Valley filter and valley valve in graphene

Rycerz, Adam; Tworzydło, J.; Beenakker, C. W. J.

doi:10.1038/nphys547

Cited by 1,633 publications

(1,538 citation statements)

References 33 publications

(32 reference statements)

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“…Experimental evidence of valley confinement has been seen in monolayer MoS 2 , where the carrier populations in distinct valleys can be controlled by optically exciting the samples with circularly polarized light, as recently demonstrated by three independent groups [26][27][28] . This development may be the first step towards a new field of valleytronic devices 155,156 . These spin, orbit and valley properties are quite distinctive in TMDCs and may lead to as yet unforeseen applications.…”

Section: Spin Orbit and Valley Interactionsmentioning

confidence: 95%

Electronics and optoelectronics of two-dimensional transition metal dichalcogenides

et al. 2012

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699M any two-dimensional (2D) materials exist in bulk form as stacks of strongly bonded layers with weak interlayer attraction, allowing exfoliation into individual, atomically thin layers 1 . The form receiving the most attention today is graphene, the monolayer counterpart of graphite. The electronic band structure of graphene has a linear dispersion near the K point, and charge carriers can be described as massless Dirac fermions, providing scientists with an abundance of new physics 2,3 . Graphene is a unique example of an extremely thin electrical and thermal conductor 4 , with high carrier mobility 5 , and surprising molecular barrier properties 6,7 .Many other 2D materials are known, such as the TMDCs 8,9 , transition metal oxides including titania-and perovskite-based oxides 10,11 , and graphene analogues such as boron nitride (BN) 12,13 . In particular, TMDCs show a wide range of electronic, optical, mechanical, chemical and thermal properties that have been studied by researchers for decades 9,14,15 . There is at present a resurgence of scientific and engineering interest in TMDCs in their atomically thin 2D forms because of recent advances in sample preparation, optical detection, transfer and manipulation of 2D materials, and physical understanding of 2D materials learned from graphene.The 2D exfoliated versions of TMDCs offer properties that are complementary to yet distinct from those in graphene. Graphene displays an exceptionally high carrier mobility exceeding 10 6 cm 2 V -1 s -1 at 2 K (ref. 16) and exceeding 10 5 cm 2 V -1 s -1 at room temperature for devices encapsulated in BN dielectric layers 5 ; because pristine graphene lacks a bandgap, however, fieldeffect transistors (FETs) made from graphene cannot be effectively switched off and have low on/off switching ratios. Bandgaps can be engineered in graphene using nanostructuring [17][18][19] , chemical functionalization 20 and applying a high electric field to bilayer graphene 21 , but these methods add complexity and diminish mobility. In contrast, several 2D TMDCs possess sizable bandgaps around 1-2 eV (refs 9,14), promising interesting new FET and optoelectronic devices.TMDCs are a class of materials with the formula MX 2 , where M is a transition metal element from group IV (Ti, Zr, Hf and so on), group V (for instance V, Nb or Ta) or group VI (Mo, W and so on), and X is a chalcogen (S, Se or Te). These materials form layered structures of the form X-M-X, with the chalcogen atoms in two hexagonal planes separated by a plane of metal atoms, as shown in Fig. 1a. Adjacent layers are weakly held together to form the bulk crystal in a variety of polytypes, which vary in stacking orders and metal atom coordination, as shown in Fig. 1e. The overall symmetry of TMDCs is hexagonal or rhombohedral, and the metal atoms have octahedral or trigonal prismatic coordination. The electronic properties of TMDCs range from metallic to semiconducting, as summarized in Table 1. There are also TMDCs that exhibit exotic behaviours such as charge density waves ...

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Section: Spin Orbit and Valley Interactionsmentioning

confidence: 95%

Electronics and optoelectronics of two-dimensional transition metal dichalcogenides

et al. 2012

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“…This necessarily induces intervalley mixing at the corners between two subsequent zigzag nanoribbon segments. This mixing is very strong in the lowest mode of the ring, where the direction of motion and the valley is tightly coupled in each arm of the hexagonal ring 16,22 ͑the zigzag edge is therefore another example ͑Color online͒ Ring conductance assuming a constant interaction model with charging energy U for the first 12 electrons in the conduction band ͑E Ͼ 0͒: At ⌽ =0 ͑dashed͒, the conductance shows a fourfold symmetry as a function of Fermi energy E F in the leads due to spin and valley degeneracies. At finite magnetic flux ͑ ⌽ / ⌽ 0 = 0.1, full line͒, the conductance peaks shift due to breaking of the valley degeneracy.…”

Section: Spectrum For a Hexagonal Ring With Zigzag Edgesmentioning

confidence: 99%

Aharonov-Bohm effect and broken valley degeneracy in graphene rings

et al. 2007

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We analyze theoretically the electronic properties of Aharonov-Bohm rings made of graphene. We show that the combined effect of the ring confinement and applied magnetic flux offers a controllable way to lift the orbital degeneracy originating from the two valleys, even in the absence of intervalley scattering. The phenomenon has observable consequences on the persistent current circulating around the closed graphene ring, as well as on the ring conductance. We explicitly confirm this prediction analytically for a circular ring with a smooth boundary modeled by a space-dependent mass term in the Dirac equation. This model describes rings with zero or weak intervalley scattering so that the valley isospin is a good quantum number. The tunable breaking of the valley degeneracy by the flux allows for the controlled manipulation of valley isospins. We compare our analytical model to another type of ring with strong intervalley scattering. For the latter case, we study a ring of hexagonal form with lattice-terminated zigzag edges numerically. We find for the hexagonal ring that the orbital degeneracy can still be controlled via the flux, similar to the ring with the mass confinement.

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“…Theoretical researches on graphene nanostructures have started much earlier [16][17][18][19] but speed up after it was realized that such systems are promising building blocks for a solid-state quantum computer [20,21]. In attempt to operate on a solid-state qubit [22] in graphene, one needs to deal with an obstacle that electrons occur in two degenerate families, corresponding to the presence of two different valleys in the band structure.…”

Section: Introductionmentioning

confidence: 99%

Electron Transport and Quantum-Dot Energy Levels in Z-Shaped Graphene Nanoconstriction with Zigzag Edges

Rycerz

2010

Acta Phys. Pol. A

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Motivated by recent advances in fabricating graphene nanostructures, we find that an electron can be trapped in Z-shaped graphene nanoconstriction with zigzag edges. The central section of the constriction operates as a single-level quantum dot, as the current flow towards the adjunct sections (rotated by 60 • ) is strongly suppressed due to mismatched valley polarization, although each section in isolation shows maximal quantum value of the conductance G 0 = 2 e 2 /h. We further show that the trapping mechanism is insensitive to the details of constriction geometry, except from the case when widths of the two neighboring sections are equal. The relation with earlier studies of electron transport through symmetric and asymmetric kinks with zigzag edges is also established.

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Valley filter and valley valve in graphene

Cited by 1,633 publications

References 33 publications

Electronics and optoelectronics of two-dimensional transition metal dichalcogenides

Electronics and optoelectronics of two-dimensional transition metal dichalcogenides

Aharonov-Bohm effect and broken valley degeneracy in graphene rings

Electron Transport and Quantum-Dot Energy Levels in Z-Shaped Graphene Nanoconstriction with Zigzag Edges

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