Topological Valley Current in Non-Uniformly Strained Graphene

In graphene, electrons reside in binary valleys that can be used for information processing. Breaking the valley degeneracy requires breaking inversion symmetry, typically achieved by non-uniform strain, such as a strain gradient [1]. In fact, a strain gradient applies a valley-dependent pseudo magnetic field Bps [2]. However, a full physical picture of valley requires an understanding of how Bps alters valley transport and connects to emerging phenomena such as the valley Hall effect.
Here, we report the transport evidence of global pseudo-Landau levels and valley edge current induced by Bps. We fabricated strained graphene transistors with a strain gradient of 0.8%/µm. We measured the longitudinal resistance Rxx dependence on the carrier density and magnetic field. In the Rxx plot, we observed clear Landau levels. Remarkably, we observed secondary oscillations emerging around each Landau level, which disperse linearly with the applied magnetic field, in direct comparison to the pristine graphene case [3]. Such oscillations, named as pseudo-Landau level, signal an equivalent magnetic field of 0.5 ± 0.1 T. Since Bps is purely strain-driven, we expect these pseudo-Landau levels to still exist under zero external field. Indeed, at zero magnetic field, resistance oscillates periodically with carrier density. The zero-feild oscillation allows us to independently confirm the existence of Bps.
Unlike a real magnetic field, Bps acts oppositely on carriers in different valleys. Therefore, the total effective field, Bps + Breal, leads to preferred valley polarization. We examined the transport of valley-polarized current by measuring the current along opposite edges, where we observed different currents flowing, indicating a significant edge current. In the unpolarized case, the edge current consists of two electron flows from different valleys, which cancel each other out. We attribute the observed edge current to the net flow of polarized valley carriers. This valley edge current is the first demonstration of topological valley transport in monolayer graphene.
In summary, we observed the first experimental evidence of Bps-induced topological valley current. This work provides a foundation for inducing valley polarization and directing valley carriers via a pseudo-magnetic field. We note that our method is broadly applicable to other material systems, such as MoS2 and WSe2, where strong spin-orbit coupling locks the spin and valley degrees of freedom. Manipulating valley and spin carriers offers a next-generation, energy-efficient computing paradigm [4].

[1] Phys. Rev. Lett. 115, 245501(2015)
[2] Rev. Mod. Phys. 81, 109 (2009)
[3] Nature 438, 201–204 (2005)
[4] Nat Rev Mater 1, 16055 (2016)