Efficient Linear Scaling Approach for Computing the Kubo Hall Conductivity
arXiv:1501.05100 · doi:10.1103/PhysRevB.91.165117
Abstract
We report an order-N approach to compute the Kubo Hall conductivity for disorderd two-dimensional systems reaching tens of millions of orbitals, and realistic values of the applied external magnetic fields (as low as a few Tesla). A time-evolution scheme is employed to evaluate the Hall conductivity using a wavepacket propagation method and a continued fraction expansion for the computation of diagonal and off-diagonal matrix elements of the Green functions. The validity of the method is demonstrated by comparison of results with brute-force diagonalization of the Kubo formula, using (disordered) graphene as system of study. This approach to mesoscopic system sizes is opening an unprecedented perspective for so-called reverse engineering in which the available experimental transport data are used to get a deeper understanding of the microscopic structure of the samples. Besides, this will not only allow addressing subtle issues in terms of resistance standardization of large scale materials (such as wafer scale polycrystalline graphene), but will also enable the discovery of new quantum transport phenomena in complex two-dimensional materials, out of reach with classical methods.
submitted PRB paper
References in corpus (25)
- Two-Dimensional Gas of Massless Dirac Fermions in Graphene
- Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
- Quantum Spin Hall Insulator State in HgTe Quantum Wells
- Anomalous Hall effect
- Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
- Room-Temperature Quantum Hall Effect in Graphene
- Anderson Transitions
- Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
- Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure
- Electronic Properties of Disordered Two-Dimensional Carbon
- Cloning of Dirac fermions in graphene superlattices
- Quantum-limited shot noise in graphene
- Quantum Hall Ferromagnetism in Graphene
- Electron transport in disordered graphene
- Intervalley scattering, long-range disorder, and effective time reversal symmetry breaking in graphene
- Spin and valley quantum Hall ferromagnetism in graphene
- Quantum Hall Effect of Dirac Fermions in Graphene: Disorder Effect and Phase Diagram
- Real-space calculation of the conductivity tensor for disordered topological matter
- Magnetoresistance in Disordered Graphene: The Role of Pseudospin and Dimensionality Effects Unraveled
- Quantum Hall effect in polycrystalline graphene: The role of grain boundaries
- Splitting of the Zero-Energy Landau Level and Universal Dissipative Conductivity at Critical Points in Disordered Graphene
- Quantum Hall Effect in Hydrogenated Graphene
- Quantum Hall criticality and localization in graphene with short-range impurities at the Dirac point
- Quantum transport in chemically functionalized graphene at high magnetic field: Defect-Induced Critical States and Breakdown of Electron-Hole Symmetry
- Quantum oscillations in graphene in the presence of disorder and interactions
Cited by in corpus (12)
- Linear Scaling Quantum Transport Methodologies
- Quantum Hall effect and semiconductor to semimetal transition in biased black phosphorus
- Spin Hall Effect and Origins of Nonlocal Resistance in Adatom-Decorated Graphene
- Covariant conservation laws and the spin Hall effect in Dirac-Rashba systems
- Unconventional Features in the Quantum Hall Regime of Disordered Graphene: Percolating Impurity States and Hall Conductance Quantization
- Quantum Hall studies of a Semi-Dirac Nanoribbon
- Efficient numerical method for evaluating normal and anomalous time-domain equilibrium Green's functions in inhomogeneous systems
- Efficient Time-Domain Approach for Linear Response Functions
- Quantum Hall effect and Landau levels without spatial long-range correlations
- Wigner-Weyl calculus in Keldysh technique
- Optical Hall response of bilayer graphene: the manifestation of chiral hybridised states in broken mirror symmetry lattices
- Trigonal warping, pseudodiffusive transport, and finite-system version of the Lifshitz transition in magnetoconductance of bilayer-graphene Corbino disks