Visualizing Strain-Induced Pseudomagnetic Fields in Graphene through an hBN Magnifying Glass

Jiang, Yuhang; Mao, Jinhai; Duan, Junxi; Lai, Xinyuan; Watanabe, Kenji; Taniguchi, Takashi; Andrei, Eva Y.

doi:10.1021/acs.nanolett.6b05228

Cited by 143 publications

(147 citation statements)

References 30 publications

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“…However, unlike our observed linear scaling (implying ∝ , in Fig. 3d), the energies of those peaks were reported 14,20,24,25 to scale as ∝ √ . Previous studies have observed equally spaced peaks in LDOS spectra in graphene and attributed them to confinement effects 26 .…”

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confidence: 92%

Strain Modulated Superlattices in Graphene

et al. 2020

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Strain engineering of graphene takes advantage of one of the most dramatic responses of Dirac electrons enabling their manipulation via strain-induced pseudo-magnetic fields. Numerous theoretically proposed devices, such as resonant cavities and valley filters, as well as novel phenomena, such as snake states, could potentially be enabled via this effect. These proposals, however, require strong, spatially oscillating magnetic fields while to date only the generation and effects of pseudo-gauge fields which vary at a length scale much larger than the magnetic length have been reported. Here we create a periodic pseudo-gauge field profile using periodic strain that varies at the length scale comparable to the magnetic length and study its effects on Dirac electrons. A periodic strain profile is achieved by pulling on graphene with extreme (>10%) strain and forming nanoscale ripples, akin to a plastic wrap pulled taut at its edges. Combining scanning tunneling microscopy and atomistic calculations, we find that spatially oscillating strain results in a new quantization different from the familiar Landau quantization observed in previous studies. We also find that graphene ripples are characterized by large variations in carbon-carbon bond length, directly impacting the electronic coupling between atoms, which within a single ripple can be as different as in two different materials. The result is a single graphene sheet that effectively acts as an electronic superlattice. Our results thus also establish a novel approach to synthesize an effective 2D lateral heterostructure -by periodic modulation of lattice strain. Main Text:Due to its high electronic mobility, optical transparency, mechanical strength and flexibility, graphene is attractive for electronic applications 1,2 . However, several factors prevent the realization of common electronic applications. For example, the lack of a band gap prevents an effective off-state in graphene transistors. Furthermore, Klein tunneling 3 , in which electrons pass through an electrostatic barrier with perfect transmission, prevents electron confinement by traditional gating methods. Figure 1. Engineering periodic pseudo electric and magnetic fields at strained interfaces: (a)High(low) density of carbon atoms and hence electrons are created in regions marked by lightblue (yellow) regions due to a strain gradient. This inhomogeneous charge distribution results in an electric field (green arrows). (b) Stretching of bonds cause the Dirac cones at K and K' points to shift symmetrically (yellow) from their original unstrained positions (light-blue) in the reciprocal space. As a momentum shift can be interpreted as generating a pseudo-vector potential term eA/c 15 , (where is the electronic charge and is the velocity of light) this creates pseudo-magnetic fields with opposite signs at the two valleys. (c) The strain associated with rippling creates rare (yellow) and dense (turquoise) regions in the graphene, effectively acting as two different materials in a superlattice. (d) Pseudo...

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confidence: 92%

Strain Modulated Superlattices in Graphene

et al. 2020

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“…In the second case of fold-like structures, graphene is positioned on top of an otherwise flat substrate and it is either mechanically or naturally folded 37 or wrinkled (due to relaxation of underlying lattice mistmatch induced strains), with the length of these structures much longer than their respective widths. Alternatively, it may be deposited on top of carefully designed substrates where folds form under deposition 31 . In the bump scenario, the membrane bends out of plane to accommodate to the roughness of the underlying surface while in the fold, it bends as it folds or wrinkles.…”

Section: Continuum Field Description Of Strain In Graphenementioning

confidence: 99%

Local versus extended deformed graphene geometries for valley filtering

Zhai

Sandler

2018

Phys. Rev. B

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The existence of two-inequivalent valleys in the band structure of graphene has motivated the search of mechanisms that allow their separation and control for potential device applications. Among the several schemes proposed in the literature, strain-induced out-of-plane deformations (occurring naturally or intentionally designed in graphene samples), ranks among the best candidates to produce separation of valley currents. Because valley filtering properties in these structures is, however, highly dependent on the type of deformation and setups considered, it is important to identify the relevant factors determining optimal operation and detection of valley currents. In this paper we present a comprehensive comparison of two typical deformations commonly found in graphene samples: local centro-symmetric bubbles and extended folds/wrinkles. Using the Dirac model for graphene and the second-order Born approximation we characterize the scattering properties of the bubble deformation, while numerical transmission matrix methods are used for the fold-like deformations. In both cases, we obtain the dependence of valley polarization on the geometrical parameters of deformations, and discuss their possible experimental realizations. Our study reveals that extended deformations act as better valley filters in broader energy ranges and present more robust features against variations of geometrical parameters and incident current directions.

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“…In recent years, much progress has been achieved in the area of substrate engineering for graphene. 8,63 Setups like those reported in Ref. 63, for example, create a periodic strain modulation in graphene deposited on top of SiO 2 nanospheres.…”

Section: Discussionmentioning

confidence: 87%

Sublattice symmetry breaking and Kondo-effect enhancement in strained graphene

et al. 2019

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Kondo physics in doped monolayer graphene is predicted to exhibit unusual features due to the linear vanishing of the pristine material's density of states at the Dirac point. Despite several attempts, conclusive experimental observation of the phenomenon remains elusive. One likely obstacle to identification is a very small Kondo temperature scale TK in situations where the chemical potential lies near the Dirac point. We propose tailored mechanical deformations of monolayer graphene as a means of revealing unique fingerprints of the Kondo effect. Inhomogeneous strains are known to produce specific alternating changes in the local density of states (LDOS) away from the Dirac point that signal sublattice symmetry breaking effects. Small LDOS changes can be amplified in an exponential increase or decrease of TK for magnetic impurities attached at different locations. We illustrate this behavior in two deformation geometries: a circular "bubble" and a long fold, both described by Gaussian displacement profiles. We calculate the LDOS changes for modest strains and analyze the relevant Anderson impurity model describing a magnetic atom adsorbed in either a "top-site" or a "hollow-site" configuration. Numerical renormalization-group solutions of the impurity model suggest that higher expected TK values, combined with distinctive spatial patterns under variation of the point of graphene attachment, make the top-site configuration the more promising for experimental observation of signatures of the Kondo effect. The strong strain sensitivity of TK may lift top-site Kondo physics into the range experimentally accessible using local probes such as scanning tunneling microscopy.

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Visualizing Strain-Induced Pseudomagnetic Fields in Graphene through an hBN Magnifying Glass

Cited by 143 publications

References 30 publications

Strain Modulated Superlattices in Graphene

Strain Modulated Superlattices in Graphene

Local versus extended deformed graphene geometries for valley filtering

Sublattice symmetry breaking and Kondo-effect enhancement in strained graphene

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