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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 60, Issue 5: 057401(2017) https://doi.org/10.1007/s11433-017-9011-7

Majorana zero mode in the vortex of an artificial topological superconductor

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  • ReceivedFeb 20, 2017
  • AcceptedFeb 21, 2017
  • PublishedFeb 28, 2017
PACS numbers

Abstract

Majorana fermion (MF), an exotic particle that is identical to its own antiparticle, was recently found in solid matter as a quasiparticle excitation, the Majorana zero mode (MZM), in the vortex of an artificial topological superconductor (TSC). This artificial TSC, first proposed by Fu and Kane in 2008, is a heterostructure made of a topological insulator Bi2Te3 and an s-wave superconductor NbSe2. This paper will briefly review the experimental progresses based on the Bi2Te3/NbSe2 heterostructure. All evidences are self-consistent and reveal that the MZM exists in the center of vortex. Those experimental results are also supported by theory. This finding is a milestone in the research of Majorana fermions in solid state physics and a starting point of MZM’s application in topological quantum computation.


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  • Figure 1

    (Color online) (a) Crystal structure of Bi2Se3; (b) top view along the z direction; (c) side view of the quintuple layer structure [22].

  • Figure 2

    (Color online) Band structures of Bi2Se3 and Bi2Te3. Theoretical calculated band structures of Bi2Se3 (a) and Bi2Te3 (b) [22]; angle-resolved photoemission spectrum (ARPES) measurements of band structures of Bi2Se3 (c) and Bi2Te3 (d) [23,24].

  • Figure 3

    (Color online) Morphology of Bi2Se3 on NbSe2. (a) An STM image of 450 nm×450 nm 1QL Bi2Se3 on NbSe2; (b) interfacial structure in the vacant area of (a); (c) atomic resolution image of 1QL Bi2Se3; (d) an STM image of 250 nm×250 nm 2QL Bi2Se3 on NbSe2; (e) line profile of the blue dashed line on (d); (f) structure of Bi2Se3 thin films on NbSe2.

  • Figure 4

    (Color online) Superconductivity on the surface of Bi2Se3/NbSe2 heterostructure. (a) Layer dependence of proximity induced superconducting gaps in Bi2Se3 films; (b) values of superconducting gaps obtained by BCS fitting as a function of layers or film thicknesses. The dashed line in (a) and (b) are just guidances for eyes; (c) superconducting gaps versus applied magnetic fields which is vertical to the sample surfaces on 3QL films; (d) proximity induced superconducting gaps as a function of temperature measured on 3QL films.

  • Figure 5

    (Color online) Spectroscopically resolved proximity-induced topological superconductivity. (a) ARPES dispersion maps of Bi2Se3/NbSe2 as a function of Bi2Se3 film thickness. The blue arrows quantitatively depict the spin texture configuration in the ultrathin limit. The length of the arrow is proportional to the magnitude of the spin polarization; (b) ARPES dispersion map of a 4QL Bi2Se3 film measured at T=12 K using an incident photon energy of 18 eV; (c) ARPES spectra at fixed momentum k1 (the topological surface states); (d) symmetrized ARPES spectra at k1; (e) ARPES spectra at fixed momentum k2 (bulk band states); (f), (g) symmetrized ARPES spectra at ±k1, ±k2 and ±k3 at T∼1 K. The surface state gap (±k1) is further fitted (blue curves) by a BCS function taking into account its spin-momentum-locking and Dirac dispersion properties, whereas the bulk gap is fitted (black curves) by the Dynes function (g); (h) ARPES dispersion map of a 4QL Bi2Se3 film measured with an incident photon energy of 50 eV; ARPES spectra (i) and symmetrized ARPES spectra (j) at fixed momentum k1. The insets of (c), (i) show an ARPES dispersion map near the Fermi level at a low temperature of T∼1 K at photon energies of 18 and 50 eV, respectively [30].

