Nonlocal topological valley transport at large valley Hall angles

Abstract

Berry curvature hot spots in two-dimensional materials with broken inversion symmetry are responsible for the existence of transverse valley currents, which give rise to giant nonlocal dc voltages. Recent experiments in high-quality gapped graphene have highlighted a saturation of the nonlocal resistance as a function of the longitudinal charge resistivity $\rho_{{\rm c}, xx}$, when the system is driven deep into the insulating phase. The origin of this saturation is, to date, unclear. In this work we show that this behavior is fully compatible with bulk topological transport in the regime of large valley Hall angles (VHAs). We demonstrate that, for a fixed value of the valley diffusion length, the dependence of the nonlocal resistance on $\rho_{{\rm c}, xx}$ weakens for increasing VHAs, transitioning from the standard $\rho^3_{{\rm c}, xx}$ power-law to a result that is independent of $\rho_{{\rm c}, xx}$.Comment: 5 pages, 3 figure

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

“…Interestingly, the very recent experiments [25] on quasiballistic hBN/G/hBN heterostructures exhibiting metallic-like r xx have measured R NL that does not scale as r µ xx 3 at low temperatures T;1.5 K (such cubic scaling is restored at T;40 K). Also, deep into the insulating regime (i.e., with large ρ xx ) R NL becomes independent of ρ xx [5].…”

“…The recent measurements [1] of a sharply peaked nonlocal resistance R NL in a narrow energy range near the Dirac point (DP) of multiterminal graphene on hexagonal-boron nitride (G/hBN) heterostructures have been interpreted as the manifestation of the valley Hall effect (VHE) [2][3][4][5]. In this interpretation, injecting charge current I 3 between leads 3 and 4 of the device illustrated in figure 1 generates a VH current in the first crossbar flowing from lead 1 to lead 2, which traverses the channel of length L (;4 μm in the experiments [1]), and is finally converted into a nonlocal voltage V NL between leads 5 and 6 by the inverse VHE in the second crossbar.…”

“…However, s xy v is not directly observable. An attempt to connect s xy v to observable nonlocal resistance is made [1,4,5] using semiclassical transport theory [16], which assumes diffusive transport with ℓ v as the valley diffusion length [5]. However, semiclassical transport theory is not applicable [17,18] to electronic transport near the DP.…”

“…It has been argued [1,4,5] that experimental confirmation of topological valley currents carried by the Fermi sea states just beneath the bulk gap E g is achieved by observing different dependences encoded in equation (1), such as r µ R xx NL 3 and µℓ R e L NL v . However, such dependences were originally derived [16] for the diffusive spin Hall current as the mediative current between the two crossbars, and they can be observed for different types of mediative currents as long as they propagate by diffusion (as demonstrated by the measurements of nonlocal resistance in multiterminal graphene due to direct and inverse spin Hall effect [11]).…”

Anomalous Nonlocal Resistance and Spin-Charge Conversion Mechanisms in Two-Dimensional Metals

“…Solutions for Eq. (6) with these boundary conditions can be obtained via numerical integration [40,41]. To obtain analytical results, however, we assume that the aspect ratio is large (L W ) and the width is smaller than the spin diffusion length (W s ) .…”