Confining and repulsive potentials from effective non-Abelian gauge fields in graphene bilayers

Abstract

We investigate the effect of shear and strain in graphene bilayers, under conditions where the distortion of the lattice gives rise to a smooth one-dimensional modulation in the stacking sequence of the bilayer. We show that strain and shear produce characteristic Moiré patterns which can have the same visual appearance on a large scale, but representing graphene bilayers with quite different electronic properties. The different features in the low-energy electronic bands can be ascribed to the effect of a fictitious non-Abelian gauge field mimicking the smooth modulation of the stacking order. Strained and sheared bilayers show a complementary behavior, which can be understood from the fact that the non-Abelian gauge field acts as a repulsive interaction in the former, expelling the electron density away from the stacking domain walls, while behaving as a confining interaction leading to localization of the electronic states in the sheared bilayers. In this latter case, the presence of the effective gauge field explains the development of almost flat low-energy bands, resembling the form of the zeroth Landau level characteristic of a Dirac fermion field. The estimate of the gauge field strength in those systems gives a magnitude of the order of several tens of tesla, implying a robust phenomenology that should be susceptible of being observed in suitably distorted bilayer samples.

Emergent flat band lattices in spatially periodic magnetic fields

“…periodic strain or Zeeman field that may be easier to implement experimentally. Since the continuum description of graphene moiré also has the form of Dirac electrons subject to non-Abelian gauge potentials [29][30][31], it is possible to use similar arguments to understand the origin of the moiré flat bands as well.…”

“…One main task of this paper is to provide practical ways of realizing 2D flat bands with different crystalline symmetries by design, not relying on moiré structures, thus enabling exploration of exotic phases in a larger parameter space. This is made possi-ble through a more generic understanding of the origin of moiré flat bands, which motivates us to replace the moiré potential [29][30][31] by periodic external magnetic fields or other artificial crystal potentials such as Zeeman or strain fields [32][33][34][35], that can now be created and controlled experimentally.…”

One-Dimensional Moiré Physics and Chemistry in Heterostrained Bilayer Graphene

“…The strain-induced gaps arise from the potential difference between the layers, resulting in a pseudoscalar effective potential as a transverse electric field . This effect adds to the strain-induced local gauge fields that result in a valley-dependent pseudomagnetic field capable of polarizing the pseudospin. − The width of these moiré bands ( w v and w c ) decreases with the magnitude of the strain, yet features are sensitive to the magnitude and direction of the strain exerted. For compressive heterostrain, smaller strains lead to flatter bands, and simultaneously, Δ vc increases while Δ v–1 and Δ c+1 decrease, interpreted as valence and conduction bands moving away from each other.…”

WKB estimate of bilayer graphene's magic twist angles

“…At a discrete set of magic twist angles, bilayer graphene develops low-energy flat bands [1,2] that lead to strong correlation physics including surprising superconductivity [3][4][5][6][7][8], novel orbital magnetism [9][10][11], and the quantum anomalous Hall effect [12][13][14]. The presence of narrow bands has recently been attributed to a twist-angle-dependent non-abelian SU(2) gauge field experienced by the two-dimensional (2D) Dirac fermions in bilayer graphene [2,[15][16][17]. In the case of 2D Dirac fermions with a magnetic field represented by an abelian U(1) gauge field, it has long been known that robust zeroenergy states appear at any magnetic field strength [18][19][20][21], with degeneracy equal to the total number of flux quanta [22,23].…”