Acta Physica Sinica, Volume. 69, Issue 11, 110301-1(2020)
Fig. 1. Fe-based superconductors (FeSCs) as a better Majorana platform: (a) The original idea for searching Majorana zero mode (MZM) in FeSCs; (b) the typical band structure of FeSCs, the orbital characters of each band are as follows: α (d
Fig. 2. The mechanism of topological band structure and band inversion of Fe(Te, Se): (a) First-principle calculation of band structure of FeSe (without SOC), the size of red circles represents the components of p
Fig. 3. Experimental observation of the linear dispersion of Dirac surface states in FeTe0.55Se0.45[100]: (a) The matrix element effect which defines the selection rule of ARPES intensity, depending on relationship between photon polarization and electron orbitals; (b) the Dirac surface states observed under p-polarization; (c) the d
Fig. 4. Spin-momentum locking and isotropic superconducting gap on the Dirac surface state: (a) The spin-momentum locking feature in FeTe0.55Se0.45 single crystal[100]; (b), (c) spin-resolved ARPES data measured along Cut 1 and Cut 2 in panel (a), respectively[100]; (d) temperature dependent energy distribution curves measured at
Fig. 5. Evidence of Dirac semimetal phase in FeTe0.55Se0.45 single crystal[101]: (a), (b) The spin-integrated and spin-resolved ARPES spectrum around
Fig. 6. The discovery of vortex Majorana zero mode in FeTe0.55Se0.45 single crystal: (a) The theoretical prediction of vortex MZMs in FeTe0.55Se0.45 single crystal[100]; (b) STM topography of FeTe0.55Se0.45 single crystal[102]; (c) zero-bias conductance map which shows vortex lattice[102]; (d) a sharp zero-bias conductance peak measured at the center of a vortex. In order to make sure the observation is indeed a zero energy vortex bound state, three careful checks are listed as follows. First of all, to make sure that the signal measured is indeed from vortex bound state[102]: (e) ZBC map after and before applying a magnetic field. It shows the local environment of the vortex is clean and free of impurities[102]; (f) ZBCP is stable under different tunneling barriers. Secondly, to make sure that the observed ZBCP is truly a single peak[102]; (g) FWHM of ZBCP measured under different tunneling barriers; (h), (i) the observed ZBCP is truly a zero mode[102]. (h) is the simultaneous measured
Fig. 7. The wavefunction of vortex Majorana zero mode[102]: (a) A zero bias conductance map of a topological vortex; (b) a d
Fig. 8. Quasiparticle poisoning of vortex Majorana zero modes[102]: (a) Three vortex Majorana zero modes measured on different locations, the FWHM of ZBCP at the center of the vortex core is larger when the SC gap around the vortex core is softer; (b) a zero bias conductance map of vortex and line-cut intensity plot of Majorana zero modes measured under 0.55 K (left) and 4.2 K (right), respectively; (c) temperature evolution of ZBCPs in a vortex core. The gray curves are numerically broadened 0.55 K data at each temperature; (d) amplitude of the ZBCPs of three vortex MZMs under different temperatures. The amplitude is defined as the peak-valley difference of the ZBCP; (e) left panel:
Fig. 9. Topological vortex phase transition in the three-dimensional vortex line model. The first line: Evolution of the band structure of a topological material by tuning the chemical potentials. The second line: Evolution of the low energy vortex bound state at
Fig. 10. Resonance Andreev reflection induced Majorana quantum conductance: (a) Conventional electron resonance tunneling in a semiconductor heterostructure[207]; (b) the wavefucntion of conventional resonance tunneling[105]; (c) two tips cross-tunneling can be regarded as a replacement of semiconductor heterostructure for realizing semiconductor heterostructure under the condition of equal hopping amplitude around the two tips (;
Fig. 11. Variable-tunnel-coupling STM method and the observation of conductance plateau of vortex Majorana zero modes[105]: (a) The tunnel coupling strength can be changed by the tip-sample separation distance under the effect of STM regulation loop; (b) a three-dimensional plot of tunnel coupling dependent measurement, d
Fig. 12. Surface Dirac electron induced half-integer level shift of vortex bound states: (a) Half-odd-integer quantized level sequences of vortex bound states in a conventional s-wave superconductor. There are only parabolic bulk bands involved[104]; (b) the quantum limit is difficult to reach in conventional s-wave superconductors, so that a large ZBCP observed in the center of vortex core is generally due to multiple overlapping of densely packed non-zero peaks[231]; (c) integer quantized level sequences of the vortex bound state in Fu-Kane model. The intrinsic spin Berry phase carried by Dirac surface states induces the half-integer level shift[104]; (d) the zero-doping limit is defined as the chemical potential is approaching the energy of the Dirac point. In this case, a vortex MZM is the only allowed subgap bound state[104]; (e) the theoretical calculated angular momentum resolved wavefunction of BdG eigenstate, the blue and green curves are spin down and up components, respectively[210]. Insert: The calculated spin-integrated 2 D local density of states of three lowest levels of vortex bound states in the case of (c) and (a), respectively[104]; (f) theoretical calculated eigenvalue of BdG Hamiltonian near the zero chemical potential limit.
