Calvin J. Tabert

Valley-spin polarization in the magneto-optical response of silicene and other similar 2D crystals.

We calculate the magneto-optical conductivity and electronic density of states for silicene, the silicon equivalent of graphene, and similar crystals such as germanene. In the presence of a perpendicular magnetic field and electric field gating, we note that four spin- and valley-polarized levels can be seen in the density of states, and transitions between these levels lead to similarly polarized absorption lines in the longitudinal, transverse Hall, and circularly polarized dynamic conductivity. While previous spin and valley polarization predicted for the conductivity is only present in the response to circularly polarized light, we show that distinct spin and valley polarization can also be seen in the longitudinal magneto-optical conductivity at experimentally attainable energies. The frequency of the absorption lines may be tuned by the electric and magnetic field to onset in a range varying from THz to the infrared. This potential to isolate charge carriers of definite spin and valley label may make silicene a promising candidate for spin- and valleytronic devices.

Magneto-Optical Conductivity of Silicene and Other Buckled Honeycomb Lattices

Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1 Canada andGuelph-Waterloo Physics Institute, University of Guelph, Guelph, Ontario N1G 2W1 Canada(Dated: August 23, 2013)The magneto-optical longitudinal, transverse Hall and circularly-polarized response of siliceneand other materials described by a Kane-Mele Hamiltonian are calculated. Particular attention ispaid to the effects of an external electric field and finite charge doping. The energy of interbandtransitions can be tuned by varying the electric field. The onset frequency of the absorptive peaksmoves differently between the topological insulator and band insulator regimes. This may be used toverify experimentally the existence of the two insulating phases as well as provide a measure of thespin-orbit band gap. The zeroth Landau level splits between four spin and valley distinct energiesresulting in valley-spin-polarized levels in the density of states. With charge doping, transitionsbetween these levels allow for a spin- and valley-polarized response in the conductivity wherebycharge carriers of specific spin and valley index can be isolated by tuning the incident photonfrequency. Increasing the chemical potential is shown to redistribute spectral weight from interbandtransitions to a strong low-energy intraband response. For large chemical potential, this intrabandfeature is associated with the semiclassical cyclotron resonance frequency which is shown to linearlyincrease with magnetic field.

Optical signatures of the tunable band gap and valley-spin coupling in silicene

We investigate the optical response of the silicene and similar materials, such as germanene, in the presence of an electrically tunable band gap for variable doping. The interplay of spin orbit coupling, due to the buckled structure of these materials, and a perpendicular electric field gives rise to a rich variety of phases: a topological or quantum spin Hall insulator, a valley-spin-polarized metal and a band insulator. We show that the dynamical conductivity should reveal signatures of these different phases which would allow for their identification along with the determination of parameters such as the spin orbit energy gap. We find an interesting feature where the electric field tuning of the band gap might be used to switch on and off the Drude intraband response. Furthermore, in the presence of spin-valley coupling, the response to circularly polarized light as a function of frequency and electric field tuning of the band gap is examined. Using right- and left-handed circular polarization it is possible to select a particular combination of spin and valley index. The frequency for this effect can be varied by tuning the band gap.

AC/DC spin and valley Hall effects in silicene and germanene

The intrinsic spin and valley Hall conductivities of silicene, germanene and other similar two dimensional crystals are explored theoretically. Particular attention is given to the effects of the intrinsic spin-orbit coupling, electron doping and the type of insulating phase of the system (i.e., a topological insulator or a band insulator) which can be tuned by a perpendicular electric field. At finite frequency, the transverse edge to which carriers of particular spin and valley label flow can be controlled such that an accumulation of a particular combination of spin and valley index can be obtained. The direction of flow is found to be dependent on the type of insulating phase. The magnitude of the Hall conductivity response is enhanced from the DC values at certain incident photon frequencies associated with the onset of interband transitions. Analytic results are presented for both the DC and finite frequency results.

Dynamical polarization function, plasmons, and screening in silicene and other buckled honeycomb lattices

The authors study the dynamical polarizability and dielectric function in buckled honeycomb lattices taking into account the intrinsic spin-orbit interaction and sub-lattice onsite potential difference. By varying the relative strength of these parameters, they show that the imaginary part of the dynamical polarizability depicts signatures of topological insulator, valley-spin polarized metal and trivial band insulator phases.

Optical conductivity of twisted bilayer graphene

We calculate the finite-frequency conductivity of bilayer graphene with a relative twist between the layers. The low frequency response at zero doping shows a flat conductivity with value twice that of the monolayer case and at higher frequency a strong absorption peak occurs. For finite doping, the low frequency flat absorption is modified into a peak about zero frequency (the Drude response) accompanied by an interband edge which results from the transfer of spectral weight from interband to intraband absorption due to Pauli blocking. If the system is doped sufficiently such that the chemical potential reaches beyond the low-energy saddle point in the twisted bilayer band structure, a strong low frequency absorption peak appears at an energy related to an effective interlayer hopping energy, which may be used to identify this parameter and confirm the existence of the saddle point which gives rise to a low energy van Hove singularity in the electronic density of states.

Erratum: Optical and transport properties in three-dimensional Dirac and Weyl semimetals [Phys. Rev. B93, 085426 (2016)]

Within a Kubo formalism, we study dc transport and ac optical properties of 3D Dirac and Weyl semimetals. Emphasis is placed on the approach to charge neutrality and on the differences between Dirac and Weyl materials. At charge neutrality, the zero-temperature limit of the dc conductivity is not universal and also depends on the residual scattering model employed. However, the Lorenz number L retains its usual value L0. With increasing temperature, the Wiedemann-Franz law is violated. At high temperatures, L exhibits a new plateau at a value dependent on the details of the scattering rate. Such details can also appear in the optical conductivity, both in the Drude response and interband background. In the clean limit, the interband background is linear in photon energy and always extrapolates to the origin. This background can be shifted to the right through the introduction of a massless gap. In this case, the extrapolation can cut the axis at a finite photon energy as is observed in some experiments. It is also of interest to differentiate between the two types of Weyl semimetals: those with broken time-reversal symmetry and those with broken spatialinversion symmetry. We show that, while the former will follow the same behaviour as the 3D Dirac semimetals, for the zero magnetic field properties discussed here, the latter type will show a double step in the optical conductivity at finite doping and a single absorption edge at charge neutrality. The Drude conductivity is always finite in this case, even at charge neutrality.

Magnetization of the metallic surface states in topological insulators.

We calculate the magnetization of the helical metallic surface states of a topological insulator. We account for the presence of a small sub-dominant Schrödinger piece in the Hamiltonian in addition to the dominant Dirac contribution. This breaks particle-hole symmetry. The cross-section of the upper Dirac cone narrows while that of the lower cone broadens. The sawtooth pattern seen in the magnetization of the pure Dirac limit as a function of chemical potential (μ) is shifted; but, the quantization of the Hall plateaus remains half integral. This is verified by taking the derivative of the magnetization with respect to μ. We compare our results with those when the non-relativistic piece dominates over the relativistic contribution and the quantization is integral. Analytic results for the magnetic oscillations are obtained where we include a first order correction in the ratio of non-relativistic to relativistic magnetic energy scales. Our fully quantum mechanical derivations confirm the expectation of semiclassical theory except for a small correction to the expected phase. There is a change in the overall amplitude of the magnetic oscillations. The Dingle and temperature factors are modified.