Quantum Hall Criticality and Localization in Graphene with Short-Range Impurities at the Dirac Point

Gattenlöhner, S.; Hannes, Wolf-Rüdiger; Ostrovsky, P. M.; Gornyi, I. V.; Mirlin, A. D.; Titov, M.

doi:10.1103/physrevlett.112.026802

Cited by 24 publications

(31 citation statements)

References 72 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is illustrated in Fig. 2 (a) where the conductivity peak at E = 0 is consistent with recent numerical calculations [14,24] and its convergence is only achieved for M > 6000.…”

supporting

confidence: 90%

Real-Space Calculation of the Conductivity Tensor for Disordered Topological Matter

2015

View full text Add to dashboard Cite

We describe an efficient numerical approach to calculate the longitudinal and transverse Kubo conductivities of large systems using Bastin's formulation [1]. We expand the Green's functions in terms of Chebyshev polynomials and compute the conductivity tensor for any temperature and chemical potential in a single step. To illustrate the power and generality of the approach, we calculate the conductivity tensor for the quantum Hall effect in disordered graphene and analyze the effect of the disorder in a Chern insulator in Haldane's model on a honeycomb lattice.PACS numbers: 71.23. An,72.15.Rn,71.30.+h One of the most important experimental probes in condensed matter physics is the electrical response to an external electrical field. In addition to the longitudinal conductivity, in specific circumstances, a system can present a transverse conductivity under an electrical perturbation. The Hall effect [2] and the anomalous Hall effect in magnetic materials [3] are two examples of this type of response. Paramagnetic materials with spin-orbit interaction can also present transverse spin currents [4]. There are also the quantized versions of the three phenomena: while the quantum Hall effect (QHE) was observed more than 30 years ago [5], the quantum spin Hall effect (QSHE) and the quantum anomalous Hall effect (QAHE) could only be observed [6, 7] with the recent discovery of topological insulators, a new class of quantum matter [8].In the linear response regime, the conductivity tensor can be calculated using the Kubo formalism [9]. The Hall conductivity can be easily obtained in momentum space in terms of the Berry curvature associated with the bands [10]. The downside of working in momentum space, however, is that the robustness of a topological state in the presence of disorder can only be calculated perturbatively [11]. Real-space implementations of the Kubo formalism for the Hall conductivity, on the other hand, allow the incorporation of different types of disorder in varying degrees, while providing flexibility to treat different geometries. Real-space techniques, however, normally require a large computational effort. This has generally restricted their use to either small systems at any temperature [12,13], or large systems at zero temperature [14].In this Letter, we propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula [1] and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method [16]. There are few numerical methods that use Chebyshev expansions to calculate the longitudinal DC conductivity [17][18][19][20] and transverse conductivity [14,21] at zero temperature. An advantage of our approach is the possibility of obtaining both conductivities for large systems in a single calculation step, independe...

show abstract

“…This is illustrated in Fig. 2 (a) where the conductivity peak at E = 0 is consistent with recent numerical calculations [14,24] and its convergence is only achieved for M > 6000.…”

supporting

confidence: 90%

Real-Space Calculation of the Conductivity Tensor for Disordered Topological Matter

2015

View full text Add to dashboard Cite

show abstract

“…In this article, by using efficient computational methods, we provide tangible numerical insight into the rich physics of the QHE in disordered graphene, backing up the single-particle scenarios [38][39][40][41][42]44] in which dense distributions of defects can explain the formation of a zero-energy plateau in disordered graphene [29,30] and the presence of sets of extended states in Hall measurements [28,31]. In the presence of single vacancies (SVs) and double vacancies (DVs), critical states are found to preclude the formation of the usual graphene LLs.…”

Section: Introductionmentioning

confidence: 99%

Unconventional features in the quantum Hall regime of disordered graphene: Percolating impurity states and Hall conductance quantization

et al. 2016

View full text Add to dashboard Cite

We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy band gap and Landau-level degeneracy breaking. By using efficient real-space transport methodologies, we compute both the dissipative and Hall conductivities of large-size graphene sheets with random distribution of model single and double vacancies. By analyzing the scaling of transport coefficients with defect density, system size, and magnetic length, we elucidate the origin of anomalous quantum Hall features as magnetic-fielddependent impurity states, which percolate at some critical energies. These findings shed light on unidentified states and quantum-transport anomalies reported experimentally.

show abstract

“…Vacancy-defective graphene belongs to the chiral orthogonal ensemble (class BDI in the Altland-Zirnbauer classification of random fermion models [3]). The vanishing of the β function of the effective nonlinear sigma model (NLσM) led Ostrovsky et al to conjecture a line of fixed points with nonuniversal metallic conductivity of the order of the conductance quantum σð0Þ ≈ e 2 =h [22][23][24]. However, the validity of the NLσM of the BDI class has been questioned, as vacancies are infinitely strong scatterers, not amenable to perturbative analysis [12].…”

mentioning

confidence: 99%

“…The focus of this Letter is on vacancy-induced ZEMs, recently implicated in a controversy regarding the exact nature of the quantum transport at the Dirac point [19][20][21][22]. Vacancy-defective graphene belongs to the chiral orthogonal ensemble (class BDI in the Altland-Zirnbauer classification of random fermion models [3]).…”

mentioning

confidence: 99%

Critical Delocalization of Chiral Zero Energy Modes in Graphene

2015

View full text Add to dashboard Cite

Graphene subjected to chiral-symmetric disorder is believed to host zero energy modes (ZEMs) resilient to localization, as suggested by the renormalization group analysis of the underlying nonlinear sigma model. We report accurate quantum transport calculations in honeycomb lattices with in excess of 10 9 sites and fine meV resolutions. The Kubo dc conductivity of ZEMs induced by vacancy defects (chiral BDI class) is found to match 4e 2 =πh within 1% accuracy, over a parametrically wide window of energy level broadenings and vacancy concentrations. Our results disclose an unprecedentedly robust metallic regime in graphene, providing strong evidence that the early field-theoretical picture for the BDI class is valid well beyond its controlled weak-coupling regime.

show abstract

Quantum Hall Criticality and Localization in Graphene with Short-Range Impurities at the Dirac Point

Cited by 24 publications

References 72 publications

Real-Space Calculation of the Conductivity Tensor for Disordered Topological Matter

Real-Space Calculation of the Conductivity Tensor for Disordered Topological Matter

Unconventional features in the quantum Hall regime of disordered graphene: Percolating impurity states and Hall conductance quantization

Critical Delocalization of Chiral Zero Energy Modes in Graphene

Contact Info

Product

Resources

About