Merging and alignment of Dirac points in a shaken honeycomb optical lattice

We investigate the effects of Rashba and intrinsic spin-orbit couplings (SOC) in graphynes. First, we develop a general method to address spin-orbit couplings within the tight-binding theory. Then, we apply this method to α-, β-, and γ-graphyne, and determine the SOC parameters in terms of the microscopic hopping and on-site energies. We find that for α-graphyne, as in graphene, the intrinsic SOC opens a non-trivial gap, whereas the Rashba SOC splits each Dirac cone into four. In β-and γ-graphyne, the Rashba SOC can lead to a Lifshitz phase transition, thus transforming the zero-gap semiconductor into a gapped system or vice versa, when pairs of Dirac cones annihilate or emerge. The existence of internal (within the benzene ring) and external SOC in these compounds allows us to explore a myriad of phases not available in graphene.

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“…Merging of the Dirac cones and the corresponding gap opening in shaken honeycomb optical lattices have been recently studied in Ref. [34].…”

Section: Discussionmentioning

confidence: 99%

Tight-binding theory of spin-orbit coupling in graphynes

2014

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“…An illustrative example is the merging of Dirac cones upon a deformation of the honeycomb lattice that introduces anisotropies along the different hopping directions. 33 This anisotropy may be driven by shaking 34 or by superposing different square optical lattices and tuning the relative weight of each of them.…”

Section: 28mentioning

confidence: 99%

Dirac cones beyond the honeycomb lattice: A symmetry-based approach

Miert

Smith

2016

Phys. Rev. B

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Recently, several new materials exhibiting massless Dirac fermions have been proposed. However, many of these do not have the typical graphene honeycomb lattice, which is often associated with Dirac cones. Here, we present a classification of these different two-dimensional Dirac systems based on the space groups, and discuss our findings within the context of a minimal two-band model. In particular, we show that the emergence of massless Dirac fermions can be attributed to the mirror symmetries of the materials. Moreover, we uncover several novel Dirac systems that have up to twelve inequivalent Dirac cones, and show that these can be realized in (twisted) bilayers. Hereby, we obtain systems with an emergent SU(2N) valley symmetry with N=1,2,4,6,8,12. Our results pave the way to engineer different Dirac systems, besides providing a simple and unified description of materials ranging from square-and β-graphynes, to Pmmn-Boron, TiB2, phosphorene, and anisotropic graphene.

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“…Our analysis, when restricted to linear polarization and high-frequency regime, agrees with the results obtained in shaken optical lattices. 25 In addition, we also consider different field polarizations and finite frequency effects. Importantly, at lower frequencies, we find that the coupling between the Floquet bands, that characterize the properties of the driven system, gives rise to out-of-equilibrium phases with no analogue in the static system in which multiple PDPs emerge.…”

Section: Introductionmentioning

confidence: 99%

Merging of Dirac points and Floquet topological transitions in ac-driven graphene

2013

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We investigate the effect of an in-plane ac electric field coupled to electrons in the honeycomb lattice and show that it can be used to manipulate the Dirac points of the electronic structure. We find that the position of the Dirac points can be controlled by the amplitude and the polarization of the field for high-frequency drivings, providing a new platform to achieve their merging, a topological transition which has not been observed yet in electronic systems. Importantly, for lower frequencies we find that the multiphoton absorptions and emissions processes yield the creation of additional pairs of Dirac points. This provides an additional method to achieve the merging transition by just tuning the frequency of the driving. Our approach, based on Floquet formalism, is neither restricted to specific choice of amplitude or polarization of the field, nor to a low-energy approximation for the Hamiltonian.

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Merging and alignment of Dirac points in a shaken honeycomb optical lattice

Cited by 44 publications

References 44 publications

Tight-binding theory of spin-orbit coupling in graphynes

Tight-binding theory of spin-orbit coupling in graphynes

Dirac cones beyond the honeycomb lattice: A symmetry-based approach

Merging of Dirac points and Floquet topological transitions in ac-driven graphene

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