Theory of Valley Hall Conductivity in Graphene with Gap

Ando, Tsuneya

doi:10.7566/jpsj.84.114705

Cited by 44 publications

(48 citation statements)

References 115 publications

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“…The supercell is either clean or it contains long-or short-range disorder (delineated in appendix D) as additional terms in the on-site energy ε i . In the clean limit, we confirm [15] that σ xy v =2e 2 /h is quantized inside the gap (figure 4(a)), as well as that the Fermi sea states just beneath the gap provide the main contribution to it [3]. For longrange disorder that does not mix valleys, σ xy v remains close to the clean limit, but within a smaller energy range than E g (figure 4(a)) due to disorder-induced broadening of the states [15].…”

supporting

confidence: 64%

“…The numerically exact result in figure 2(c), for a G/hBN system described by the same simplistic Hamiltonian employed [1][2][3][4]15] to obtain s ¹ 0 xy v , is clearly incompatible with the interpretation of ¹ R 0 NL based on the picture of topological valley currents carried by the Fermi sea states just beneath the gap [3]. Such currents are conjectured to be persistent and circulating in equilibrium [3], but they become mediative VH currents connecting the two crossbars in figure 1 under the application of a bias voltage.…”

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confidence: 99%

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Deciphering the origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride with ab initio quantum transport: Fermi surface edge currents rather than Fermi sea topological valley currents

et al. 2018

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The recent observation (Gorbachev et al 2014 Science 346 448) of nonlocal resistance R NL near the Dirac point (DP) of multiterminal graphene on aligned hexagonal-boron nitride (G/hBN) has been interpreted as the consequence of topological valley Hall currents carried by the Fermi sea states just beneath the bulk gap E g induced by inversion symmetry breaking. However, the corresponding valley Hall conductivity s xy v , quantized inside E g , is not directly measurable. Conversely, the Landauer-Büttiker formula, as a numerically exact approach to observable nonlocal transport quantities, yields R NL ≡ 0 for the same simplistic Hamiltonian of gapped graphene that generates s ¹ 0 xy v OPEN ACCESS RECEIVED

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supporting

confidence: 64%

mentioning

confidence: 99%

Deciphering the origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride with ab initio quantum transport: Fermi surface edge currents rather than Fermi sea topological valley currents

et al. 2018

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“…The valley related physics can be investigated either using the Dirac's equation [25,44,45] or by performing non-local transport calculations using the Landauer-Büttiker formalism in Hall bar geometries [24,25]. The former can be cumbersome for arbitrary types of disorder, while the later becomes computationally prohibitive for large scale systems.…”

mentioning

confidence: 99%

“…[44] in the continuous limit, and takes into account all the contributions of intravalley and intervalley scattering to the conductivity through the full Hamiltonian.…”

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confidence: 99%

Valley-polarized quantum transport generated by gauge fields in graphene

2017

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We report on the possibility to simultaneously generate in gaphene a bulk valley-polarized dissipative transport and a quantum valley Hall effect by combining strain-induced gauge fields and real magnetic fields. Such unique phenomenon results from a "resonance/anti-resonance" effect driven by the superposition/cancellation of superimposed gauge fields which differently affect time reversal symmetry. The onset of a valley-polarized Hall current concomitant to a dissipative valley-polarized current flow in the opposite valley is revealed by a e 2 /h Hall conductivity plateau. We employ efficient linear scaling Kubo transport methods combined with a valley projection scheme to access valley-dependent conductivities and show that the results are robust against disorder.In graphene and other two-dimensional materials, degenerate valleys of energy bands, well-separated in momentum space, constitute a discrete degree of freedom for low-energy carriers, provided intervalley mixing is negligible (case of long range disorder). Such valley degree of freedom can then be seen as a nonvolatile information carrier, provided that it can be coupled to external probes. Similarly to research in graphene spintronics [1,2], valleytronics and controlling the valley degree of freedom in graphene and other 2D materials has attracted a considerable attention [3][4][5], and many studies have investigated different options to realize valley polarized current or to filter electrons with a given valley polarization [6][7][8][9][10][11][12]. In presence of broken inversion symmetry, the valley index is also predicted to play a similar role as the spin degree of freedom in phenomena such as Hall transport, magnetization, optical transition selection rules, and chiral edge modes [13][14][15][16]. Recently, it has been shown that for modest levels of strain, graphene can also sustain a classical valley Hall effect that can be detected in nonlocal transport measurements [17]. All this stimulates the search for efficient control of valley dynamics by magnetic, electric, and optical means, which would form the basis of valley based information processing.On the other hand, it was soon realized that nonuniformly strained graphene can be modeled by the inclusion of a gauge field in the effective Hamiltonian (though it is not Berry-like). Such gauge field preserves time reversal symmetry, but induces pseudomagnetic fields (PMFs) of opposite signs in the two valleys forming the low-energy electronic bandstructure [18]. In particular, mechanical deformations aligned along three main crystallographic directions were predicted to generate strong gauge fields, acting effectively as an uniform magnetic field, opening the possibility to trigger a pseudomagnetic quantum Hall effect for strained superlattices [19]. Experimentally, evidences of PMFs with values varying from few tens up to hundreds of Tesla have been reported [20,21]. Finally, Gorbachev and coworkers recently measured intriguingly large nonlocal resistance signals in a situation where the alig...

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“…In recent years there have been theoretical 2,7,[21][22][23][24] and experimental 5,25-28 studies of VHE. Due to the similarity between SHE and VHE, most existing theoretical proposals for VHE are based on essentially the same physical mechanism as for SHE 13,36 , where either bulk or local valley-resolved perturbations are required.…”

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confidence: 99%

Geometric valley Hall effect and valley filtering through a singular Berry flux

Huang

et al. 2017

Phys. Rev. B

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Conventionally, a basic requirement to generate valley Hall effect (VHE) is that the Berry curvature for conducting carriers in the momentum space be finite so as to generate anomalous deflections of the carriers originated from distinct valleys into different directions. We uncover a geometric valley Hall effect (gVHE) in which the valley-contrasting Berry curvature for carriers vanishes completely except for the singular points. The underlying physics is a singular non-π fractional Berry flux located at each conical intersection point in the momentum space, analogous to the classic AharonovBohm effect of a confined magnetic flux in real space. We demonstrate that, associated with gVHE, exceptional skew scattering of valley-contrasting quasiparticles from a valley-independent, scalar type of impurities can generate charge neutral, transverse valley currents. As a result, the massless nature of the quasiparticles and their high mobility are retained. We further demonstrate that, for the particular Berry flux of π/2, gVHE is considerably enhanced about the skew scattering resonance, which is electrically controllable. A remarkable phenomenon of significant practical interest is that, associated with gVHE, highly efficient valley filtering can arise. These phenomena are robust against thermal fluctuations and disorders, making them promising for valleytronics applications.

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Theory of Valley Hall Conductivity in Graphene with Gap

Cited by 44 publications

References 115 publications

Deciphering the origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride with ab initio quantum transport: Fermi surface edge currents rather than Fermi sea topological valley currents

Deciphering the origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride with ab initio quantum transport: Fermi surface edge currents rather than Fermi sea topological valley currents

Valley-polarized quantum transport generated by gauge fields in graphene

Geometric valley Hall effect and valley filtering through a singular Berry flux

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