Robust and Clean Majorana Zero Mode in the Vortex Core of High-Temperature Superconductor $\mathbf{(}{\mathrm{Li}}_{0.84}{\mathrm{Fe}}_{0.16}\mathbf{)}\mathrm{OHFeSe}$

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Robust and Clean Majorana Zero Mode in the Vortex Core of High-Temperature Superconductor $({Li}_{0.84} {Fe}_{0.16}) OHFeSe$

Qin Liu, Chen Chen, Tong Zhang, Rui Peng, Ya-Jun Yan, Chen-Hao-Ping Wen, Xia Lou, Yu-Long Huang, Jin-Peng Tian, Xiao-Li Dong, Guang-Wei Wang, Wei-Cheng Bao, Qiang-Hua Wang, Zhi-Ping Yin, Zhong-Xian Zhao, and Dong-Lai Feng

Phys. Rev. X 8, 041056 – Published 28 December 2018

Abstract

The Majorana fermion, which is its own antiparticle and obeys non-Abelian statistics, plays a critical role in topological quantum computing. It can be realized as a bound state at zero energy, called a Majorana zero mode (MZM), in the vortex core of a topological superconductor, or at the ends of a nanowire when both superconductivity and strong spin orbital coupling are present. A MZM can be detected as a zero-bias conductance peak (ZBCP) in tunneling spectroscopy. However, in practice, clean and robust MZMs have not been realized in the vortices of a superconductor because of contamination from impurity states or other closely packed Caroli–de Gennes-Matricon (CdGM) states, which hampers further manipulations of MZMs. Here, using scanning tunneling spectroscopy, we show that a ZBCP well separated from the other discrete CdGM states exists ubiquitously in the cores of free vortices in the defect-free regions of $({Li}_{0.84} {Fe}_{0.16}) OHFeSe$ , which has a superconducting transition temperature of 42 K. Moreover, a Dirac-cone-type surface state is observed by angle-resolved photoemission spectroscopy, and its topological nature is confirmed by band calculations. The observed ZBCP can naturally be attributed to a MZM arising from the chiral topological surface state of a bulk superconductor. Thus, $({Li}_{0.84} {Fe}_{0.16}) OHFeSe$ provides an ideal platform for studying MZMs and topological quantum computing.

Received 27 July 2018

DOI:https://doi.org/10.1103/PhysRevX.8.041056

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Majorana bound states Superconducting gap Superconductivity Topological superconductors Vortices in superconductors

Density functional theory development Dynamical mean field theory Scanning tunneling microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Qin Liu^1,2,3, Chen Chen^1,3, Tong Zhang^1,3,*, Rui Peng^1,3, Ya-Jun Yan^1,3, Chen-Hao-Ping Wen^1,3, Xia Lou^1,3, Yu-Long Huang⁴, Jin-Peng Tian⁴, Xiao-Li Dong⁴, Guang-Wei Wang⁵, Wei-Cheng Bao^6,7, Qiang-Hua Wang^3,6, Zhi-Ping Yin^5,†, Zhong-Xian Zhao⁴, and Dong-Lai Feng^1,3,‡

¹State Key Laboratory of Surface Physics, Department of Physics, and Advanced Materials Laboratory, Fudan University, Shanghai 200438, China
²Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang, Sichuan 621908, China
³Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
⁴Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
⁵Department of Physics and Center for Advanced Quantum Studies, Beijing Normal University, Beijing 100875, China
⁶National Laboratory of Solid State Microstructures & School of Physics, Nanjing University, Nanjing, 210093, China
⁷Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, China

^*tzhang18@fudan.edu.cn
^†yinzhiping@bnu.edu.cn
^‡dlfeng@fudan.edu.cn

Popular Summary

About 80 years ago, physicist Ettore Majorana proposed the existence of fermions that are their own antiparticles. Now, these Majorana fermions are attracting a lot of attention for their potential use in certain quantum computing applications. While it is possible to create Majorana-fermion-like states in a topological superconductor, it is very difficult to do so cleanly because of large Fermi energies or the required impurities in the material. Here, we experimentally break through this difficulty.

Majorana fermions can be realized as a bound state at zero energy, known as a Majorana zero mode (MZM). Using scanning tunneling spectroscopy, we detect the unique signature of a MZM in defect-free regions of the topological superconductor $({Li}_{0.84} {Fe}_{0.16}) OHFeSe$ . The intrinsic nontrivial topology of this system enables the realization of a MZM without the need to introduce impurities in the FeSe layer, which was a requirement in previous work.

