Experimental review on Majorana zero-modes in hybrid nanowires

AbstractAs the condensed matter analog of Majorana fermion, the Majorana zero-mode is well known as a building block of fault-tolerant topological quantum computing. This review focuses on the recent progress of Majorana experiments, especially experiments about semiconductor-superconductor hybrid devices. We first sketch Majorana zero-mode formation from a bottom-up view, which is more suitable for beginners and experimentalists. Then, we survey the status of zero-energy state signatures reported recently, from zero-energy conductance peaks, the oscillations, the quantization, and the interactions with extra degrees of freedom. We also give prospects of future experiments for advancing one-dimensional semiconductor nanowire-superconductor hybrid materials and devices.

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Nearly quantized conductance plateau of vortex zero mode in an iron-based superconductor

Science ◽

10.1126/science.aax0274 ◽

2019 ◽

pp. eaax0274 ◽

Cited By ~ 20

Author(s):

Shiyu Zhu ◽

Lingyuan Kong ◽

Lu Cao ◽

Hui Chen ◽

Michał Papaj ◽

...

Keyword(s):

Bound States ◽

Zero Mode ◽

Finite Energy ◽

Scanning Tunneling Spectroscopy ◽

Scanning Tunneling ◽

Tunneling Conductance ◽

Zero Energy ◽

Tunnel Coupling ◽

Topological Quantum ◽

The Continuum

Majorana zero modes (MZMs) are spatially-localized zero-energy fractional quasiparticles with non-Abelian braiding statistics that hold promise for topological quantum computing. Owing to the particle-antiparticle equivalence, MZMs exhibit quantized conductance at low temperature. By utilizing variable-tunnel-coupled scanning tunneling spectroscopy, we study tunneling conductance of vortex bound states on FeTe0.55Se0.45 superconductors. We report observations of conductance plateaus as a function of tunnel coupling for zero-energy vortex bound states with values close to or even reaching the 2e2/h quantum conductance (here e is the electron charge and h is Planck’s constant). In contrast, no plateaus were observed on either finite energy vortex bound states or in the continuum of electronic states outside the superconducting gap. This behavior of the zero-mode conductance supports the existence of MZMs in FeTe0.55Se0.45.

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Observation of magnetic adatom-induced Majorana vortex and its fusion with field-induced Majorana vortex in an iron-based superconductor

10.21203/rs.3.rs-72679/v1 ◽

2020 ◽

Author(s):

Peng Fan ◽

Fazhi Yang ◽

Guojian Qian ◽

Hui Chen ◽

Yu-Yang Zhang ◽

...

Keyword(s):

Magnetic Field ◽

Bound States ◽

Zero Mode ◽

Fault Tolerant ◽

Abrikosov Vortex ◽

Zero Modes ◽

Topological Quantum ◽

Iron Based ◽

Dual Origin ◽

Single Material

Abstract Braiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the fusion of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and Majorana zero mode induced by magnetic Fe adatoms deposited on the surface and the realization of its fusion with a nearby field-induced Majorana vortex in iron-based superconductor FeTe0.55Se0.45. We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures.

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Kitaev’s Chain Model and Majorana Zero Modes

Physics and High Technology ◽

10.3938/phit.29.018 ◽

2020 ◽

Vol 29 (6) ◽

pp. 3-7

Author(s):

Sangjun JEON ◽

Kwang-Yong CHOI

Keyword(s):

Conceptual Development ◽

Fault Tolerant ◽

Condensed Matter ◽

Majorana Fermion ◽

Quantum Computers ◽

Chain Model ◽

Zero Energy ◽

Experimental Realization ◽

Zero Modes ◽

History Of

A Majorana Fermion (MF), defined as a particle that is its own anti-particle, can be engineered in the form of quasi-particles appearing in condensed matter systems. Majorana zero modes (MZMs), topologically protected zero-energy states, can exist at the topological phase boundary of one- or two-dimensional systems. These MZMs follow non-Abelian statistics and can be used as a building block for fault-tolerant quantum computers. Here, we introduce the conceptual development of MZMs based on Kitaev’s chain model and give a brief history of the experimental realization of MZMs.

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Observation of magnetic adatom-induced Majorana vortex and its hybridization with field-induced Majorana vortex in an iron-based superconductor

Nature Communications ◽

10.1038/s41467-021-21646-x ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Peng Fan ◽

Fazhi Yang ◽

Guojian Qian ◽

Hui Chen ◽

Yu-Yang Zhang ◽

...

Keyword(s):

Magnetic Field ◽

Bound States ◽

Zero Mode ◽

Fault Tolerant ◽

Abrikosov Vortex ◽

Zero Modes ◽

Topological Quantum ◽

Iron Based ◽

Dual Origin ◽

Single Material

AbstractBraiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the coupling of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and the Majorana zero mode induced by magnetic Fe adatoms deposited on the surface. We observe its hybridization with a nearby field-induced Majorana vortex in iron-based superconductor FeTe0.55Se0.45. We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures.

