Disordered graphene and boron nitride in a microwave tight-binding analog

Barkhofen, Sonja; Bellec, Matthieu; Kuhl, Ulrich; Mortessagne, Fabrice

doi:10.1103/physrevb.87.035101

Cited by 35 publications

(48 citation statements)

References 56 publications

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“…Alternatively, discrete photonic systems (e. g. photonic lattices or microwave cavities), with graphene-like structures, have been employed as condensed-matter analogues [12][13][14][15]. In microwave experiments, the tightbinding form of graphene's Hamiltonian [16] can be established by using a honeycomb lattice of evanescently coupled dielectric resonators [14,15].…”

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confidence: 99%

“…In microwave experiments, the tightbinding form of graphene's Hamiltonian [16] can be established by using a honeycomb lattice of evanescently coupled dielectric resonators [14,15]. Dirac points and signature of the linear dispersion relation have been observed [13][14][15].…”

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confidence: 99%

“…We establish a twodimensional tight-binding regime where the electromagnetic field is mostly confined within the discs and spreads out evanescently. The experimental details are described in [14,15]. Via a movable loop-antenna, the reflected signal S 11 is measured over a given frequency range at the disc positions r using a vectorial network analyzer.…”

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Topological Transition of Dirac Points in a Microwave Experiment

et al. 2013

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By means of a microwave tight-binding analogue experiment of a graphene-like lattice, we observe a topological transition between a phase with a point-like band gap characteristic of massless Dirac fermions and a gapped phase. By applying a controlled anisotropy on the structure, we investigate the transition directly via density of states measurements. The wave function associated with each eigenvalue is mapped and reveals new states at the Dirac point, localized on the armchair edges. We find that with increasing anisotropy, these new states are more and more localized at the edges.

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Topological Transition of Dirac Points in a Microwave Experiment

et al. 2013

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“…[21][22][23][24] Such experiments are well controlled and easy to perform (in comparison to experiments with real graphene or polyacetylene) and hence, offer a versatile tool to investigate in detail the properties of these systems. In this article, we study the ballistic single-electron transport through small graphene nanoribbons by microwave transmission experiments.…”

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confidence: 99%

Transport gap engineering by contact geometry in graphene nanoribbons: Experimental and theoretical studies on artificial materials

et al. 2017

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Electron transport in small graphene nanoribbons is studied by microwave emulation experiments and tight-binding calculations. In particular, it is investigated under which conditions a transport gap can be observed. Our experiments provide evidence that armchair ribbons of width 3m + 2 with integer m are metallic and otherwise semiconducting, whereas zigzag ribbons are metallic independent of their width. The contact geometry, defining to which atoms at the ribbon edges the source and drain leads are attached, has strong effects on the transport. If leads are attached only to the inner atoms of zigzag edges, broad transport gaps can be observed in all armchair ribbons as well as in rhomboid-shaped zigzag ribbons. All experimental results agree qualitatively with tight-binding calculations using the nonequilibrium Green's function method.

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“…The data processing from reflexion measure- (9) of Ref. [25]). The horizontal dashed lines indicate the gap labelling for an infinite lattice.…”

Section: Figmentioning

confidence: 99%

Energy landscape in a Penrose tiling

et al. 2016

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Since their spectacular experimental realisation in the early 80's [1], quasicrystals [2] have been the subject of very active research, whose domains extend far beyond the scope of solid state physics. In optics, for instance, photonic quasicrystals have attracted strong interest [3] for their specific behaviour, induced by the particular spectral properties, in light transport [4][5][6], plasmonic [7] and laser action [8]. Very recently, one of the most salient spectral feature of quasicrystals, namely the gap labelling [9], has been observed for a polariton gas confined in a one dimensional quasi-periodic cavity [10]. This experimental result confirms a theory which is now very complete in dimension one [11,12]. In dimension greater than one, the theory is very far from being complete. Furthermore, some intriguing phenomena, like the existence of self-similar eigenmodes can occur [13]. All this makes two dimensional experimental realisations and numerical simulations pertinent and attractive. Here, we report on measurements and energy-scaling analysis of the gap labelling and the spatial intensity distribution of the eigenstates for a microwave Penrose-tiled quasicrystal. Far from being restricted to the microwave system under consideration, our results apply to a more general class of systems.Quasicrystals are alloys that are ordered but lack translational symmetry. In dimension two, they can be modelled with a collection of polygons (tiles) that cover the whole plane, so that each pattern (a sub-collection of tiles) appears, up to translation, with a given density but the tiling is not periodic. A typical example is given by the Penrose tiling [14]. Here, we implement a microwave realisation of a Penrose-tiled lattice using a set of coupled dielectric resonators [see Fig. 1 (a)]. The microwave setup used has shown its versatility by successfully addressing various physical situations ranging from Anderson localisation [15] to topological phase transition in graphene [16], and provided the first experimental realisation of the Dirac oscillator [17].We establish a two-dimensional tight-binding regime [18], where the electromagnetic field is mostly confined within the resonators. For an isolated resonator, only a single mode is important in a broad spectral range around the bare frequency E b 6.65 GHz. This mode spreads out evanescently, so that the coupling FIG. 1:Microwave Penrose-tiled quasicrystal. (a) Diamond-vertex Penrose-tiled quasicrystal, where the tiling is superposed to guide the eye (thin diamonds in green). The sites of the lattice are occupied by dielectric resonators (ceramic cylinders of 5 mm height and 8 mm diameter) with a high index of refraction (n = 6). The lattice is sandwiched between two aluminium plates (the upper one is not shown). The microwaves are excited by a movable loop antenna. (b) Experimentally obtained DOS as a function of frequency, the white and gray zones indicate the main frequency bands, Ei, and the gaps, ∆Ei, respectively. The bare frequency E b is indicated by the wh...

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Disordered graphene and boron nitride in a microwave tight-binding analog

Cited by 35 publications

References 56 publications

Topological Transition of Dirac Points in a Microwave Experiment

Topological Transition of Dirac Points in a Microwave Experiment

Transport gap engineering by contact geometry in graphene nanoribbons: Experimental and theoretical studies on artificial materials

Energy landscape in a Penrose tiling

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