Winding Vector: How to Annihilate Two Dirac Points with the Same Charge

Montambaux, Gilles; Lim, Lih-King; Fuchs, Jean-Noël; Piéchon, Frédéric

doi:10.1103/physrevlett.121.256402

Cited by 49 publications

(58 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, our experiments provide a recipe for the implementation of Dirac cones in solid state materials: the touching of a flat and a dispersive band with winding R = 2 evolves into two Dirac cones in the presence of strain. This behaviour has been predicted for other lattice geometries 36 , and it presents a natural playground to investigate the transition between different topological phases when particle interactions are present 41,42 or when time reversal symmetry is broken. Polaritons are particularly well suited to study these scenarios: thanks to their excitonic component they present significant repulsive interactions in the high density regime 43 and they are sensitive to external magnetic fields, allowing the implementation of quantum Hall phases 44,45 .…”

Section: Topological Invariants Of Tilted and Type-iii Dirac Conessupporting

confidence: 62%

“…S4). This is a topological Lifshitz transition in which two Dirac cones with opposite topological charge merge and annihilate, predicted for standard s-band graphene 4,36 and reported in photonic 7,8 and atomic 5,6 honeycomb lattices and in black phosphorus 9 . At the merging point (4 = 0.5, Fig.…”

Section: Tilted and Semi-dirac Conesmentioning

confidence: 60%

“…Matrix elements coupling the high and low energy manifolds are treated in a second order perturbation theory 38 . In this form, the winding of L can be calculated as a winding vector 36…”

Section: Topological Invariants Of Tilted and Type-iii Dirac Conesmentioning

confidence: 99%

See 2 more Smart Citations

Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene

et al. 2019

View full text Add to dashboard Cite

The extraordinary electronic properties of Dirac materials, the two-dimensional partners of Weyl semimetals, arise from the linear crossings in their band structure. When the dispersion around the Dirac points is tilted, the emergence of intricate transport phenomena has been predicted, such as modified Klein tunnelling, intrinsic anomalous Hall effects and ferrimagnetism. However, Dirac materials are rare, particularly with tilted Dirac cones. Recently, artificial materials whose building blocks present orbital degrees of freedom have appeared as promising candidates for the engineering of exotic Dirac dispersions. Here we take advantage of the orbital structure of photonic resonators arranged in a honeycomb lattice to implement photonic lattices with semi-Dirac, tilted and, most interestingly, type-III Dirac cones that combine flat and linear dispersions. The tilted cones emerge from the touching of a flat and a parabolic band with a non-trivial topological charge. These results open the way to the synthesis of orbital Dirac matter with unconventional transport properties and, in combination with polariton nonlinearities, to the study of topological and Dirac superfluids in photonic lattices.

show abstract

Section: Topological Invariants Of Tilted and Type-iii Dirac Conessupporting

confidence: 62%

Section: Tilted and Semi-dirac Conesmentioning

confidence: 60%

See 1 more Smart Citation

Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene

et al. 2019

View full text Add to dashboard Cite

show abstract

“…The lower pair evolves from the M and the Γ point. Its merging/emergence at time-reversal invariant momenta (TRIM) resembles a situation we already encountered in the two-band model on a staggered Mielke lattice [25]. There, we provided a complete scenario of a (+−) going into a (++) Dirac pair.…”

Section: B Energy Spectrummentioning

confidence: 59%

“…The evolution of the lower two bands then raises the question of how the two distinct fusion scenarios of Dirac points can be smoothly connected, namely, a (+−) pair of Dirac points emerging at M evolving into a (++) pair merging at Γ. Actually, a similar phenomenon has been studied by us in a two-band model, the staggered Mielke lattice [25]. While the integer-valued winding number characterizes the circulation of the Dirac spinor on the great circle of the Bloch sphere, the great circle itself is not fixed generally -it evolves according to the Hamiltonian parameters.…”

Section: Introductionmentioning

confidence: 84%

Dirac points emerging from flat bands in Lieb-kagome lattices

et al. 2020

Self Cite

View full text Add to dashboard Cite

The energy spectra for the tight-binding models on the Lieb and kagomé lattices both exhibit a flat band. We present a model which continuously interpolates between these two limits. The flat band located in the middle of the three-band spectrum for the Lieb lattice is distorted, generating two pairs of Dirac points. While the upper pair evolves into graphene-like Dirac cones in the kagomé limit, the low energy pair evolves until it merges producing the band-bottom flat band. The topological characterization of the Dirac points is achieved by projecting the Hamiltonian on the two relevant bands in order to obtain an effective Dirac Hamiltonian. The low energy pair of Dirac points is particularly interesting in this respect: when they emerge, they have opposite winding numbers, but as they merge, they have the same winding number. This apparent paradox is due to a continuous rotation of their states in pseudo-spin space, characterized by a winding vector. This simple, but quite rich model, suggests a way to a systematic characterization of two-band contact points in multiband systems.

show abstract

Foray into the topology of poly‐bi‐[8]‐annulenylene

Muruganandam,

Sajjan,

Kais

2023

Natural Sciences

View full text Add to dashboard Cite

Analyzing phase transitions using the inherent geometrical attributes of a system has garnered enormous interest over the past few decades. The usual candidate often used for investigation is graphene—the most celebrated material among the family of tri‐coordinated graphed lattices. We show in this report that other inhabitants of the family demonstrate equally admirable structural and functional properties that at its core are controlled by their topology. Two interesting members of the family are cyclooctatrene (COT) and COT‐based polymer: poly‐bi‐[8]‐annulenylene, both in one and two dimensions that have been investigated by polymer chemists over a period of 50 years for its possible application in batteries exploiting its conducting properties. A single COT unit is demonstrated herein to exhibit topological solitons at sites of a broken bond similar to an open one‐dimensional Su–Schrieffer–Heeger (SSH) chain. We observe that poly‐bi‐[8]‐annulenylene in one dimension mimics two coupled SSH chains in the weak coupling limit, thereby showing the presence of topological edge modes. In the strong coupling limit, we investigate the different parameter values of our system for which we observe zero‐energy modes. Further, the application of an external magnetic field and its effects on the band flattening of the energy bands has also been studied. In two dimensions, poly‐bi‐[8]‐annulenylene forms a square‐octagon lattice which upon breaking time‐reversal symmetry goes into a topological phase forming noise‐resilient edge modes. We hope our analysis would pave the way for synthesizing such topological materials and exploiting their properties for promising applications in optoelectronics, photovoltaics, and renewable energy sources.Key Points We show in this paper tri‐coordinated lattice systems: cylooctatrene (COT) and COT‐based polymer: poly‐bi‐[8]‐annulenylene exhibit exotic topological properties. Flat bands are generated upon application of tailored magnetic flux for poly‐bi‐[8]‐annulenylene in one dimension. Insights from this paper open the possibility of using these polymers as an experimental ground to observe many flat‐band and topology‐related phenomena.

show abstract

Winding Vector: How to Annihilate Two Dirac Points with the Same Charge

Cited by 49 publications

References 32 publications

Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene

Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene

Dirac points emerging from flat bands in Lieb-kagome lattices

Foray into the topology of poly‐bi‐[8]‐annulenylene

Contact Info

Product

Resources

About