Control of Giant Topological Magnetic Moment and Valley Splitting in Trilayer Graphene

Giant orbital magnetic moments and paramagnetic shift in artificial relativistic atoms and molecules

“…The value of 𝜇 observed in this work are orders of magnitude larger than those observed in natural atoms 28 and semiconductor QDs [29][30][31] , and are also several times larger than those observed in Bernal-stacked bilayer graphene (BLG) QDs 32,33 (Table 1). Although similar 𝜇 values have been observed in Bernal-stacked trilayer graphene (TLG) QDs 34 , the findings in this work have several distinctions/advantages. Briefly, graphene QDs can achieve similar 𝜇 with a smaller QD size and maintain linear splitting within a larger 𝐵 range compared to TLG QDs (further discussion in SI section S11).…”

Proximity spin-orbit and exchange coupling in ABA and ABC trilayer graphene van der Waals heterostructures

“…Depending on the stacking order of the three layers, either ABA or ABC, very different electronic structures can be realized with distinct features in electronic and spin transport [71,72] and gate-tunable SOC [73]. TLG is also important from the topological perspective, since the ABC structure potentially hosts quantum spin Hall and quantum valley Hall states [74], while there is evidence for a giant topological magnetic moment in ABA TLG [75]. Also interesting is the energetics of the different stackings; see, for example, Ref.…”

Flat Bands for Electrons in Rhombohedral Graphene Multilayers with a Twin Boundary

“…For the structures with a small number of layers, there are well‐articulated Dirac points with large orbital magnetic moment concentrated at them and g v ≈ 10 3 , like observed earlier in ABA graphene trilayer. [ 28 ] To mention, magnetic moments of mirror‐symmetric bands are controlled by the environment‐induced surface energy, Δ s , and can be tuned across the range g v ≈ 10– d v ≈ 10 3 , in contrast to the mirror‐antisymmetric bands. Similarly to rhombohedral graphite, individual Dirac points become almost indiscernible with a growing number of layers, [ 14 ] the magnetic moment spreads over a broader range of momenta with the maximum g v ≈ 100 shifting away from the $${{\bm{K}}_ \pm }$$ points.…”

“…This includes Berry curvature of the bands and the associated magnetic moments, described in the literature in terms of valley g-factors. Large magnetic moment affects the transport measurements, quantum dot spectra, [28,[32][33][34] valley-polarized currents, [35] or an anomalous contribution to the Hall conductivity. [14] Such an analysis is particularly easy to perform for mirror-symmetric nABAn films, where the 4 × 4 Hamiltonian is reduced to a pair of effective 2 × 2 Hamiltonians, one for mirror-symmetric (s) and the other for mirror-antisymmetric (as) bands.…”

“…Below, we use the following values of parameters implemented in Equation ( 1): v = 1.02 × 10 6 m s -1 , v 3 = 0.102 × 10 6 m s -1 , v 4 = 0.022 × 10 6 m s -1 , γ 1 = 390 meV, Δ′ = 25 meV, γ 2 = −17 meV, γ 5 = 38 meV. [12,28] In addition, we account for energy shift, Δ s , of the surface orbitals that captures the influence of the encapsulation and other environmental conditions.…”