  • Figure 6

    (Color online) Abrikosov vortices on Bi2Te3/NbSe2 heterostructure at different magnetic field. (a), (b) 0.75 T for NbSe2 and 3QL Bi2Te3; (c), (d) 0.25 T for 2QL and 5QL Bi2Te3; (e) the calculated magnetic flux of a vortex.

  • Figure 7

    (Color online) A series of STS spectra measured at various magnetic fields at a vortex center of 5QL Bi2Te3/NbSe2 (a), bare NbSe2 (b), and 2QL Bi2Te3/NbSe2 (c). A dramatic drop in the peak intensity is clearly seen at 0.18 T in (a) [20].

  • Figure 8

    (Color online) (a) A series of STS spectra curves measured along the line starting from the vortex core to the edge of the vortex, showing the peak of bound states splits into two at positions away from the vortex center; (b) the color image of (a) for a better view. The split peak positions in the STS spectra are marked by red crosses, and the dotted lines superimposed on the crosses indicate the start point of the peak splitting; (c)-(g) the experimental results for 2QL-6QL samples, following the similar data process of (b); (h) a summary of the start points of the peak split, showing a crossover at 4QL. Figure adapted from ref. [20].

  • Figure 9

    (Color online) (a)-(d) The LDOS as a function of radius r and energy E. Dotted curves are guides for the eye; (e) spatial distribution of the MBS, with open circles for numerical results and solid curves for analytical results. Figure adapted from ref. [37].

  • Figure 10

    (Color online) A paramagnetic normal lead (N) is coupled to a TSC with Majorana end states. The MZM is denoted by the horizontal line inside the bulk gap of the TSC. (a) Electrons with a specific spin polarization can undergo equal-spin Andreev reflections in which an electron is reflected as a hole with the same spin; (b) electrons with opposite spin are totally reflected as electrons with unchanged spin; (c) realizing a topological superconductor using a Rashba semiconducting wire in proximity to an s-wave superconductor and in a magnetic field. The Rashba direction is denoted as nR. Figure adapted from ref. [38].

  • Figure 11

    (Color online) (a) Illustration of spin-selective Andreev reflection in spin polarized (M↑) STM/STS on a vortex center r=0 in an interface of a topological insulator and s-wave superconductor. An incoming spin-up electron of zero energy is reflected as an outgoing spin-up hole induced by Majorana zero mode with spin-up at r=0, which gives out a higher tunneling conductance; (b) an incoming spin-down electron of zero energy is reflected directly because of the mismatch of the spins of the electron and the Majorana zero mode, which results in a lower tunneling conductance.

  • Figure 12

    (Color online) (a) Zero bias dI/dV mapping of a vortex at 0.1 T with the spin nonpolarized tip on the topological superconductor 5QL Bi2Te3/NbSe2; (b) dI/dV at the vortex center measured with a fully spin polarized tip. Red curves are for tip polarization M parallel to magnetic field B, and black curves are for M antiparallel to B. In the measurements, B=0.1 T and temperature T=30 mK. The blue lateral lines give the average values of the intensities in multimeasurements, the vertical bars are the standard error bars. The intensity of the conductance with M parallel to B is about 14% higher than that with M antiparallel to B; (c) dI/dV at 10 nm away from the center of a vortex measured with a fully spin polarized tip, where the tunneling is found independent of the spin polarization. Figure adapted from ref. [21].

  • Figure 13

    (Color online) dI/dV curves at the center of a vortex core measured with a fully spin polarized tip. Red curves are for polarization M parallel to B, and black curves are for M antiparallel to B. (a) and (b) for 3QL Bi2Te3 on NbSe2 and bare NbSe2. In the measurements, B=0.1 T; (c) for 5QL Bi2Te3 on NbSe2 at B=0.22 T. The measurement temperature T=30 mK for all curves. The blue lateral lines give the average values of the intensities in multimeasurements; the vertical bars are the standard error bars. Figure adapted from ref. [21].

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