Erratum: Integral quantum Hall effect in graphene: Zero and finite Hall field [Phys. Rev. B<b>83</b>, 075427 (2011)]

The electronic properties of monolayer phosphorene are exotic due to its puckered structure and large intrinsic direct band gap. We derive and discuss its band structure in the presence of a perpendicular magnetic field. Further, we evaluate the magneto-optical Hall and longitudinal optical conductivities, as functions of temperature, magnetic field, and Fermi energy, and show that they are strongly influenced by the magnetic field. The imaginary part of the former and the real part of the latter exhibit regular interband oscillations as functions of the frequency ω in the range ℏω ∼ 1.5 − 2 eV. Strong intraband responses in the latter and week ones in the former occur at much lower frequencies. The magneto-optical response can be tuned in the microwave-to-terahertz and visible frequency ranges in contrast with a conventional two-dimensional electron gas or graphene in which the response is limited to the terahertz regime. This ability to isolate carriers in an anisotropic structure may make phosphorene a promising candidate for new optical devices.

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“…(13) gives results similar to those of graphene [27]. Following the procedure adopted for the component σ …”

Section: Linear Response Conductivitiesmentioning

confidence: 65%

Magneto-optical transport properties of monolayer phosphorene

2015

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“…In order to calculate the electrical conductivity in the presence of Zeeman and hybridization interactions and a perpendicular magnetic field, we will follow the formulation of Ref. 23, which is derived from the general Liouville equation. 21,22 To obtain the longitudinal contribution, we assume that the electrons are elastically scattered by randomly distributed charged impurities, which is the dominant scattering mechanism at low temperature.…”

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confidence: 99%

“…The Hall conductivity is obtained from the nondiagonal elements of the conductivity tensor as [21][22][23] …”

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Quantum magnetotransport properties of ultrathin topological insulator films

Tahir

Sabeeh

Schwingenschlögl

2013

Journal of Applied Physics

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We study the quantum magnetotransport in ultrathin topological insulator films in an external magnetic field considering hybridization between the upper and lower surfaces of the film. We investigate the two possible mechanisms for splitting of Landau levels, Zeeman and hybridization effects, and show that their interplay leads to minima in the collisional and Hall conductivities with a metal-to-insulator phase transition at the charge neutrality point. Hall plateaus arise at unusual multiples of e2/h. Evidence of a quantum phase transition for the zeroth and splitting of the higher Landau levels is found from the temperature and magnetic field dependences of the transport.

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“…We evaluate their band structure and the longitudinal and Hall conductivities using linear response theory [25,26].…”

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confidence: 99%

Unconventional quantum Hall effect in Floquet topological insulators

Tahir

Vasilopoulos

Schwingenschlögl

2016

J. Phys.: Condens. Matter

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We study an unconventional quantum Hall effect for the surface states of ultrathin Floquet topological insulators in a perpendicular magnetic field. The resulting band structure is modified by photon dressing and the topological property is governed by the low-energy dynamics of a single surface. An exchange of symmetric and antisymmetric surface states occurs by reversing the light's polarization. We find a novel quantum Hall state in which the zeroth Landau level undergoes a phase transition from a trivial insulator state, with Hall conductivity σyx = 0 at zero Fermi energy, to a Hall insulator state with σyx = e 2 /2h. These findings open new possibilities for experimentally realizing nontrivial quantum states and unusual quantum Hall plateaux at (±1/2, ±3/2, ±5/2, ...)e 2 /h. In the regime of the integral quantum Hall effect (IQHE) for conventional, two-dimensional (2D) systems, e.g., in a GaAs/AlGaAs heterostructure, the Hall conductivity takes the values 2(n+1)e 2 /h = (2, 4, 6, ...) e 2 /h, where h is the Planck constant, e the electron charge, and n an integer. In graphene though the IQHE plateaux appear at 4(n + 1/2)e 2 /h = (±2, ±6, ±10, ...) e 2 /h [1], and the "half integer" aspect is hidden under the 4-fold degeneracy associated with the spin and valley degrees of freedom [2]. More recently, the IQHE has been assessed for silicene [3] and MoS 2 [4] in which the spinorbit interaction rearranges, as in 2D systems [5], the Landau levels (LLs) in two groups and the plateaux appear at integer values of e 2 /h due to a double degeneracy (±0, ±1, ±2, ±4, ±6, ...). In topological insulators (TIs) electrons on both top and bottom surfaces contribute to the Hall conductivity and its plateaux, due to the surface degeneracy, have heights 2(n + 1/2) e 2 /h = (±0, ±1, ±3, ±5, ...)e 2 /h [6-8]. Though the quest for a genuine "half-integer" QHE is long, a QHE like (n + 1/2) e 2 /h = (±0, ±1/2, ±3/2, ±5/2, ...) e 2 /h without any degeneracy prefactor, has not been observed. Then one wonders whether a "half-integer" QHE is possible in TIs by breaking their surface degeneracy.TIs More recently, the surface states of TIs driven by circularly polarized off-resonant light have become a subject of strong interest [17][18][19][20]. TIs driven by external timeperiodic perturbations are known as Floquet TIs (FTIs). * udo.schwingenschlogl@kaust.edu.sa For such systems it is convenient to use the Floquet theory [18]. In the appropriate frequency regime the offresonant light cannot generate real photon absorption or emission due to energy conservation. Accordingly, it does not directly excite electrons but instead modifies the electron band structure through second-order virtual-photon absorption processes. Averaged over time these processes result in an effective static alteration of the band structure. Illuminating, e.g., graphene or silicene with offresonant light generates a Haldane-type gap [21].Floquet bands were first realized in photonic crystals [22] and have been verified by recent experiments on the surface states of...

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Erratum: Integral quantum Hall effect in graphene: Zero and finite Hall field [Phys. Rev. B83, 075427 (2011)]

Cited by 13 publications

References 2 publications

Magneto-optical transport properties of monolayer phosphorene

Magneto-optical transport properties of monolayer phosphorene

Quantum magnetotransport properties of ultrathin topological insulator films

Unconventional quantum Hall effect in Floquet topological insulators

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