap at k=0 was clearly visible when the Zeeman energy was equal to the induced gap. Second, splitting of the zero-bias-peak was observed at low and high Zeeman field; likely to result from spatial coupling of the two Majorana states. Third, the zero-bias-peak was found to be robust in a wide range of chemical potential (assumed to be within the k=0 gap). While these observations agree with the presence of a Majorana quasi-particle (though the peak height is much smaller than expected, maybe due to the finite temperature of the experiment), the available data does not exclude other effects that may result with a similar zero bias peak (such as, interference, disorder, multi-bands, Kondo correlation).

Quoting Wilczek: “Whatever the fate of these particular explorations, there is no doubt that Majorana's central idea, which long seemed peripheral, has secured a place at the core of theoretical physics"[9].

References:
[1] Ettore Majorana, "Teoria simmetrica dell’elettrone e del positrone", Il Nuovo Cimento, 171 (1937). Abstract.
[2] A. Yu. Kitaev, "Unpaired Majorana fermions in quantum wires". Physics Uspekhi, 44, 131 (2001). Full Article.
[3] Liang Fu and Charles Kane, "Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator", Physical Review Letters 100, 096407 (2008). Abstract.
[4] Roman M. Lutchyn, Jay D. Sau and Sankar Das Sarma, "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures", Physical Review Letters, 105, 077001 (2010). Abstract.
[5] Yuval Oreg, Gil Refael, and Felix von Oppen, "Helical Liquids and Majorana Bound States in Quantum Wires", Physical Review Letters, 105, 177002 (2010). Abstract.
[6] V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, "Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices", Science 336, 1003 (2012). Abstract. 2Physics Article.
[7] M. T. Deng, C. L. Yu, G. Y. Huang, M. Larsson, P. Caroff, H. Q. Xu, "Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device", arXiv: 1204.4130 (2012).
[8] Anindya Das, Yuval Ronen, Yonathan Most, Yuval Oreg, Hadas Shtrikman, Moty Heiblum, "Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions", Nature Physics, 8, 887–895 (2012). Abstract.
[9] Frank Wilczek, "Majorana Returns", Nature Physics, 5, 614 (2009). Abstract.