Optical Hall conductivity of systems with gapped spectral nodes

Hill, Antonio; Sinner, Andreas; Ziegler, K.

doi:10.1140/epjb/e2012-30887-1

Cited by 12 publications

(11 citation statements)

References 35 publications

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“…(21) agrees with the recent result of Ref. 27, as well as that of Ref. 28, and is referred to as the optical Hall conductivity.…”

Section: A Conductivitiessupporting

confidence: 91%

“…The overall behaviour is similar to that in Ref. 27, where even higher temperatures were considered, and rests on the tacit assumption that at these elevated temperatures other factors, e.g., phonons, are unable to significantly weaken this divergence or put into question the applicability of the formalism. In our case such factors are somewhat taken into account through the use of c.…”

Section: Finite Temperaturessupporting

confidence: 75%

“…IV B. The appearance of the singularity for a ¼ 1 is related to the onset of particle-hole excitations 27 for hx > 2jD z j; namely, for hx > 2jD z j, the electrons can absorb photons from the external ac field and create particle-hole pairs, whereas this effect is forbidden for hx < 2jD z j.…”

Section: A Conductivitiesmentioning

confidence: 99%

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Transport on the surface of a topological insulator

Vargiamidis

Vasilopoulos

2014

Journal of Applied Physics

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We study theoretically dc and ac transport on the surface of a three-dimensional topological insulator when its time-reversal symmetry is broken. Starting with a Kubo formula, we derive an explicit expression for the dc Hall conductivity, valid for finite temperatures. At zero temperature this expression gives the dc half-quantum Hall conductivity, provided the Fermi level lies in the gap. Corrections when the Fermi level is outside the gap and scattering by impurities are quantified. The longitudinal conductivity is also examined. At finite frequencies, we find a modified Drude term in r xx (x) and logarithmic, frequency-dependent corrections in r yx (x). The ac Hall conductivity exhibits a robust logarithmic singularity for excitation energies equal to the gapwidth. For these energies, we also find that the power spectrum, which is pertinent to optical experiments, exhibits drastic increase. The Hall conductivity remains almost unaffected for temperatures up to approximately 300 K. V C 2014 AIP Publishing LLC. [http://dx.

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“…(21) agrees with the recent result of Ref. 27, as well as that of Ref. 28, and is referred to as the optical Hall conductivity.…”

Section: A Conductivitiessupporting

confidence: 91%

Section: Finite Temperaturessupporting

confidence: 75%

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Transport on the surface of a topological insulator

Vargiamidis

Vasilopoulos

2014

Journal of Applied Physics

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“…For |p 0 | ≥ 2|m|, the AC field excites particle-hole pairs which can propagate unhindered for p 0 = ±2|m|. This is the origin of the resonance [52][53][54] . For large frequencies, the AC field dominates the mass gap that protects the topological phase.…”

Section: A Off-diagonal Responsementioning

confidence: 99%

Momentum-dependent mass and AC Hall conductivity of quantum anomalous Hall insulators and their relation to the parity anomaly

Tutschku

Böttcher

Meyer

et al. 2020

Phys. Rev. Research

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The Dirac mass of a two-dimensional QAH insulator is directly related to the parity anomaly of planar quantum electrodynamics, as shown initially in Phys. Rev. Lett. 52, 18 (1984). In this work, we connect the additional momentum-dependent Newtonian mass term of a QAH insulator to the parity anomaly. By calculating the effective action, we reveal that the Newtonian mass term acts like a parity-breaking element of a high-energy regularization scheme. As such, it is directly related to the parity anomaly. In addition, the calculation of the effective action allows us to determine the finite frequency correction to the DC Hall conductivity of a QAH insulator. We derive that the leading order AC correction contains a term proportional to the torsional Hall viscosity. This paves the way to measure this non-dissipative transport coefficient via electrical or magneto-optical experiments. Moreover, we prove that the Newtonian mass significantly changes the resonance structure of the AC Hall conductivity in comparison to pure Dirac systems like graphene.

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“…Such a framework inadvertently excludes the contribution of the longitudinal conductivity. On physical grounds, we expect that if the frequency of the ambient radiation is larger than the insulator's band gap, the insulator can absorb radiation to create particlehole pairs which results in a nonzero longitudinal conductivity at that frequency [16]. This consideration, as well as the physical requirement that the response function should vanish for an infinitely large frequency, behooves one to consider the full frequency dispersion of the conductivity tensor.…”

Section: Introductionmentioning

confidence: 99%

Spontaneous emission of a quantum emitter near a Chern insulator: interplay of time reversal symmetry breaking and van Hove singularity

Lu,

Arifa,

Hong

2020

Preprint

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We consider the generic problem of a two-level quantum emitter near a two-dimensional Chern insulator in the dipole approximation, and study how the frequency-dependent response and electronic density of states of the insulator modifies the transition rate of the emitter between the ground and excited levels. To this end, we obtain the full real-frequency behavior of the conductivity tensor by performing a tight-binding calculation based on the Qi-Wu-Zhang model and using a Kubo formula, and derive the full electromagnetic Green tensor of the system, which breaks Onsager reciprocity. This enables us to find that for frequencies smaller than the maximum band gap, the system is sensitive to time reversal symmetry-breaking, whereas for much larger frequencies the system becomes insensitive, with implications for the discrimination of the state of a circularly polarised dipole emitter. We also study the impact of a van Hove singularity on the surface-induced correction to the transition rate, finding that it can enhance its amplitude by a few orders of magnitude compared to the case where the conductivity is set to its static value. By considering configurations in which the dipole is circularly polarised or parallel with the surface of the Chern insulator, we find that the surface correction to the transition rate can exhibit a novel decay with sine integral-like oscillations.

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Optical Hall conductivity of systems with gapped spectral nodes

Cited by 12 publications

References 35 publications

Transport on the surface of a topological insulator

Transport on the surface of a topological insulator

Momentum-dependent mass and AC Hall conductivity of quantum anomalous Hall insulators and their relation to the parity anomaly

Spontaneous emission of a quantum emitter near a Chern insulator: interplay of time reversal symmetry breaking and van Hove singularity

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