Conductance quantization and snake states in graphene magnetic waveguides

Abstract

We consider electron waveguides (quantum wires) in graphene created by suitable inhomogeneous magnetic fields. The properties of uni-directional snake states are discussed. For a certain magnetic field profile, two spatially separated counter-propagating snake states are formed, leading to conductance quantization insensitive to backscattering by impurities or irregularities of the magnetic field.PACS numbers: 75.70.Ak

Landau Levels and Edge States in Graphene with Strong Spin-Orbit Coupling

“…In Sec. 5, we turn to a waveguide geometry, defined by a suitable inhomogeneous magnetic field [25,26,27,28,29,30,31,32,33,34]. We show that the SOIs give rise to inter-esting spin textures of the chiral states propagating in the waveguides.…”

“…We focus on parameter set (B), since for set (A), the spin splitting is minimal and less interesting. The spectrum consists of two qualitatively different states, namely states of bulk Landau character for large |k x |L, and a set of propagat-ing waveguide modes [28]. The spectral asymmetry seen in Fig.…”

“…The dominant splitting, which is already present for ∆ = λ = 0, comes from the splitting of symmetric and antisymmetric linear combinations of the Landau states for y < −L and y > L with increasing overlap in the waveguide region [28]. Asymptotically, the dispersion relation of all positive-energy snake states is E(k x → +∞) hv F k x [28]. For intermediate k x and (∆ , λ ) = 0, however, we get spin-split snake states out of the previously spin-degenerate states.…”

“…For ∆ = λ = A x = V = 0, both cases (ε = ±1) have been studied in detail in Ref. [28]. Technically, one determines the eigenstates and the spectrum, E(k x ), by matching the wavefunctions in the three different regions, which results in an energy quantization condition.…”

“…In this section, we consider a spatially inhomogeneous situation, where a magnetic waveguide [27,28,29] along the x-direction can be realized. Since the problem remains homogeneous along the x-direction, p x =hk x is still conserved.…”