Valley-polarized quantum transport generated by gauge fields in graphene

Abstract

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...

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

“…We use Δ=29 meV [13] to compute R NL in figure 2(c) for G/hBN channel with zigzag edges, as well as to compute its band structure (figure A1(f) in appendix A) exhibiting gapped flat bands [32]. Figure 4(a) shows s xy v , computed using the Kubo formula [35,37] combined with a valley-projection scheme [10,39], for a rhomboid supercell of G/hBN with periodic boundary conditions described byĤ TB in equation (12). 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 .…”

“…The valley-projection scheme [10,39] we employ for numerically exact calculations of the VH conductivity s xy v in figure 4 via the real-space Kubo formula [36,37] relies on the artificial separation of the BZ of graphene into K and ¢ K regions with different chirality. In this scheme, the current defined over the whole BZ is separated into an electronic current due electrons in the K ( ¢ K ) valley.…”

Valleytronics in merging Dirac cones: All-electric-controlled valley filter, valve, and universal reversible logic gate

“…The ballistic transport picture has been widely used in the modeling of valleyfiltering effect in nanostructures [1,[17][18][19][20][21][22][23][24][25][26][27][28][29]31,34]. In realistic device, the inevitable presence of impurities, defects, and many-body effects can quantitatively change the results, but the valley-filtering effect shall qualitatively remain robust as recently demonstrated for the case of strained graphene [30].…”

Electron dynamics in strained graphene

“…Interesting transport phenomena can also be explored in terms of the interplay of external magnetic field and strain-induced pseudo-magnetic field. 106 As the external magnetic field affects the two valleys equally, while the pseudo-magnetic field exhibits opposite signs, the balance between the two valleys will be broken. An ideal proposal for valley filtering considers adding an external magnetic field with the same magnitude as the constant pseudo-magnetic field in triaxially strained graphene, where electrons in one valley experiences vanishing magnetic field, while those in the other valley feel a magnetic field twice the intensity of the external field.…”

“…An ideal proposal for valley filtering considers adding an external magnetic field with the same magnitude as the constant pseudo-magnetic field in triaxially strained graphene, where electrons in one valley experiences vanishing magnetic field, while those in the other valley feel a magnetic field twice the intensity of the external field. 106 Moreover, in the presence of a strong external magnetic field, the bulk bands of the system will be gapped by the development of Landau levels. One can then explore the transport phenomena due to the confined states that propagate only along the folds discussed in Sect.…”