Emergence of Ferromagnetism Due to Spontaneous Symmetry Breaking in a Twisted Bilayer Graphene Nanoflex

Abstract

Twisted bilayer graphene exhibits many intriguing behaviors ranging from superconductivity to the anomalous Hall effect to ferromagnetism at a magic angle of ∼1°. Here, using a first-principles approach, we reveal ferromagnetism in a twisted bilayer graphene nanoflex. Our results demonstrate that when the energy gap of a twisted nanoflex approaches zero, electronic instability occurs and a ferromagnetic gap state emerges spontaneously to lower the energy. Unlike the observed ferromagnetism at a magic angle in the graphene bilayer, we notice the ferromagnetic phase appearing aperiodically between 0 and 30° in the twisted nanoflex. The origin of electronic instability at various twist angles is ascribed to the several higher-symmetry phases that are broken to lower the energy resulting from an aperiodic modulation of the interlayer interaction in the nanoflex. Besides unraveling a spin-pairing mechanism for the reappearance of the nonmagnetic phase, we have found orbitals at the boundary of nanoflex contributing to ferromagnetism.

Phase transition from a nonmagnetic to a ferromagnetic state in a twisted bilayer graphene nanoflake: the role of electronic pressure on the magic-twist

“…This suggests a plausible tuning of complex periodicity of the many-electron IEC energy strength in a BLGNF upon applying electronic pressure. Similar to our previous observation, 49 we have also noticed the transition from an NM phase to an FM phase as ΔE g approaches zero. Analysis of frontier states at the transition point indicated the highest occupied and lowest unoccupied orbitals to be isomorphic and energy degenerate (see Fig.…”

“…4), and the localized electronic states emanating from the p-orbital of boundary C-atoms (see Fig. S1 in ESI †), as observed before, 49 are found to contribute to the ferromagnetism. To gain further insights into the origin of phase transition and shift in θ M , we have examined the electronic instability in the nanoflake by calculating the energy gap (ΔE g ) between the highest occupied and lowest unoccupied electronic states in the NM phase as a function of twist angle.…”

“…Furthermore, additional control of IEC using hydrostatic pressure to tune the electronic properties has been demonstrated recently in BLG and graphene Moiré superlattice structures. [45][46][47] Motivated by these pioneering discoveries in 2D BLG, in our earlier work, 49 we explored the effect of rotational alignment between the layers and hence the IEC in a zero-dimensional (0-D) bilayer graphene nanoflake (BLGNF). The quantum confinement effect in a 0-D twisted BLGNF that provided further control of quasiparticles' behavior revealed rich IEC-dependent physics in this system.…”

“…Though the AA stacked structure is energetically less stable as compared to the AB stacked structure, it has been shown to exhibit interesting phase transformation upon twisting. 49 The choice of the nanoflake dimension in this study stems from our earlier investigation 49 that demonstrated the minimum dimension requirement to observe the phase transition in an AA stacked bilayer graphene nanoflake. Atomic arrangements in the nanoflake are taken from the energy-optimized 2-D bilayer graphene structure; the dangling bonds at the edge of carbon atoms are saturated with hydrogen atoms.…”

“…Motivated by these pioneering discoveries in 2D BLG, in our earlier work, 49 we explored the effect of rotational alignment between the layers and hence the IEC in a zero-dimensional (0-D) bilayer graphene nanoflake (BLGNF). The quantum confinement effect in a 0-D twisted BLGNF that provided further control of quasiparticles’ behavior revealed rich IEC-dependent physics in this system.…”