Higher-order Floquet topological phases with corner and bulk bound states

Rodriguez-Vega, Martin; Kumar, Abhishek; Seradjeh, Babak

doi:10.1103/physrevb.100.085138

Cited by 125 publications

(67 citation statements)

References 56 publications

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“…Recently, the authors in Refs. [32][33][34][35] constructed Floquet second-order TI/Scs. Particularly, the authors of Ref.…”

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confidence: 99%

Floquet higher-order topological insulators and superconductors with space-time symmetries

Peng

2020

Phys. Rev. Research

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Floquet higher-order topological insulators and superconductors (HOTI/SCs) with an order-two space-time symmetry or antisymmetry are classified. This is achieved by considering unitary loops, whose nontrivial topology leads to the anomalous Floquet topological phases, subject to a spacetime symmetry/antisymmetry. By mapping these unitary loops to static Hamiltonians with an order-two crystalline symmetry/antisymmetry, one is able to obtain the K groups for the unitary loops and thus complete the classification of Floquet HOTI/SCs. Interestingly, we found that for every order-two nontrivial space-time symmetry/antisymmetry involving a half-period time translation, there exists a unique order-two static crystalline symmetry/antisymmetry, such that the two symmetries/antisymmetries give rise to the same topological classification. Moreover, by exploiting the frequency-domain formulation of the Floquet problem, a general recipe that constructs model Hamiltonians for Floquet HOTI/SCs is provided, which can be used to understand the classification of Floquet HOTI/SCs from an intuitive and complimentary perspective. CONTENTS 32 A. Equivalent classification with symmetrized evolution operators 32 B. Decomposition of time evolution operators 32 C. Order of HOTI/SCs and symmetry-breaking mass terms 32 References 33

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“…Recently, the authors in Refs. [32][33][34][35] constructed Floquet second-order TI/Scs. Particularly, the authors of Ref.…”

mentioning

confidence: 99%

Floquet higher-order topological insulators and superconductors with space-time symmetries

Peng

2020

Phys. Rev. Research

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“…6 are not the primitive reciprocal lattice vectors, might be used to generate fractal photonic spectra, such as the Hofstadter butterfly [25]. Higher order topological phases other than those characterized by the Chern number [26] might also be realized in Floquet photonic crystals. With strong Bloch-wave modulations readily implementable on microchips, Floquet photonic crystals open the door to the realization of a plethora of optical phenomena [4,6] and light-matter phases [27,28] with broken time-reversal symmetry, in a practical cavity-free architecture.…”

Section: Arxiv:190202887v1 [Physicsoptics] 7 Feb 2019mentioning

confidence: 99%

Anomalous Quantum Hall Effect of Light in Bloch-Wave Modulated Photonic Crystals

Fang

Wang

2019

Phys. Rev. Lett.

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Effective magnetic fields have enabled unprecedented manipulation of neutral particles including photons. In most studied cases, the effective gauge fields are defined through the phase of mode coupling between spatially discrete elements, such as optical resonators and waveguides in the case for photons. Here, in the paradigm of Bloch-wave modulated photonic crystals, we show creation of effective magnetic fields for photons in conventional dielectric continua for the first time, via Floquet band engineering. By controlling the phase and wavevector of Bloch waves, we demonstrated anomalous quantum Hall effect for light with distinct topological band features due to delocalized wave interference. Based on a cavity-free architecture, in which Bloch-wave modulations can be enhanced using guided-resonances in photonic crystals, the study here opens the door to the realization of effective magnetic fields at large scales for optical beam steering and topological light-matter phases with broken time-reversal symmetry.Photons, being charge neutral, are not susceptible to magnetic fields. Recently, several methods have been proposed to create effective magnetic fields for photons, including chiral mode coupling [1] and dynamic index modulation [2], leading to topological photonic states [3,4] and nonreciprocal light propagation [5,6]. In the scheme of dynamic index modulation, the effective gauge field is equivalent to the phase of a point modulation that is exerted to mediate the coupling between two spatially localized optical resonators with different frequencies [2]. Such a revelation enables analogies between modulated optical resonator lattices and condensed matter systems under magnetic fields via commonly used tight-binding models, which also imposes challenges for experimental realization and practical uses. However, it is unknown how to create effective magnetic fields for photons in a continuum of conventional dielectrics, where electromagnetic fields are delocalized, invalidating the notion of local phase of mode coupling for effective gauge fields. Here, we study a new paradigm of dynamically modulated continua, that is photonic crystals subject to Bloch-wave modulations, in which spatial gauge fields for photons can be created via Floquet band engineering [7,8]. In this approach, the continuum modulation induces static-band hybridization, leading to an equation of motion for electromagnetic waves that resembles that of charged particles under magnetic fields.The paradigm of modulated electromagnetic continuum not only extends the concept of effective magnetic fields for photons to a largely unexplored yet experimentally accessible regime, but also reveals topological photonic effects that have not been demonstrated before. As we will show, by selecting the wavevectors of Bloch-wave modulations, net effective magnetic flux through the unit cell of photonic crystals vanishes. Nevertheless, the Floquet bands can still attain nonzero Chern numbers in * kfang3@illinois.edu the presence of time-reversal symmetry...

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“…Higher-order topological phases have been studied in systems protected by order-two symmetries (e.g., reflection and inversion symmetry [22][23][24][26][27][28]), rotational invariance [25,29,30], and combinations of the above [31][32][33]. Gapless hinge and corner excitations may also appear in interacting models [34,35], Floquet phases [36,37] and can coexist with gapless surface states [38]. Higher-order topology does not necessarily rely on an underlying regular lattice, but can be also found in quasicrystals respecting certain spatial symmetries [39,40].…”

Section: Introductionmentioning

confidence: 99%

Second-order bulk-boundary correspondence in rotationally symmetric topological superconductors from stacked Dirac Hamiltonians

2020

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Two-dimensional second-order topological superconductors host zero-dimensional Majorana bound states at their boundaries. In this work, focusing on rotation-invariant crystalline topological superconductors, we establish a bulk-boundary correspondence linking the presence of such Majorana bound states to bulk topological invariants introduced by Benalcazar et al. We thus establish when a topological crystalline superconductor protected by rotational symmetry displays second-order topological superconductivity. Our approach is based on stacked Dirac Hamiltonians, using which we relate transitions between topological phases to the transformation properties between adjacent gapped boundaries. We find that in addition to the bulk rotational invariants, the presence of Majorana boundary bound states in a given geometry depends on the interplay between weak topological invariants and the location of the rotation center relative to the lattice. We provide numerical examples for our predictions and discuss possible extensions of our approach.

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Higher-order Floquet topological phases with corner and bulk bound states

Cited by 125 publications

References 56 publications

Floquet higher-order topological insulators and superconductors with space-time symmetries

Floquet higher-order topological insulators and superconductors with space-time symmetries

Anomalous Quantum Hall Effect of Light in Bloch-Wave Modulated Photonic Crystals

Second-order bulk-boundary correspondence in rotationally symmetric topological superconductors from stacked Dirac Hamiltonians

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