Our work presents an ideal and practical platform to further study the properties of MZMs, explore their manipulation, and construct MZM-based quantum bits, all of which opens a new, clear route to rapid progress in the fundamental understanding and potential applications of MZMs.

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Vol. 8, Iss. 4 — October - December 2018

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Condensed Matter Physics

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Figure 1
Band structure and topological surface states of $({Li}_{1 - x} {Fe}_{x}) OHFeSe$ . (a) Crystal structure (left), surface Brillouin zone (upper right), and schematic of the projection from the 3D to 2D Brillouin zone on the (001) surface (lower right) of $({Li}_{1 - x} {Fe}_{x}) OHFeSe$ . (b) Band structure of $({Li}_{0.75} {Fe}_{0.25}) OHFeSe$ along the $M − Γ − Z − (R)$ direction, represented by spectral functions calculated by DFT combined with DMFT methods [more extended band structure is shown in Fig. S1(a)]. The dashed circle indicates the small SOC gap at the crossing point of Se $4 p_{z}$ and Fe $3 d_{x z}$ bands. The dashed rectangle corresponds to the left half of the energy-momentum range of panel (c). (c) Calculated bulk and surface states on the (001) surface along the $\bar{Γ} - \bar{M}$ direction, illustrated by the spectral function. Dirac-cone-like topological surface states (TSS) centered at $\bar{Γ}$ connect the bulk valence band (BVB) and conduction band (BCB). The BVB and BCB are mainly composed of $3 d_{x z}$ and $3 d_{y z}$ orbitals along this direction, respectively. (d) Photoemission intensity of $({Li}_{0.84} {Fe}_{0.16}) OHFeSe$ measured across $\bar{Γ}$ along cut #1 in panel (a). The dashed curves show the bulk band structure determined by second derivatives. The green dashed rectangle corresponds to the energy-momentum range of panel (e). (e) An enlargement of data in panel (d) near $E_{F}$ at the $\bar{Γ}$ point. Finite spectral weight can be clearly observed within the bulk band gap. (f) Second derivative of the photoemission intensity in the marked region of panel (e), where a Dirac-cone-like dispersion can be seen. (g) Momentum distribution curves (MDCs) of the data in panel (e) in the energy range of $- 28 meV - 2 meV$ (normalized by the intensity near $k_{/ /} = 0$ ). Red markers indicate the Dirac-cone-like dispersion extracted from the two-Lorentzian-peak fitting (blue and dashed curves). (h) The FWHM obtained from the one-peak fit [shown in Fig. S2(a)], as a function of energy. Error bars represent 95% confidence bounds. (i) $E − k$ dispersion extracted from the two-peak fit in panel (g), and the linear fit around the crossing point. Error bars represent 95% confidence bounds of the fitted peak position. (j) Photoemission intensity taken along cut #2 across $\bar{M}$ in panel (a). The dashed curve shows the dispersion of the bulk electron band. (k) The energy distribution curves (EDCs) of the data in panel (j) after dividing by Fermi-Dirac distribution. (l) Symmetrized EDC near the Fermi crossing of the $M$ pocket, where a superconducting gap of around 10 meV is observed (indicated by red arrows). All the data were measured at 5.6 K using 21.2-eV photons.
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Figure 2
Topography, superconducting gap, QPI, and vortex mapping of $({Li}_{0.84} {Fe}_{0.16}) OHFeSe$ film. (a) Topographic image of a cleaved film ( $V_{b} = 1 V$ , $I = 5 pA$ ). Inset: The lattice of the FeSe surface ( $V_{b} = 50 mV$ , $I = 20 pA$ ). A dimerlike defect is marked by the circle. (b) Typical $d I / d V$ spectra taken on the FeSe surface at 0.4 K ( $V_{b} = - 20 mV$ , $I = 60 pA$ ) and on the $({Li}_{0.84} {Fe}_{0.16}) OH$ surface at 4.2 K ( $V_{b} = - 20 mV$ , $I = 60 pA$ ). Note that $Δ_{1}$ and $Δ_{2}$ refer to the smaller and larger gaps, respectively. (c) Fits of the superconducting gap (blue dots) to a single isotropic gap function (gray dashed curve), a single anisotropic gap function (red curve), and a double