Spontaneous persistent currents in a quantum spin Hall insulator

We present a mechanism for persistent charge current. Quantum spin Hall insulators hold dissipationless spin currents in their edges so that, for a given spin orientation, a net charge current flows which is exactly compensated by the counterflow of the opposite spin. Here we show that ferromagnetic order in the edge upgrades the spin currents into persistent charge currents without applied fields. For that matter, we study the Hubbard model including Haldane-Kane-Mele spin-orbit coupling in a zigzag ribbon and consider the case of graphene. We find three electronic phases with magnetic edges that carry currents reaching 0.4 nA, comparable to persistent currents in metallic rings, for the small spin-orbit coupling in graphene. One of the phases is a valley half metal.

Impurity states in the quantum spin Hall phase in graphene

Two-dimensional insulators with time-reversal symmetry can have two topologically different phases, the quantum spin Hall and the normal phase. The former is revealed by the existence of conducting edge states that are topologically protected. Here we show that the reaction to impurity, in bulk, is radically different in the two phases and can be used as a marker for the topological phase. Within the context of the Kane-Mele model for graphene, we find that strictly normalizable in-gap impurity states only occur in the quantum spin Hall phase and carry a dissipationless current whose chirality is determined by the spin and pseudospin of the residing electron.

A new code for the Hall-driven magnetic evolution of neutron stars

Over the past decade, the numerical modeling of the magnetic field evolution in astrophysical scenarios has become an increasingly important field. In the crystallized crust of neutron stars the evolution of the magnetic field is governed by the Hall induction equation. In this equation the relative contribution of the two terms (Hall term and Ohmic dissipation) varies depending on the local conditions of temperature and magnetic field strength. This results in the transition from the purely parabolic character of the equations to the hyperbolic regime as the magnetic Reynolds number increases, which presents severe numerical problems. Up to now, most attempts to study this problem were based on spectral methods, but they failed in representing the transition to large magnetic Reynolds numbers. We present a new code based on upwind finite differences techniques that can handle situations with arbitrary low magnetic diffusivity and it is suitable for studying the formation of sharp current sheets during the evolution. The code is thoroughly tested in different limits and used to illustrate the evolution of the crustal magnetic field in a neutron star in some representative cases. Our code, coupled to cooling codes, can be used to perform long-term simulations of the magneto-thermal evolution of neutron stars.

Quantum Hall effect in gapped graphene heterojunctions

We model the quantum Hall effect in heterostructures made of two gapped graphene stripes with different gaps, Δ1 and Δ2. We consider two main situations, Δ1=0,Δ2≠0, and Δ1=−Δ2. They are different in a fundamental aspect: only the latter features kink states that, when intervalley coupling is absent, are protected against backscattering. We compute the two-terminal conductance of heterostructures with channel length up to 430 nm, in two transport configurations, parallel and perpendicular to the interface. By studying the effect of disorder on the transport along the boundary, we quantify the robustness of kink states with respect to backscattering. Transport perpendicular to the boundary shows how interface states open a backscattering channel for the conducting edge states, spoiling the perfect conductance quantization featured by the homogeneously gapped graphene Hall bars. Our results can be relevant for the study of graphene deposited on hexagonal boron-nitride, as well as to model graphene with an interaction-driven gapped phase with two equivalent phases separated by a domain wall.

Quantum spin Hall phase in multilayer graphene

The so-called quantum spin Hall phase is a topologically nontrivial insulating phase that is predicted to appear in graphene and graphenelike systems. In this paper we address the question of whether this topological property persists in multilayered systems. We consider two situations: purely multilayer graphene and heterostructures where graphene is encapsulated by trivial insulators with a strong spin-orbit coupling. We use a four-orbital tight-binding model that includes full atomic spin-orbit coupling and we calculate the Z2 topological invariant of the bulk states as well as the edge states of semi-infinite crystals with armchair termination. For homogeneous multilayers we find that even when the spin-orbit interaction opens a gap for all possible stackings, only those with an odd number of layers host gapless edge states while those with an even number of layers are trivial insulators. For heterostructures where graphene is encapsulated by trivial insulators, it turns out that interlayer coupling is able to induce a topological gap whose size is controlled by the spin-orbit coupling of the encapsulating materials, indicating that the quantum spin Hall phase can be induced by proximity to trivial insulators.

Quantum anomalous Hall effect in graphene coupled to skyrmions

Skyrmions are topologically protected spin textures, characterized by a topological winding number N, that occur spontaneously in some magnetic materials. Recent experiments have demonstrated the capability to grow graphene on top Fe/Ir, a system that exhibits a two-dimensional skyrmion lattice. Here we show that a weak exchange coupling between the Dirac electrons in graphene and a two-dimensional skyrmion lattice withN = ±1 drives graphene into a quantum anomalous Hall phase, with a band gap in bulk, a Chern number C = 2N, and chiral edge states with perfect quantization of conductance G = 2N e2 h . Our findings imply that the topological properties of the skyrmion lattice can be imprinted in the Dirac electrons of graphene.

Orbital Magnetization of Quantum Spin Hall Insulator Nanoparticles

Both spin and orbital degrees of freedom contribute to the magnetic moment of isolated atoms. However, when inserted in crystals, atomic orbital moments are quenched because of the lack of rotational symmetry that protects them when isolated. Thus, the dominant contribution to the magnetization of magnetic materials comes from electronic spin. Here we show that nanoislands of quantum spin Hall insulators can host robust orbital edge magnetism whenever their highest occupied Kramers doublet is singly occupied, upgrading the spin edge current into a charge current. The resulting orbital magnetization scales linearly with size, outweighing the spin contribution for islands of a few nm in size. This linear scaling is specific of the Dirac edge states and very different from Schrodinger electrons in quantum rings. By modeling Bi(111) flakes, whose edge states have been recently observed, we show that orbital magnetization is robust with respect to disorder, thermal agitation, shape of the island, and crystallographic direction of the edges, reflecting its topological protection.

Noncollinear magnetic phases and edge states in graphene quantum Hall bars

Application of a perpendicular magnetic field to charge neutral graphene is expected to result in a variety of broken symmetry phases, including antiferromagnetic, canted, and ferromagnetic. All these phases open a gap in bulk but have very different edge states and noncollinear spin order, recently confirmed experimentally. Here we provide an integrated description of both edge and bulk for the various magnetic phases of graphene Hall bars making use of a noncollinear mean field Hubbard model. Our calculations show that, at the edges, the three types of magnetic order are either enhanced (zigzag) or suppressed (armchair). Interestingly, we find that preformed local moments in zigzag edges interact with the quantum spin Hall like edge states of the ferromagnetic phase and can induce backscattering.