Quantum Nature of Edge Magnetism in Graphene

Golor, Michael; Wessel, Stefan; Schmidt, Manuel

doi:10.1103/physrevlett.112.046601

Cited by 67 publications

(71 citation statements)

References 32 publications

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“…It is known that the ground state for the Heisenberg model on a finite bipartite lattice is a spin singlet. According to the DMRG calculations, we find that the ground state30 is very close to the Néel state. Figure 4 shows the magnetization profiles 〈 S z ( r )〉 in the lowest-energy state of ∑ r S z ( r ) = 0 for the Heisenberg model with a local Zeeman field − hS z ( r 0 ) applied to the center site r 0 at the upper edge.…”

Section: Discussionmentioning

confidence: 68%

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Edge magnetism of Heisenberg model on honeycomb lattice

Hikihara

Lee

et al. 2017

Sci Rep

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Edge magnetism in graphene sparks intense theoretical and experimental interests. In the previous study, we demonstrated the existence of collective excitations at the zigzag edge of the honeycomb lattice with long-ranged Néel order. By employing the Schwinger-boson approach, we show that the edge magnons remain robust even when the long-ranged order is destroyed by spin fluctuations. Furthermore, in the effective field-theory limit, the dynamics of the edge magnon is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterpart. By performing density-matrix renormalization group calculations, we show that the robustness may be attributed to the closeness between the ground state and the Néel state. The existence of edge magnon is not limited to the honeycomb structure, as demonstrated in the rotated-square lattice with zigzag edges as well. The universal behavior indicates that the edge magnons may attribute to the uncompensated edges and can be detected in many two-dimensional materials.

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Section: Discussionmentioning

confidence: 68%

“…The importance to understand the boundary effects in the Heisenberg model is echoed by plausible edge magnetism in graphene nanoribbons192021222324252627282930. By bottom-up approaches, graphene materials with atomic-sharp zigzag edges have been fabricated successfully.…”

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confidence: 99%

Edge magnetism of Heisenberg model on honeycomb lattice

Hikihara

Lee

et al. 2017

Sci Rep

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“…At the same time, however, these results sugggest that the material may be not too far from a possible transition into an ordered state. Other QMC calculations also find sizable charge-density and spin-current correlations, although they do not become long-ranged within the accessible parameter region [31]. Furthermore, a uniform and isotropic strain of about 15% can be expected to induce an interaction-driven metal-insulator transition in graphene [32].…”

Section: Introductionmentioning

confidence: 99%

Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization

et al. 2016

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We study the competition of spin-and charge-density waves and their quantum multicritical behavior for the semimetal-insulator transitions of low-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawa theory with two order parameters as a model for graphene and a growing number of other two-dimensional Dirac materials allows us to describe the physics near the multicritical point at which the semimetallic and the spin-and charge-density-wave phases meet. With the help of a functional renormalization group approach, we are able to reveal a complex structure of fixed points, the stability properties of which decisively depend on the number of Dirac fermions N f . We give estimates for the critical exponents and observe crucial quantitative corrections as compared to the previous first-order expansion. For small N f , the universal behavior near the multicritical point is determined by the chiral Heisenberg universality class supplemented by a decoupled, purely bosonic, Ising sector. At large N f , a novel fixed point with nontrivial couplings between all sectors becomes stable. At intermediate N f , including the graphene case (N f = 2) no stable and physically admissible fixed point exists. Graphene's phase diagram in the vicinity of the intersection between the semimetal, antiferromagnetic and staggered density phases should consequently be governed by a triple point exhibiting first-order transitions.

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“…In fact, a recent paper investigated edge spin polarization for large systems, e.g., 10 4 carbon atoms, and it concluded that if the environment time scale τ env is much shorter than τ qd , the system is pushed into the same classical Néel-like state again and again. As a result, the state cannot decay, which is known as the quantum Zeno effect [89]. Furthermore, our results do not require perfect spin polarization at opposite zigzag edges.…”

Section: Conclusion and Discussionmentioning

confidence: 70%

Quantum chaotic tunneling in graphene systems with electron-electron interactions

et al. 2014

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An outstanding and fundamental problem in contemporary physics is to include and probe the many-body effect in the study of relativistic quantum manifestations of classical chaos. We address this problem using graphene systems described by the Hubbard Hamiltonian in the setting of resonant tunneling. Such a system consists of two symmetric potential wells separated by a potential barrier, and the geometric shape of the whole domain can be chosen to generate integrable or chaotic dynamics in the classical limit. Employing a standard mean-field approach to calculating a large number of eigenenergies and eigenstates, we uncover a class of localized states with near-zero tunneling in the integrable systems. These states are not the edge states typically seen in graphene systems, and as such they are the consequence of many-body interactions. The physical origin of the non-edge-state type of localized states can be understood by the one-dimensional relativistic quantum tunneling dynamics through the solutions of the Dirac equation with appropriate boundary conditions. We demonstrate that, when the geometry of the system is modified to one with chaos, the localized states are effectively removed, implying that in realistic situations where many-body interactions are present, classical chaos is capable of facilitating greatly quantum tunneling. This result, besides its fundamental importance, can be useful for the development of nanoscale devices such as graphene-based resonant-tunneling diodes.

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Quantum Nature of Edge Magnetism in Graphene

Cited by 67 publications

References 32 publications

Edge magnetism of Heisenberg model on honeycomb lattice

Edge magnetism of Heisenberg model on honeycomb lattice

Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization

Quantum chaotic tunneling in graphene systems with electron-electron interactions

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