Berry Curvature Dipole in Strained Graphene: A Fermi Surface Warping Effect

Abstract

It has been recently established that optoelectronic and non-linear transport experiments can give direct access to the dipole moment of the Berry curvature in non-magnetic and non-centrosymmetric materials. Thus far, non-vanishing Berry curvature dipoles have been shown to exist in materials with substantial spin-orbit coupling where low-energy Dirac quasiparticles form tilted cones. Here, we prove that this topological effect does emerge in two-dimensional Dirac materials even in the complete absence of spin-orbit coupling. In these systems, it is the warping of the Fermi surface that triggers sizeable Berry dipoles. We show indeed that uniaxially strained monolayer and bilayer graphene, with substrate-induced and gate-induced band gaps respectively, are characterized by Berry curvature dipoles comparable in strength to those observed in monolayer and bilayer transition metal dichalcogenides.

Spin–valley Hall phenomena driven by Van Hove singularities in blistered graphene

“…The Berry curvature peaks around Γ correspond to the avoided band crossing points between the VBM and CBM, as can be seen in the 3D band. This shift from the actual K to L points is due to local symmetry change, and this phenomenon has also been observed in strained graphene 44 . Furthermore, the inversion symmetry breaking induced by lattice deformation generates Rashba splitting, which can be seen in the spin texture of the VBM and CBM, as shown in Fig.…”

Nonlinear Hall Effect with Time‐Reversal Symmetry: Theory and Material Realizations

“…Graphene has been put forward as a paradigmatic example of a spin–orbit‐free material with a non‐vanishing BCD. [ 79 ] Importantly, experimental signatures of a non‐linear Hall effect with time‐reversal symmetry have been recently found in corrugated bilayer graphene. [ 80 ] As we will discuss below, the origin of the non‐linear Hall effect in graphene does not stem from the Dirac cone shifting mechanism of bilayer WTe 2 .…”

“…The anisotropy in the Fermi velocity combined with the warping of the Fermi surface instead produces a distortion of the Fermi lines (see Figure ) that endows the system with a non‐zero BCD even if an explicit tilt term is absent. [ 79 ] Precisely as for the case of TMDs both the gapped Dirac cones contribute in an equal manner to the total BCD. [ 14 ] Note also that a finite value of the BCD occurs even if the strain‐induced renormalization of the warping coefficients is disregarded (cf.…”

“…The appearance of a non‐vanishing BCD in the system can be understood considering the Berry curvature properties in this strain‐free () case. [ 79 ] As shown in Figure 8a the central Dirac cone has a symmetric Berry curvature and thus it gives a vanishing contribution to the BCD. When taken by themselves, the leg Dirac cones instead have only a mirror symmetric Berry curvature profile and therefore their contribution to the BCD is non‐zero.…”

Eshelby-twisted three-dimensional moiré superlattices

“…Within the Boltzmann picture of transport and the relaxation time approximation, Sodemann and Fu derived the Hall-current response to the electric field up to the second order [37]. The nonlinear Hall effect in inversion-asymmetric systems has attracted great attention in recent years [38][39][40][41][42][43][44].…”