Two-Dimensional Second-Order Topological Insulator in Graphdiyne

Sheng, Xian‐Lei; Chen, Cong; Liu, Huiying; Chen, Zi-Yu; Yu, Zhi‐Ming; Zhao, Y. X.; Yang, Shengyuan A.

doi:10.1103/physrevlett.123.256402

Cited by 246 publications

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“…A paradigmatic example is the family of topological insulators which manifest quantized dipole moments in their bulk and charge fractionalization at their boundaries [1][2][3], epitomized by the inversion-symmetric onedimensional Su-Schieffer-Hegger model [4]. This property of boundary charge fractionalization has recently been generalized through the discovery of higher-order topological insulators (HOTIs) whose topology is solely protected by crystalline symmetries and which can host corner fractional charges in 2D and 3D [5][6][7][8][9][10][11][12][13][14].…”

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confidence: 99%

Bound states in the continuum of higher-order topological insulators

2020

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We show that lattices with higher-order topology can support corner-localized bound states even in the absence of a bulk energy gap. Topological bound states in these phases thus constitute condensed matter realizations of bound states in the continuum (BICs). We propose a method for the direct identification of BICs in condensed matter settings and use it to demonstrate the existence of BICs in a concrete lattice model. Although the onset for these states is given by corner-induced filling anomalies in certain topological crystalline phases, additional symmetries are required to protect the BICs from hybridizing with their degenerate bulk states. We analytically demonstrate the protection mechanism for BICs in this model and numerically show how breaking this mechanism transforms the BICs into resonances. Our work shows that topological bulk-boundary correspondences are immune to the existence of interfering bulk bands, expanding the search space for crystalline topological phases.arXiv:1908.05687v2 [cond-mat.str-el]

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confidence: 99%

Bound states in the continuum of higher-order topological insulators

2020

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“…The existence of HOTIs and the lessons from the study of TI(QAHI)/SC heterostructures lead us to ask the natural question that whether * yanzhb5@mail.sysu.edu.cn Majorana corner modes (MCMs, i.e., MZMs bound at the corners) or chiral Majorana hinge modes (CMHMs) can also be achieved in a HOTI/SC heterostructure. It is worth noting that such a question is quite timely as recently the electronic material candidates for SOTIs, both in two dimensions (2D) and three dimensions (3D), are growing [57][58][59][60][61][62][63]. Moreover, signature of MZM has also been observed in a heterostructure which consists of a bismuth thin film (a SOTI with TRS [57]), a conventional s-wave SC, and magnetic iron clusters [64].…”

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confidence: 99%

“…As our proposed scheme requires neither special pairings nor magnetic fields, we believe it should be simple to implement experimentally. Consider the fast growth of material candidates for SOTIs [57][58][59][60][61][62][63], we can foresee that such novel heterostructures will be synthesised and investigated in the near future. Experimentally, MCMs and CMHMs can be probed by STM techniques [64] and transport experiments [97].…”

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confidence: 99%

Majorana corner and hinge modes in second-order topological insulator/superconductor heterostructures

Yan

2019

Phys. Rev. B

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As platforms of Majorana modes, topological insulator (quantum anomalous Hall insulator)/superconductor (SC) heterostructures have attracted tremendous attention over the past decade. Here we substitute the topological insulator by its higher-order counterparts. Concretely, we consider second-order topological insulators (SOTIs) without time-reversal symmetry and investigate SOTI/SC heterostructures in both two and three dimensions. Remarkably, we find that such novel heterostructures provide natural realizations of second-order topological superconductors (SOTSCs) which host Majorana corner modes in two dimensions and chiral Majorana hinge modes in three dimensions. As here the realization of SOTSCs requires neither special pairings nor magnetic fields, such SOTI/SC heterostructures are outstanding platforms of Majorana modes and may have wide applications in future.Over the past decade, topological superconductors (TSCs) have attracted continuous and tremendous attention[1-9]. Among various TSCs, one-dimensional (1d) and twodimensional (2d) TSCs without time-reversal symmetry (TRS) have attracted particular interest as they harbor Majorana zero modes (MZMs) at their boundaries[10-12] and in the cores of vortices [13][14][15][16], respectively. Owing to their fractional nature, MZMs are ideal candidates to construct nonlocal qubits immune to local decoherence[10]. Moreover, owing to their non-Abelian statistics [17], their braiding operations are found to realize elementary quantum gates. Thus, MZMs are believed to be building blocks of topological quantum computation [18] and have been actively sought in experiments [19][20][21][22][23][24][25][26][27][28][29].As is known, odd-parity superconductors (SCs) provide natural realizations of TSCs, however, they are unfortunately rare in nature. In a seminal paper [14], Fu and Kane pointed out that topological insulator (TI)/SC heterostructures provide an effective realization of odd-parity superconductivity. Accordingly, in the presence of magnetic field, vortices emerging in such heterostructures are found to carry MZMs. In a later influential paper[30], Qi et al pointed out that quantum anomalous Hall insulator (QAHI)/SC heterostructures provide a simple realization of 2d chiral TSCs which harbor not only vortex-core MZMs, but also chiral Majorana edge modes. These two theoretical works have triggered a lot of experimental works on TI(QAHI)/SC heterostructures [28,29,[31][32][33][34][35][36][37][38][39][40][41], and remarkable progress in detecting vortex-core MZMs has been witnessed in recent years [28,29,40,41].Very recently, TIs and TSCs have been generalized to include their higher-order counterparts [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Importantly, higher-order TIs (HOTIs) and TSCs (HOTSCs) have extended the conventional bulk-boundary correspondence. Accordingly, an n-th order TI or TSC in d dimensions host (d − n)dimensional boundary modes. For instance, a second-order TI (SOTI) in 2d and 3d host zero-dimensional (0d) corner modes an...

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“…Figure 3l depicts the profile of corner states, demonstrating their confinement to the corners of the crystal. Other realizations of higher-order TIs have been reported in [332][333][334][335][336][337][338][339][340][341][342][343][344][345][346].…”

Section: Higher-order Topological Insulatorsmentioning

confidence: 99%

Topological wave insulators: a review

Zangeneh-Nejad¹,

Alù²,

Fleury³

2020

Comptes Rendus. Physique

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Originally discovered in condensed matter systems, topological insulators (TIs) have been ubiquitously extended to various fields of classical wave physics including photonics, phononics, acoustics, mechanics, and microwaves. In the bulk, like any other insulator, electronic TIs exhibit an excessively high resistance to the flow of mobile charges, prohibiting metallic conduction. On their surface, however, they support one-way conductive states with inherent protection against certain types of disorder and defects, defying the common physical wisdom of electronic transport in presence of impurities. When transposed to classical waves, TIs open a wealth of exciting engineering-oriented applications, such as robust routing, lasing, signal processing, switching, etc., with unprecedented robustness against various classes of defects. In this article, we first review the basic concept of topological order applied to classical waves, starting from the simple onedimensional example of the Su-Schrieffer-Heeger (SSH) model. We then move on to two-dimensional wave TIs, discussing classical wave analogues of Chern, quantum Hall, spin-Hall, Valley-Hall, and Floquet TIs. Finally, we review the most recent developments in the field, including Weyl and nodal semimetals, higherorder topological insulators, and self-induced non-linear topological states.

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Two-Dimensional Second-Order Topological Insulator in Graphdiyne

Cited by 246 publications

References 76 publications

Bound states in the continuum of higher-order topological insulators

Bound states in the continuum of higher-order topological insulators

Majorana corner and hinge modes in second-order topological insulator/superconductor heterostructures

Topological wave insulators: a review

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