Optical 
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-insulators: Topological obstructions to optical Wannier functions in the atomistic susceptibility tensor

Mechelen, Todd Van; Bharadwaj, Sathwik; Jacob, Zubin; Slager, Robert-Jan

doi:10.1103/physrevresearch.4.023011

Cited by 9 publications

(8 citation statements)

References 75 publications

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“…Therefore, the optical N-invariant and the bulk-boundary correspondence relating robust topologically protected edge states to bulk topology are fundamentally different from the 'Krein index' . We emphasize that the topological hydrodynamic excitations in this paper have important implications beyond the linearized continuum model and can be generalized to include the lattice symmetry and local-field effects [17]. The topological protection is robust beyond the linear regime.…”

Section: Optical N-invariantmentioning

confidence: 86%

“…The optical N-invariant classifies the electromagnetic topology in the presence of electron-electron interactions through the bulk atomistic susceptibility tensor. It was shown that the optical N-invariant is the winding number of the atomistic susceptibility tensor [17]. This response function tensor is a many-body Green's function of the system, which has both spatial and temporal dispersion (i.e.…”

Section: Optical N-invariantmentioning

confidence: 99%

“…Recently, a new topological electromagnetic phase of graphene characterized by the optical N-invariant (N ∈ Z) was proposed [16,17]. This new topological phase arises only in the hydrodynamic regime of the interacting many-body electron system.…”

Section: Introductionmentioning

confidence: 99%

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Optical N-plasmon: topological hydrodynamic excitations in graphene from repulsive Hall viscosity

Sun,

Van Mechelen,

Bharadwaj

et al. 2023

New J. Phys.

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Edge states occurring in Chern and quantum spin-Hall phases are signatures of the topological electronic band structure in two-dimensional (2D) materials. Recently, a new topological electromagnetic phase of graphene characterized by the optical N-invariant was proposed. Optical N-invariant arises from repulsive Hall viscosity in hydrodynamic many-body electron systems, distinct from the Chern and Z2 invariants. In this paper, we introduce the topologically protected edge excitation -- optical N-plasmon of interacting many-body electron systems in the topological optical N-phase. These optical N-plasmons are signatures of the topological plasmonic band structure in 2D materials. We demonstrate that optical N-plasmons exhibit unique dispersion relations, stability against various boundary conditions and edge profiles when compared with the topologically trivial edge magneto plasmons. Based on the optical N-plasmon, we design an ultra sub-wavelength broadband topological hydrodynamic circulator, which is a chiral quantum radio-frequency circuit component crucial for information routing and interfacing quantum-classical computing systems. Furthermore, we reveal that optical N-plasmons can be effectively tuned by the neighboring dielectric environment without breaking the topological properties. Our work provides a smoking gun signature of topological electromagnetic phases occuring in two-dimensional materials arising from repulsive Hall viscosity.

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Section: Optical N-invariantmentioning

confidence: 86%

Section: Optical N-invariantmentioning

confidence: 99%

See 1 more Smart Citation

Optical N-plasmon: topological hydrodynamic excitations in graphene from repulsive Hall viscosity

Sun,

Van Mechelen,

Bharadwaj

et al. 2023

New J. Phys.

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“…The past decade has witnessed an ever increasing interest in topological matter. Topological insulators and semi-metals provide [1][2][3] in this regard a direct route to mimic intrinsic topological features and, owing to the inclusion of (crystalline) symmetries, a broad range of results have been achieved [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. While on a case by case bases the synergy between topology and geometry has been rather well established, the past years have seen a reinvigorated interest in the geometrical side.…”

mentioning

confidence: 99%

Quantum geometry beyond projective single bands

Bouhon¹,

Timmel²,

Slager³

2023

Preprint

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The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many geometrical concepts for single bands, the exploration of these concepts to a multi-band paradigm still promises a new field of interest. Formally, multi-band systems, featuring in particular degeneracies, have been related to projective spaces, explaining also the success of relating quantum geometrical aspects of flat band systems, albeit usually in the single band picture. Here, we propose a different route involving Plücker embeddings to represent arbitrary classifying spaces, being the essential objects that encode all the relevant topology. This paradigm allows for the quantification of geometrical quantities directly in readily manageable vector spaces that a priori do not involve projectors or the need of flat band conditions. As a result, our findings are shown to pave the way for identifying new geometrical objects and defining metrics in arbitrary multi-band systems, especially beyond the single flatband limit, promising a versatile tool that can be applied in contexts that range from response theories to finding quantum volumes and bounds on superfluid densities as well as possible quantum computations.

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“…Introduction.-Topological phases of matter [1,2] offer an intriguing regime with rich unprecedented phenomena. Although the past decade has seen remarkable theoretical progresses [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], culminating in versatile topological classification schemes [19][20][21][22][23]. These methods by and large can be traced back to evaluating symmetry representations of all the bands below an energy gap.…”

mentioning

confidence: 99%

Experimental observation of meronic topological acoustic Euler insulators

Jiang¹,

Bouhon²,

Wu³

et al. 2022

Preprint

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We report on the experimental observation of a gapped nontrivial Euler topology in an acoustic metamaterial. The topological invariant in this case is the Euler class, which characterizes the twodimensional geometry of the acoustic Bloch wave function of multiple bands in the Brillouin zone-a feature that cannot be captured by conventional topological classification schemes. Starting from a carefully designed acoustic system, we retrieve a rich phase diagram that includes the gapped Euler phase on top of non-Abelian topological nodal phases. In particular we find that the gapped phase is characterized by a meron (half-skyrmion) type topology in which the cancellation of the orbital Zak phases by Zak phases of the bands contributes in forming the characterizing winding number of the acoustic bands. Using pump-probe techniques, we are able to extract the wave functions of the acoustic Bloch bands and demonstrate the non-trivial Euler topology via a direct observation of the meron geometry of these bands in the Brillouin zone, in addition to the detection of the acoustic bulk and edge dispersions. We finally observe a topological edge state in the gapped Euler phase which is a direct manifestation of the underlying cancellation of the Zak phases. These experimental features reveal the unprecedented topological Euler phase as well as setting a benchmark for probing acoustic wave function geometry in the Brillouin zone.

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Optical N -insulators: Topological obstructions to optical Wannier functions in the atomistic susceptibility tensor

Cited by 9 publications

References 75 publications

Optical N-plasmon: topological hydrodynamic excitations in graphene from repulsive Hall viscosity

Optical N-plasmon: topological hydrodynamic excitations in graphene from repulsive Hall viscosity

Quantum geometry beyond projective single bands

Experimental observation of meronic topological acoustic Euler insulators

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