Tomonaga-Luttinger liquid parameters of magnetic waveguides in graphene

Abstract

Electronic waveguides in graphene formed by counterpropagating snake states in suitable inhomogeneous magnetic fields are shown to constitute a realization of a Tomonaga-Luttinger liquid. Due to the spatial separation of the right- and left-moving snake states, this non-Fermi liquid state induced by electron-electron interactions is essentially unaffected by disorder. We calculate the interaction parameters accounting for the absence of Galilei invariance in this system, and thereby demonstrate that non-Fermi liquid effects are significant and tunable in realistic geometries.Comment: 10 pages, 5 figures, published versio

Magnetic scattering of Dirac fermions in topological insulators and graphene

“…[32][33][34] For suitable 1D magnetic field profiles, it is possible to have magnetic waveguides (along the y-direction), 35,36 where electron-electron interaction effects play an important role. 37 Periodic magnetic fields, i.e., 1D magnetic superlattices, have also been addressed. [38][39][40][41] For radially symmetric fields, total angular momentum conservation again simplifies the problem and gives an effective 1D theory.…”

Beating oscillation and Fano resonance in the laser assisted electron transmission through graphene δ-function magnetic barriers

“…The interaction of an external uniform magnetic field with the chiral charge carriers plays an important role in manipulating the low energy properties of graphene which have been a subject of intense research in recent years 14 . On the other hand, the use of inhomogeneous magnetic field has given birth to the concept of magnetic barrier in a graphene with a view to confine the Dirac quasi-particles in the Landau levels that turns out to be an efficient tool to tailor the charge and spin transports (e.g., the suppression of the KT) in graphene based devices and has been studied exhaustively in last decade [8][9][10][15][16][17] .…”

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.…”

“…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.…”

“…Since the problem remains homogeneous along the x-direction, p x =hk x is still conserved. For the physics described below, the Zeeman coupling b gives only tiny corrections [29] and will be neglected. Moreover, there are no valley-mixing terms, thus we can focus on a single valley.…”