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Robustness of Majorana Zero-energy State in a Spin-orbit Coupled Semiconductor/superconductor Heterostructure

10.21203/rs.3.rs-882201/v1 ◽

2021 ◽

Author(s):

Zheng Wang

Keyword(s):

Differential Equation ◽

Energy State ◽

Numerical Test ◽

Spin Orbit ◽

Zero Energy ◽

Topological Quantum ◽

Linearized Stability ◽

The Stability ◽

Topological Quantum Computation ◽

Coupled Semiconductor

Abstract Based on the principle of linearized stability proposed by Lyapounov, we investigate the robustness of Majorana zero energy state (MZES), which plays an important role in topological quantum computation. Our study is different from previous works that usually explore the stability of MZES by the numerical test of some special perturbations, our treatment is suitable for arbitrary perturbations. Since our method follows the stability theory of differential equation, the results we obtained are reliable. As an example, we demonstrate it by the stability of MZES in the spin-orbit coupled semiconductor/ superconductor junction, the analytical and numerical results indicate that the MZES is unstable in this system.

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COMPLEX MASS FERMIONIC FIELDS

International Journal of Modern Physics A ◽

10.1142/s0217751x94000893 ◽

1994 ◽

Vol 09 (12) ◽

pp. 2103-2115 ◽

Cited By ~ 2

Author(s):

D.G. BARCI ◽

L.E. OXMAN

Keyword(s):

Degrees Of Freedom ◽

Order Equation ◽

Complex Conjugate ◽

Zero Energy ◽

Natural Representation ◽

Symmetric State ◽

Fermionic Field ◽

Fermionic Fields ◽

Real Mass ◽

Mass Case

We consider a fermionic field obeying a second order equation containing a pair of complex conjugate mass parameters. After obtaining a natural representation for the different degrees of freedom, we are able to construct a unique vacuum as the more symmetric state (zero energy-momentum, charge and spin). This representation, unlike the real mass case, is not holomorphic in the Grassmann variables. The vacuum eigenstate allows the calculation of the field propagator which turns out to be half advanced plus half retarded.

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Giant phonon anomalies in the proximate Kitaev quantum spin liquid α-RuCl3

Nature Communications ◽

10.1038/s41467-021-23826-1 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Haoxiang Li ◽

T. T. Zhang ◽

A. Said ◽

G. Fabbris ◽

D. G. Mazzone ◽

...

Keyword(s):

Acoustic Phonon ◽

Energy Scale ◽

Quantum Spin ◽

Majorana Fermion ◽

Spin Liquid ◽

Optical Phonons ◽

Large Intensity ◽

Topological Quantum ◽

Topological State ◽

Quantum Spin Liquid

AbstractThe Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we detect anomalous phonon effects in α-RuCl3 using inelastic X-ray scattering with meV resolution. At high temperature, we discover interlaced optical phonons intercepting a transverse acoustic phonon between 3 and 7 meV. Upon decreasing temperature, the optical phonons display a large intensity enhancement near the Kitaev energy, JK~8 meV, that coincides with a giant acoustic phonon softening near the Z2 gauge flux energy scale. These phonon anomalies signify the coupling of phonon and Kitaev magnetic excitations in α-RuCl3 and demonstrates a proof-of-principle method to detect anomalous excitations in topological quantum materials.

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Majorana zero modes in impurity-assisted vortex of LiFeAs superconductor

Nature Communications ◽

10.1038/s41467-021-24372-6 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Lingyuan Kong ◽

Lu Cao ◽

Shiyu Zhu ◽

Michał Papaj ◽

Guangyang Dai ◽

...

Keyword(s):

Quantum Computation ◽

Zero Mode ◽

Scanning Tunneling ◽

Homogeneous Material ◽

Dirac Fermions ◽

Tunneling Microscopy ◽

Zero Modes ◽

Topological Quantum ◽

One Step ◽

Topological Quantum Computation

AbstractThe iron-based superconductor is emerging as a promising platform for Majorana zero mode, which can be used to implement topological quantum computation. One of the most significant advances of this platform is the appearance of large vortex level spacing that strongly protects Majorana zero mode from other low-lying quasiparticles. Despite the advantages in the context of physics research, the inhomogeneity of various aspects hampers the practical construction of topological qubits in the compounds studied so far. Here we show that the stoichiometric superconductor LiFeAs is a good candidate to overcome this obstacle. By using scanning tunneling microscopy, we discover that the Majorana zero modes, which are absent on the natural clean surface, can appear in vortices influenced by native impurities. Our detailed analysis reveals a new mechanism for the emergence of those Majorana zero modes, i.e. native tuning of bulk Dirac fermions. The discovery of Majorana zero modes in this homogeneous material, with a promise of tunability, offers an ideal material platform for manipulating and braiding Majorana zero modes, pushing one step forward towards topological quantum computation.

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Competing ν = 5/2 fractional quantum Hall states in confined geometry

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1614543113 ◽

2016 ◽

Vol 113 (44) ◽

pp. 12386-12390 ◽

Cited By ~ 20

Author(s):

Hailong Fu ◽

Pengjie Wang ◽

Pujia Shan ◽

Lin Xiong ◽

Loren N. Pfeiffer ◽

...

Keyword(s):

Quantum Computation ◽

Filling Factor ◽

Fault Tolerant ◽

Quantum Hall ◽

Point Contact ◽

Fractional Quantum ◽

Fractional Quantum Hall ◽

Topological Quantum ◽

Quantum Point ◽

Topological Quantum Computation

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current–tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.

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