Spin-valley skyrmions in graphene at filling factor ν=−1

Abstract

We model quantum Hall skyrmions in graphene monolayer at quarter filling by a theory of CP 3 fields and study the energy minimizing skyrmions in presence of valley pseudospin anisotropy and Zeeman coupling. We present a diagram of all types of skyrmions in a wide range of the anisotropy parameters. For each type of skyrmion, we visualize it on three Bloch spheres, and present the profiles of its texture on the graphene honeycomb lattice, thus providing references for the STM/STS imaging of spin-pseudospin textures in graphene monolayer in quantum Hall regime. Besides the spin and pseudospin skyrmions for the corresponding degrees of freedom of an electron in the N = 0 Landau level, we discuss two unusual types -the "entanglement skyrmion" whose texture lies in the space of the entanglement of spin and pseudospin, as well as the "deflated pseudospin skyrmion" with partial entanglement. For all skyrmion types, we study the dependence of the energy and the size of a skyrmion on the anisotropy parameters and perpendicular magnetic field. We also propose three ways to modify the anisotropy energy, namely the sample tilting, the substrate anisotropy and the valley pseudospin analogue of Zeeman coupling.

SU(4) spin waves in the $ν=\pm1$ quantum Hall ferromagnet in graphene

“…Notice that there is experimental evidence for three of these phases [19][20][21] , indicating that the nature of the SU(4) ferromagnetic ground state may be sample and/or substrate dependent. At quarter filling ν = ±1 -the signs are related by particlehole symmetry -the phase diagram has been obtained by Lian et al 22 using the same symmetry breaking terms as Kharitonov 15 , and one obtains similar phases as in the ν = 0 case.…”

“…However, since this term does not modify substantially the phases but rather the location of their phase transitions, we consider only the dispersion in the phases of Ref. [22]. At ν = −1, there are three Goldstone mode corresponding to flipping one electron from the filled sub-LL to each one of the three empty sub-LLs.…”

Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet

“…S5). It also shows that further work can map the zoo of predicted topological excitations in this and other QHFM phases of graphene (22,23). From a broader perspective, the microscopic approach to studying valley ordering can be applied to other two-dimensional systems, such as twisted bilayer graphene.…”

“…Although transport studies have constrained aspect of the phase diagram (20,21), in the absence of microscopic measurements that probe the order parameter, the nature of the ground state of graphene at charge neutrality has remained unresolved. Also unexplored are the plethora of topological excitations these phases have been predicted to host, such as a variety of skyrmions which may have complex flavor textures and even harbor fractional charge on the scale of the magnetic length (22)(23)(24)(25). Here we use spectroscopic mapping to visualize the broken sym-Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet metry states in graphene as a function of carrier concentration, including at charge neutrality, where we find evidence for localized valley skyrmions within the Kekule phase.…”

Skyrmions in twisted bilayer graphene: stability, pairing, and crystallization

“…The strong-coupling insulators at different integer ν are all Chern ferromagnets, and starting from the fully symmetric limit, one can consider more general skyrmions where the only constraint is that locally the state is polarized within the Chern sectors. For instance, starting from the |ν| = +3 QAHI, it is possible to form a texture in both spin and pseudospin to create an 'entangled' skyrmion, akin to what happens at |ν| = 1 in the zeroth LL of monolayer graphene 91 . With the full Hamiltonian, pseudospin rotations will be gapped since the QAHI is easy-axis, while spin rotations remain lowenergy due to the SU (2) S -symmetry.…”