Gauge field induced by ripples in graphene

Guinea, F.; Horovitz, Baruch; Doussal, Pierre Le

doi:10.1103/physrevb.77.205421

Cited by 258 publications

(249 citation statements)

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“…This is reminiscent of the effect induced on charge carriers by magnetic field B applied perpendicular to the graphene plane [2,[12][13][14]. The strain-induced, pseudo-magnetic field B S or, more generally, gauge field vector potential A have opposite signs for graphene's two valleys K and K', which means that elastic deformations, unlike magnetic field, do not violate the time-reversal symmetry of a crystal as a whole [12][13][14]21,22].Based on this analogy between strain and magnetic field, we ask the following question: Is it possible to create such a distribution of strain that it results in a strong uniform pseudo-field B S and, accordingly, leads to a "pseudo-QHE" observable in zero B? The previous attempts to engineer energy gaps by applying strain [5][6][7] seem to suggest a negative answer.…”

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Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering

2009

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Among many remarkable qualities of graphene, its electronic properties attract particular interest due to a massless chiral character of charge carriers, which leads to such unusual phenomena as metallic conductivity in the limit of no carriers and the half-integer quantum Hall effect (QHE) observable even at room temperature [1-3]. Because graphene is only one atom thick, it is also amenable to external influences including mechanical deformation. The latter offers a tempting prospect of controlling graphene's properties by strain and, recently, several reports have examined graphene under uniaxial deformation [4][5][6][7][8]. Although the strain can induce additional Raman features [7,8], no significant changes in graphene's band structure have been either observed or expected for realistic strains of ~10% [9-11]. Here we show that a designed strain aligned along three main crystallographic directions induces strong gauge fields [12][13][14] that effectively act as a uniform magnetic field exceeding 10 T. For a finite doping, the quantizing field results in an insulating bulk and a pair of countercirculating edge states, similar to the case of a topological insulator [15][16][17][18][19][20]. We suggest realistic ways of creating this quantum state and observing the pseudo-magnetic QHE. We also show that strained superlattices can be used to open significant energy gaps in graphene's electronic spectrum.If a mechanical strain Δ varies smoothly on the scale of interatomic distances, it does not break the sublattice symmetry but rather deforms the Brillouin zone in such a way that the Dirac cones located in graphene at points K and K' are shifted in the opposite directions [2]. This is reminiscent of the effect induced on charge carriers by magnetic field B applied perpendicular to the graphene plane [2,[12][13][14]. The strain-induced, pseudo-magnetic field B S or, more generally, gauge field vector potential A have opposite signs for graphene's two valleys K and K', which means that elastic deformations, unlike magnetic field, do not violate the time-reversal symmetry of a crystal as a whole [12][13][14]21,22].Based on this analogy between strain and magnetic field, we ask the following question: Is it possible to create such a distribution of strain that it results in a strong uniform pseudo-field B S and, accordingly, leads to a "pseudo-QHE" observable in zero B? The previous attempts to engineer energy gaps by applying strain [5][6][7] seem to suggest a negative answer. Indeed, the hexagonal symmetry of the graphene lattice generally implies a highly anisotropic distribution of B S [21,22]. Therefore, the strain is expected to contribute primarily in the phenomena that do not average out in a random magnetic field such as weak localization [13,14]. Furthermore, a strong gauge field necessitates the opening of energy gaps due to Landau quantization, δE ≈ 400K B ⋅ (>0.1 eV for B S =10T) whereas no gaps were theoretically found for uniaxial strain as large as ≈25% [4]. The only way to induce significant gaps, ...

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Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering

2009

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“…This can be readily illustrated by considering a plain sheet of paper: try to compress it in the in-plane direction or perhaps pinch it in the center, and it will most certainly not get smaller, but will rather buckle. The importance of three-dimensional (3D) buckling in strained 2D materials has been pointed out earlier [10][11][12][13][14][15][16] . However, as accounting for 3D out-of-plane deformations significantly complicates calculations 12 , such deformations have either been omitted in theoretical studies, or the studied systems have been too small to describe the long-range corrugations 9,[17][18][19][20][21][22][23] .…”

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Atomic scale study of the life cycle of a dislocation in graphene from birth to annihilation

et al. 2013

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Dislocations, one of the key entities in materials science, govern the properties of any crystalline material. Thus, understanding their life cycle, from creation to annihilation via motion and interaction with other dislocations, point defects and surfaces, is of fundamental importance. Unfortunately, atomic-scale investigations of dislocation evolution in a bulk object are well beyond the spatial and temporal resolution limits of current characterization techniques. Here we overcome the experimental limits by investigating the two-dimensional graphene in an aberration-corrected transmission electron microscope, exploiting the impinging energetic electrons both to image and stimulate atomic-scale morphological changes in the material. The resulting transformations are followed in situ, atom-by-atom, showing the full life cycle of a dislocation from birth to annihilation. Our experiments, combined with atomistic simulations, reveal the evolution of dislocations in two-dimensional systems to be governed by markedly long-ranging out-of-plane buckling.

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“…Our mechanism is summarized as follows. An electron and its Andreev-reflected hole acquire a different amount of phase shift in the normal n-p region, due to spatially random pseudomagnetic fields induced by ripples 28,29 . The resulting random phase shifts can cause dephasing of the Andreev pairs, and hence a large reduction in the phase-coherent effect of the Josephson current near the CNP, where scattering by ripples becomes significant.…”

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“…Ripples, spatially non-uniform strains, are intrinsic structures of graphene 31 and affect the electron properties by inducing pseudomagnetic fields 28,29 . In contrast to real magnetic fields, the pseudomagnetic fields are opposite in their direction with respect to the other between the K and K 0 valleys.…”

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Complete gate control of supercurrent in graphene p–n junctions

et al. 2013

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In a conventional Josephson junction of graphene, the supercurrent is not turned off even at the charge neutrality point, impeding further development of superconducting quantum information devices based on graphene. Here we fabricate bipolar Josephson junctions of graphene, in which a p-n potential barrier is formed in graphene with two closely spaced superconducting contacts, and realize supercurrent ON/OFF states using electrostatic gating only. The bipolar Josephson junctions of graphene also show fully gate-driven macroscopic quantum tunnelling behaviour of Josephson phase particles in a potential well, where the confinement energy is gate tuneable. We suggest that the supercurrent OFF state is mainly caused by a supercurrent dephasing mechanism due to a random pseudomagnetic field generated by ripples in graphene, in sharp contrast to other nanohybrid Josephson junctions. Our study may pave the way for the development of new gate-tuneable superconducting quantum information devices.

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Gauge field induced by ripples in graphene

Cited by 258 publications

References 50 publications

Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering

Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering

Atomic scale study of the life cycle of a dislocation in graphene from birth to annihilation

Complete gate control of supercurrent in graphene p–n junctions

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