Impurity states in the quantum spin Hall phase in graphene

González, Jorge Méndez; Fernández-Rossier, J.

doi:10.1103/physrevb.86.115327

Cited by 20 publications

(19 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These edge states are protected by the time reversal symmetry and are robust with respect to the time-reversal symmetric perturbations, such as nonmagnetic impurities. It is shown that a vacancy, acting as a minimal circular inner edge, will induce novel timereversal invariant bound states in the band gap of the topological insulator [17][18][19] . Theoretically, it is also shown that the SO coupling suppresses the edge magnetism induced in the zigzag ribbon of the honeycomb lattice in the presence of electron-electron interactions 20 .…”

Section: Introductionmentioning

confidence: 99%

Effects of the spin–orbit coupling on the vacancy-induced magnetism on the honeycomb lattice

Leong

2014

Physics Letters A

View full text Add to dashboard Cite

The local magnetism induced by vacancies in the presence of the spin-orbital interaction is investigated based on the half-filled Kane-Mele-Hubbard model on the honeycomb lattice. Using the self-consistent mean-field theory, we find that the spin-orbital coupling will enhance the localization of the spin moments near a single vacancy. We further study the magnetic structures along the zigzag edges formed by a chain of vacancies. We find that the spin-orbital coupling tends to suppress the counter-polarized ferrimagnetic order on the upper and lower edges, because of the open of the spin-orbital gap. As a result, in the case of the balance number of sublattices, it will suppress completely this kind of ferrimagnetic order. But, for the imbalance case, a ferrimagnetic order along both edges exists because additional zero modes will not be affected by the spin-orbital coupling.

show abstract

Section: Introductionmentioning

confidence: 99%

Effects of the spin–orbit coupling on the vacancy-induced magnetism on the honeycomb lattice

Leong

2014

Physics Letters A

View full text Add to dashboard Cite

show abstract

“…The lack of a gap in graphene turns this E = 0 state into a resonance whose amplitude decays . In the case the quantum spin Hall phase, where a non-trivial gap is open, the vacancy creates a real mid-gap state with a normalizable wave function 64 . In both cases, the vacancy localizes an electron It must be stressed that the theorem of eq.…”

Section: Zero Modes In Bipartite Latticesmentioning

confidence: 99%

Edge states in graphene-like systems

2015

Self Cite

View full text Add to dashboard Cite

The edges of graphene and graphene like systems can host localized states with evanescent wave function with properties radically different from those of the Dirac electrons in bulk. This happens in a variety of situations, that are reviewed here. First, zigzag edges host a set of localized non dispersive state at the Dirac energy. At half filling, it is expected that these states are prone to ferromagnetic instability, causing a very interesting type of edge ferromagnetism. Second, graphene under the influence of external perturbations can host a variety of topological insulating phases, including the conventional Quantum Hall effect, the Quantum Anomalous Hall (QAH) and the Quantum Spin Hall phase, in all of which phases conduction can only take place through topologically protected edge states. Here we provide an unified vision of the properties of all these edge states, examined under the light of the same one orbital tight-binding model. We consider the combined action of interactions, spin orbit coupling and magnetic field, which produces a wealth of different physical phenomena. We briefly address what has been actually observed experimentally.

show abstract

“…1(c), where we show the map of the density of states evaluated at E = 0, finding that the main contribution for this state comes from the three to six nearest neighbors to the vacancy that belong to the sublattice opposite to that of the missing site [9,[23][24][25][26]. Of course, for the case of a noninteracting single vacancy, this problem can be dealt with using the standard T matrix theory [25,27,33]. The embedding method shows its added value when it is used to treat several vacancies or when interactions are included, as we discuss now.…”

Section: A the Embedding Techniquementioning

confidence: 99%

“…In gapped graphene structures, such as graphene with a spin-orbit gap [27], graphene nanoribbons [9], or a planar aromatic hydrocarbon molecule, the formation of an in-gap E = 0 state due to sp 3 functionalization leads trivially to a local moment formation with S = 1/2, very much as it happens for acceptors and donors in semiconductors. The zero-energy state is singly occupied by one electron that occupies a bound state.…”

Section: Introductionmentioning

confidence: 99%

Anomalous magnetism in hydrogenated graphene

et al. 2017

Self Cite

View full text Add to dashboard Cite

We revisit the problem of local moment formation in graphene due to chemisorption of individual atomic hydrogen or other analogous sp 3 covalent functionalizations. We describe graphene with the single-orbital Hubbard model, so that the H chemisorption is equivalent to a vacancy in the honeycomb lattice. To circumvent artifacts related to periodic unit cells, we use either huge simulation cells of up to 8 × 10 5 sites, or an embedding scheme that allows the modeling of a single vacancy in an otherwise pristine infinite honeycomb lattice. We find three results that stress the anomalous nature of the magnetic moment (m) in this system. First, in the noninteracting (U = 0) zero-temperature (T = 0) case, the m(B) is a continuous smooth curve with divergent susceptibility, different from the stepwise constant function found for single unpaired spins in a gapped system. Second, for U = 0 and T > 0, the linear susceptibility follows a power law ∝ T −α with an exponent of α = 0.77 different from the conventional Curie law. For U > 0, in the mean-field approximation, the integrated moment is smaller than m = 1μ B , in contrast with results using periodic unit cells. These three results highlight the fact that the magnetic response of the local moment induced by sp 3 functionalizations in graphene is different from that of local moments in gapped systems, for which the magnetic moment is quantized and follows a Curie law, and from Pauli paramagnetism in conductors, for which linear susceptibility can be defined at T = 0.

show abstract

Impurity states in the quantum spin Hall phase in graphene

Cited by 20 publications

References 37 publications

Effects of the spin–orbit coupling on the vacancy-induced magnetism on the honeycomb lattice

Effects of the spin–orbit coupling on the vacancy-induced magnetism on the honeycomb lattice

Edge states in graphene-like systems

Anomalous magnetism in hydrogenated graphene

Contact Info

Product

Resources

About