Topological properties of electronic states in multivalley two-dimensional materials, such as monoand bilayer graphene, or thin films of rhombohedral graphite, give rise to various unusual magnetotransport regimes. Here, we investigate the tunability of the topological magnetic moment (related to the Berry curvature) of electronic states in bilayer graphene using strain and vertical bias. We show how one can controllably vary the valley g-factor of the band-edge electrons, g * v , across the range 10 < |g * v | < 200, and we discuss the manifestations of the topological magnetic moment in the anomalous contribution towards the Hall conductivity and in the Landau level spectrum.FIG. 1. Top. Unstrained (left) and strained (right) bilayer graphene (BLG) with the intra-and interlayer couplings γ0,3,4 (modified by the strain) marked along the relevant hopping directions. Bottom. The magnitude of the valley g-factor at the conduction band edge of BLG, |g * v |, as a function of the interlayer asymmetry gap, ∆, for uniaxial strains of magnitude δ = 0% and 2% applied along the zigzag (ZZ) and armchair (AC) directions. A jump in |g * v | at ∆ ∼ 55 meV for δ = 0% is due to the disappearance of a central minivalley in the unstrained BLG spectrum upon the increase of the gap [1]. Inset shows |g * v | against uniaxial strain (up to δ = 4%) for various orientations of the strain tensor axes and ∆ = 20 meV (strain values used in the plot are marked by shapes). These images can also be used to characterize the effect of shear deformations described by Eq. (2) later in the text. * christian.moulsdale@postgrad.manchester.ac.uk Strain in bilayer graphene (BLG), sketched in Fig. 1, affects its low-energy electronic properties far greater than in its monolayer allotrope [2][3][4][5][6], generating qualitative changes in its low-energy spectrum close to the neutrality point. The earlier-discussed effects [2-4] of unilateral strain and shear deformations in Bernal (A B) stacked bilayers include the Lifshitz transition [7] for weakly n-doped and p-doped structures, accompanied by a redistribution (even a coalescence) of the Berry phase ±π singularities in the bilayer's electronic bands [1,2]. These changes are caused by the interplay between the intralayer and skew (AB ) interlayer hopping parameters of electrons, modified by the deformations.A transverse displacement field, induced by electrostatic gating of bilayers, is another factor that qualitatively changes their electronic properties. The displacement field generates an asymmetry between the layers, opening up a gap in the energy spectrum [1,8] and smearing the Berry phase singularities into "hot spots" of Berry curvature, Ω ± (p), located near the valley centers K ± (sign-inverted distributions are found in opposite valleys, Ω + (p) = Ω − (−p)). According to the fundamental properties of Bloch-Wannier functions [9, 10], a finite Berry curvature of the electronic bands is associated with a finite intrinsic angular momentum, therefore, a resulting magnetic moment of the plane-wave...

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We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kekulé-O coupling (KOC) modulation and a Dzyaloshinskii-Moriya interaction (DMI). Through a strain-based mechanism for inducing the KOC modulation, we identify four topological phases in terms of the KOC parameter and DMI strength. We calculate the thermal magnon Hall conductivity κ xy at low temperature in each of these phases. We predict an unconventional conductivity due to a non-zero Berry curvature emerging from band proximity effects in the topologically trivial phase. We find sign changes of κ xy as a function of the model parameters, associated with the local Berry curvature and occupation probability of the bulk bands. Throughout, κ xy can be easily tuned with external parameters such as the magnetic field and temperature.

We report the experimental investigation of transport through bilayer graphene (BLG)/chromium trihalide (CrX3; X=Cl, Br, I) van der Waals interfaces. In all cases, a large charge transfer from BLG to CrX3 takes place (reaching densities in excess of 10 13 cm −2 ), and generates an electric field perpendicular to the interface that opens a band gap in BLG. We determine the gap from the activation energy of the conductivity and find excellent agreement with the latest theory accounting for the contribution of the sigma bands to the BLG dielectric susceptibility. We further show that for BLG/CrCl3 and BLG/CrB3 the band gap can be extracted from the gate voltage dependence of the low-temperature conductivity, and use this finding to refine the gap dependence on magnetic field. Our results allow a quantitative comparison of the electronic properties of BLG with theoretical predictions and indicate the presence of correlations in electrons occupying CrX3 conduction band.