Umklapp electron-electron scattering in bilayer graphene moiré superlattice

Controlling Umklapp Scattering in a Bilayer Graphene Moiré Superlattice

“…In the SLG hBN moiré, R Uee increases monotonically with superlattice period and charge carrier density . In contrast, R Uee in the BLG moiré superlattice is predicted to depend nonmonotonically on the superlattice period . In this Letter, we experimentally verified this prediction.…”

“…Recent calculations (that treat both electron− electron Coulomb interaction and the moirésuperlattice potential perturbatively) predict that in aligned heterostructures of Bernal bilayer graphene (BLG) and hBN, Uee scattering processes should be the primary source of resistance. 5 In this Letter, we experimentally verify that in high-mobility moirésuperlattices of BLG and hBN, Uee is the dominant source of resistance near half-filling. Our studies show that the strength of Uee depends nonmonotonically on the superlattice period.…”

“…A realistic Fermi liquid is, however, not Galilean-invariant; a finite coupling to an underlying lattice provides a mechanism for the momentum relaxation of the quasiparticles via the Umklapp process . Umklapp electron–electron (Uee) scattering is the fundamental mechanism that allows the transfer of momentum from electrons to the lattice and imparts electrical resistance to the metal. − In this process, the crystal lattice gives a momentum kick to a pair of interacting electrons, backscattering them on the other side of the Fermi surface. Their quasimomentum is conserved, modulo a reciprocal lattice vector G boldk bold1 + boldk bold2 = boldk bold3 + boldk bold4 + boldG where ℏ k 1 and ℏ k 2 and ℏ k 3 and ℏ k 4 are the initial and final quasimomenta of the two electrons near the Fermi level, respectively, and G is a non-zero reciprocal lattice vector of the crystal.…”

“…To understand the number density limits over which Umklapp processes are seen, recall that at very low n / n 0 values, transport in graphene is dominated by electron–hole puddles; ,, this gives a practical lower bound of n / n 0 at which e–e scattering is detectable . A more accurate lower limit is obtained by the constraint that the Uee process imposes on Fermi wave vector k F (eq ); this sets a lower bound on | n / n 0 | equal to π/(2√3) = 0.91 (see section S4 of the Supporting Information).…”

“…A more accurate lower limit is obtained by the constraint that the Uee process imposes on Fermi wave vector k F (eq ); this sets a lower bound on | n / n 0 | equal to π/(2√3) = 0.91 (see section S4 of the Supporting Information). At the other extreme, at high number densities, one begins to encounter electron–hole scattering processes at the principal mini band edges because of the moiré-induced van Hove singularity (Figure b), which masks the Umklapp scattering process …”