Fig. 13. Observation of integer quantized vortex bound states[104]: (a) A d
Fig. 14. The inhomogeneity of material helps coexisting ordinary and topological vortices: (a) A d
Fig. 15. Spatial distribution of the two classes of vortices[104]: (a), (c), (e) Zero-bias conductance maps of three well-separated regions. The yellow solid circles mark the vortices with ZBCPs and integer quantized CdGM levels, yellow dashed circles mark the vortices with ZBCPs but its CdGM level sequences can not be fitted to integer quantization, blue solid circles mark the vortices without ZBCPs and half-integer quantized CdGM levels, and blue dashed circles mark the vortices without ZBCPs or half-integer quantized CBS levels. The green dashed lines encircle the same class of vortices. Topological vortices and ordinary vortices usually group together, which indicates topological region and trivial region coexist on the sample surface due to spatial inhomogeneity; (b), (d), (f) summary of the ratio of different types of vortices in the three regions, respectively. The data in the three regions are measured under 40 mK and 2.0 T.
Fig. 16. Mechanism of the presence or absence of MZMs in Fe(Te, Se)[104]: (a) Fe(Te, Se) single crystals are intrinsically inhomogeneous. Disappearance of Dirac surface states is possible in some regions of the (001) surface (brown color). In the conventional regions, the corresponding bulk states can be normal insulators or weak topological insulators. Consequently, the Dirac surface state moves deeper into the bulk and go around the conventional region, as indicated by the gray boundary inside the crystal. In other topological regions (gray color), where Dirac surface states remain intact, the corresponding bulk states are still in the strong topological insulating phase; (b) a schematic phase diagram of vortex MZMs appearing in topological regions (topological vortices). The gradient blue areas in (b) and (c) indicate the phase sector that MZMs can be detected by STM/S experiments. In the dark blue sector, the Majorana wave function is more localized on the sample surface, while in brighter positions, the Majorana wave function strongly hybridizes with bulk quasiparticles and moves deeper beneath the surface, leading to weak ZBCP signal measured by STM/S. The vertical axis demonstrates MZMs evolution as a function of effective temperature which can be represented by extrinsic broadening of the observed ZBCPs. The horizontal axis demonstrates the MZMs evolution as a function of quantum parameters, e.g., chemical potential (μ) measured from the Dirac point. The black dots with an arrow indicate the quantum critical points in which a vortex phase transition happens. Across the critical point, the vortex line turns to be topological trivial and MZMs disappear in the topological region. The red dashed line indicates the achievable region in experiments; (c) a schematic phase diagram of vortex MZMs appearing in conventional regions (ordinary vortices). There are no MZMs in our measurements in those vortices. The observable MZMs can only exist above the critical points when the vortex phase transition turns the trivial vortex line into a 1D topological superconductor in the conventional region.
Fig. 17. Braiding vortex MZMs and topological quantum computing. Left-top panel: Surface effective spinless p-wave pairing induce by
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Ling-Yuan Kong, Hong Ding.
Received: May. 12, 2020
Accepted: --
Published Online: Dec. 2, 2020
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