anisotropic gap function (green dashed curve). Details are described in Ref. [30]. (d) Symmetrized FFT-QPI pattern of an FeSe surface taken at $V_{b} = 5 mV$ (mapping size: $36 \times 36 {nm}^{2}$ ). (e) Color plot of FFT line cuts through $q = (π, π)$ [azimuth averaged along the dashed circle in panel (d)]. The dashed curve is a parabolic fit to the electronlike dispersion. (f) Topographic image of an FeSe surface ( $V_{b} = - 30 mV$ , $I = 40 pA$ ; size: $36 \times 36 {nm}^{2}$ ); green arrows highlight dimerlike defects. (g) ZBC map of the area in panel (f), under $B = 10 T$ . Pinned vortices are indicated by arrows. The dashed circle encloses a free vortex. If we assume that each vortex carries a flux quantum $Φ_{0} = h / 2 e$ , this area should contain $(B \times S) / Φ_{0} = 6.3$ vortices, consistent with the observed number of 7.
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Figure 3
Bound states in the free vortex cores. (a,b) $d I / d V$ spectra taken across the free vortices 1 and 2, shown in the inset images, respectively (set point: $V_{b} = - 17 mV$ , $I = 60 pA$ ). (c,d) Color plots of the spatial dependence of the $d I / d V$ spectra shown in panels (a) and (b), respectively. Dashed lines indicate the zero bias, and arrows indicate the positions of discrete low-energy states. (e,f) Topographic image and vortex mapping ( $B = 10 T$ ) of an FeSe surface, respectively. Two free vortices (3 and 4) are observed in this region. (g) $d I / d V$ spectra taken along the blue arrow in panel (e), at $T = 4.2 K$ and $B = 0 T$ . Red dashed lines trace the position of inner coherence peaks. (h,i) $d I / d V$ spectra taken along the red arrows in panel (f) across the center of vortices 3 and 4, respectively (set point: $V_{b} = - 5 mV$ , $I = 60 pA$ ). Dashed lines indicate peak positions at the vortex center.
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Figure 4
Quantitative characterization of the vortex core states. (a)–(d) Summed low-energy $d I / d V$ spectra taken near the centers of vortices 1–4. Black dots are experimental data. Red solid curves are the fits to multiple Gaussian peaks (dashed curves are the individual peaks). (e) Peak energy position (marked by red vertical rods) and FWHM (represented by the length of colored bars) of the core states of vortices 1–4, obtained from Gaussian peak fitting. The black error bars represent the ranges of peak energy fluctuations (see Sec. S8 of Ref. [30] for more details). (f) Plots of ${| E}_{2} |$ (red circles) as a function of ${(\bar{Δ_{1}})}^{2}$ and ${| E}_{1} |$ (blue circles) as a function of ${(Δ_{2}^{\max})}^{2}$ . Dashed lines are the linear fitting (see legend). (g) Spatial dependence of the intensity of the core states. Here, $I_{2}$ , $I_{1}$ , $I_{0}$ , $I_{- 1}$ , and $I_{- 2}$ represent the intensity ( $d I / d V$ values at the peak energy) of the five core states $E_{2}$ , $E_{1}$ , $E_{0}$ , $E_{- 1}$ , and $E_{- 2}$ of vortex 1. The red solid curve is the exponential fit to the decay of $E_{0}$ .
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Figure 5
Bound states in the impurity pinned vortex cores. (a,b) $d I / d V$ spectra measured on two dimerlike defects at $B = 0 T$ and $B = 10 (11) T$ ( $V_{b} = - 17 mV$ , $I = 60 pA$ ). Insets in panels (a) and (b): ZBC maps of the pinned vortex. (c,d) $d I / d V$ spectra measured along the arrows in the inset image, respectively.
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Physical Review X

Robust and Clean Majorana Zero Mode in the Vortex Core of High-Temperature Superconductor (Li0.84Fe0.16)OHFeSe

Qin Liu, Chen Chen, Tong Zhang, Rui Peng, Ya-Jun Yan, Chen-Hao-Ping Wen, Xia Lou, Yu-Long Huang, Jin-Peng Tian, Xiao-Li Dong, Guang-Wei Wang, Wei-Cheng Bao, Qiang-Hua Wang, Zhi-Ping Yin, Zhong-Xian Zhao, and Dong-Lai Feng

Phys. Rev. X 8, 041056 – Published 28 December 2018

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Robust and Clean Majorana Zero Mode in the Vortex Core of High-Temperature Superconductor $({Li}_{0.84} {Fe}_{0.16}) OHFeSe$