Platform of chiral Majorana edge modes and its quantum transport phenomena

He, James Jun; Liang, Tian; Tanaka, Yukio; Nagaosa, Naoto

doi:10.1038/s42005-019-0250-5

Cited by 28 publications

(30 citation statements)

References 84 publications

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“…The chirality emerges from an appropriate choice of driving protocol that breaks time-reversal symmetry, allowing the MMs to propagate. This mechanism is an alternative to the use of magnetic fields in quantum anomalous Hall insulators coupled to s-wave superconductors [27,[82][83][84][85][86] or in p ± ip superconducting topological insulators [24][25][26].…”

Section: B Chirality Tuningmentioning

confidence: 99%

“…(15) constructed from the lowest band stroboscopic Bloch eigenstate |u − (k) of the effective Hamiltonian in Eq. (26). One observes that the Fourier transform of the stroboscopic Berry curvature yields a correlation function that measures the overlap between the Wannier states [55][56][57][87][88][89], sandwiching the operator R xŷ − R yx ,…”

Section: A Correlation Function and Fidelity Susceptibility For Periodically Driven Kitaev Modelmentioning

confidence: 99%

“…If time-reversal symmetry (TRS) is present, as in the prototypical Kitaev model on a honeycomb lattice [20], MMs are immobile (nondispersive). For TRS breaking systems, such as chiral p-wave superconductors [23][24][25][26], MMs can propagate along the edges and acquire a chirality. The mobility of chiral MMs may inherently facilitate quantum computing procedures [27].…”

Section: Introductionmentioning

confidence: 99%

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Crossdimensional universality classes in static and periodically driven Kitaev models

et al. 2021

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The Kitaev model on the honeycomb lattice is a paradigmatic system known to host a wealth of nontrivial topological phases and Majorana edge modes. In the static case, the Majorana edge modes are nondispersive. When the system is periodically driven in time, such edge modes can disperse and become chiral. We obtain the full phase diagram of the driven model as a function of the coupling and the driving period. We characterize the quantum criticality of the different topological phase transitions in both the static and driven model via the notions of Majorana-Wannier state correlation functions and momentum-dependent fidelity susceptibilities. We show that the system hosts crossdimensional universality classes: although the static Kitaev model is defined on a two-dimensional (2D) honeycomb lattice, its criticality falls into the universality class of one-dimensional (1D) linear Dirac models. For the periodically driven Kitaev model, in addition to the universality class of prototype 2D linear Dirac models, an additional 1D nodal loop type of criticality exists owing to emergent time-reversal and mirror symmetries, indicating the possibility of engineering multiple universality classes by periodic driving. The manipulation of time-reversal symmetry allows the periodic driving to control the chirality of the Majorana edge states.

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Section: B Chirality Tuningmentioning

confidence: 99%

Section: A Correlation Function and Fidelity Susceptibility For Periodically Driven Kitaev Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Crossdimensional universality classes in static and periodically driven Kitaev models

et al. 2021

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“…Recently, QAH/SC hybrid systems have been generalized to hybrid systems with antiferromagnetic topological insulators [57,60], s-wave SC with nontrivial topology [61], or d-wave SCs [62]. Interestingly, such extended hybrid systems bring other 2D topological phases showing helical Majorana edge modes protected by a pseudo TRS [57] and multiple chiral Majorana edge modes [60][61][62]. These exotic topological surface states have provided another route for probing Majorana edge modes [61,62].…”

Section: Introductionmentioning

confidence: 99%

“…Interestingly, such extended hybrid systems bring other 2D topological phases showing helical Majorana edge modes protected by a pseudo TRS [57] and multiple chiral Majorana edge modes [60][61][62]. These exotic topological surface states have provided another route for probing Majorana edge modes [61,62]. In addition, superconducting doped topological materials, including topological insulators [63][64][65][66] and Dirac/Weyl semimetals [67][68][69][70][71][72], are a promising platform to explore topological superconductivity induced by topologically nontrivial electron states.…”

Section: Introductionmentioning

confidence: 99%

Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems

Ohashi,

Kobayashi,

Tanaka

2021

Preprint

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Quantum anomalous Hall insulator (QAH)/s-wave superconductor (SC) hybrid systems are known to be an ideal platform for realizing two-dimensional topological superconductors with chiral Majorana edge modes. In this paper we study QAH/unconventional SC hybrid systems whose pairing symmetry is p-wave, d-wave, chiral p-wave, or chiral d-wave. The hybrid systems are a generalization of the QAH/s-wave SC hybrid system. In view of symmetries of the QAH and pairings, we introduce three topological numbers to classify topological phases of the hybrid systems. One is the Chern number that characterizes chiral Majorana edge modes and the others are topological numbers associated with crystalline symmetries. We numerically calculate the topological numbers and associated surface states for three characteristic regimes that feature an influence of unconventional SCs on QAHs. Our calculation shows a rich variety of topological phases and unveils the following topological phases that are no counterpart of the s-wave case: crystalline symmetry-protected helical Majorana edge modes, a line node phase (crystalline-symmetry-protected Bogoliubov Fermi surface), and multiple chiral Majorana edge modes. The phenomena result from a nontrivial topological interplay between the QAH and unconventional SCs. Finally, we discuss tunnel conductance in a junction between a normal metal and the hybrid systems, and show that the chiral and helical Majorana edge modes are distinguishable in terms of the presence/absence of zero-bias conductance peak.

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Emergent Multifunctional Magnetic Proximity in van der Waals Layered Heterostructures

et al. 2022

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Proximity effect, which is the coupling between distinct order parameters across interfaces of heterostructures, has attracted immense interest owing to the customizable multifunctionalities of diverse 3D materials. This facilitates various physical phenomena, such as spin order, charge transfer, spin torque, spin density wave, spin current, skyrmions, and Majorana fermions. These exotic physics play important roles for future spintronic applications. Nevertheless, several fundamental challenges remain for effective applications: unavoidable disorder and lattice mismatch limits in the growth process, short characteristic length of proximity, magnetic fluctuation in ultrathin films, and relatively weak spin-orbit coupling (SOC). Meanwhile, the extensive library of atomically thin, 2D van der Waals (vdW) layered materials, with unique characteristics such as strong SOC, magnetic anisotropy, and ultraclean surfaces, offers many opportunities to tailor versatile and more effective functionalities through proximity effects. Here, this paper focuses on magnetic proximity, i.e., proximitized magnetism and reviews the engineering of magnetism-related functionalities in 2D vdW layered heterostructures for next-generation electronic and spintronic devices. The essential factors of magnetism and interfacial engineering induced by magnetic layers are studied. The current limitations and future challenges associated with magnetic proximity-related physics phenomena in 2D heterostructures are further discussed.

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Platform of chiral Majorana edge modes and its quantum transport phenomena

Cited by 28 publications

References 84 publications

Crossdimensional universality classes in static and periodically driven Kitaev models

Crossdimensional universality classes in static and periodically driven Kitaev models

Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems

Emergent Multifunctional Magnetic Proximity in van der Waals Layered Heterostructures

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