The search for large-gap quantum spin Hall (QSH) insulators and effective approaches to tune QSH states is important for both fundamental and practical interests. Based on first-principles calculations we find two-dimensional tin films are QSH insulators with sizable bulk gaps of 0.3 eV, sufficiently large for practical applications at room temperature. These QSH states can be effectively tuned by chemical functionalization and by external strain. The mechanism for the QSH effect in this system is band inversion at the Γ point, similar to the case of a HgTe quantum well. With surface doping of magnetic elements, the quantum anomalous Hall effect could also be realized.

Axions are very light, very weakly interacting particles postulated more than 30 years ago in the context of the Standard Model of particle physics. Their existence could explain the missing dark matter of the universe. However, despite intensive searches, they have yet to be detected. In this work, we show that magnetic fluctuations of topological insulators couple to the electromagnetic fields exactly like the axions, and propose several experiments to detect this dynamical axion field. In particular, we show that the axion coupling enables a nonlinear modulation of the electromagnetic field, leading to attenuated total reflection. We propose a novel optical modulators device based on this principle.PACS numbers: 78.20.Ls, 03.65.Vf The electromagnetic response of a three dimensional insulators is described by the Maxwells action S 0 = 1 8π, with material-dependent dielectric constant ǫ and magnetic permeability µ, where E and B are the electromagnetic fields inside the insulator. However, generally, it is possible to include another quadratic term in the effective action S θ = θ 2π α 2π d 3 xdtE · B, where α = e 2 / c is the fine structure constant, and θ is a parameter describing the insulator in question. In the field theory literature this effective action is known as the axion electrodynamics 1 , where θ plays the role of the axion field. Under the periodic boundary condition the partition function and all physical quantities are invariant if θ is shifted by integer multiples of 2π. Therefore all time reversal invariant insulators fall into two distinct classes described by either θ = 0 or θ = π 2 . Topological insulators are defined by θ = π and can only be connected continuously by time reversal breaking perturbations to trivial insulators defined by θ = 0. The form of the effective action implies that an electric field can induce a magnetic polarization, whereas a magnetic field can induce an electric polarization. This effect is known as the topological magneto-electric effect (TME) and θ has the meaning of the magneto-electric polarization P 3 = θ/2π. Physically the parameter θ depends on the band structure of the insulator and has a microscopic expression of the momentum space ChernSimons form 2where A αβ i (k) = −i αk| ∂ ∂ki |βk is the momentum space non-abelian gauge field, with indices α, β referring to the occupied bands. The θ parameter has been calculated explicitly for several basic models of topological insulators 2,3 . In a topological insulator the axion field gives rise to novel physical effects such as the image monopole and anyonic statistics 4 . This field, however, is static in a time-reversal invariant topological insulator. In this work, we consider the anti-ferromagnetic long range order in a topological insulator, which breaks timereversal symmetry spontaneously, so that θ becomes a dynamical axion field taking continuous values from 0 to 2π. In the following we will refer to such an antiferromagnetic insulator as a "topological magnetic insulator". We propose a minimal model i...

Quantum anomalous Hall (QAH) effect in magnetic topological insulators is driven by the combination of spontaneous magnetic moments and spin-orbit coupling. Its recent experimental discovery raises the question if higher plateaus can also be realized. Here we present a general theory for QAH effect with higher Chern numbers, and show by first-principles calculations that thin film magnetic topological insulator of Cr-doped Bi2(Se,Te)3 is a candidate for the C = 2 QAH insulator. Remarkably, whereas higher magnetic field leads to lower Hall conductance plateaus in the integer quantum Hall effect, higher magnetic moment leads to higher Hall conductance plateaus in the QAH effect. The topological phases of two-dimensional (2D) insulators with broken time reversal symmetry is characterized by the first Chern number [1], which takes integer values in the integer quantum Hall effect (IQHE). In the IQHE, electronic states of 2D electron system form Landau levels under strong external magnetic fields, and the Hall resistance is quantized into h/Ce 2 plateaus [2] contributed by dissipationless chiral states at sample edges [3] (where h is Plank's constant, e is the charge of an electron, and C is the Chern number). In principle, quantum Hall effect can exist without the external magnetic field and the associated Landau levels [4], however, the Haldane model [4] with circulating currents on a honeycomb lattice is not easy to implement experimentally. In a QAH insulator, theoretically proposed for magnetic topological insulators (TIs) [5][6][7][8][9], the ferromagnetic (FM) ordering and spin-orbit coupling (SOC) are sufficiently strong that they can give rise to a topologically nontrivial phase with finite Chern number. Recently, the QAH effect has been experimentally discovered in magnetic TI of Cr-doped (Bi,Sb) 2 Te 3 , where the C = 1 has been reached [10]. Search for QAH insulator with higher Chern numbers could be important both for fundamental and practical interests. The edge channels of the QAH insulator has been proposed as interconnects for integrated circuits [11]. However, while the edge channels of the QAH insulator conducts without dissipation, contact resistance could still limit possible application in interconnects. QAH effect with higher plateaus lowers the contact resistance, significantly improving the performance of the interconnect devices. Fractional filling of Chern insulators with C = 2 could also lead to new topological states with novel elementary excitations [12]. QAH effect with higher plateaus also shows dramatic difference between the IQHE and the QAH effect: whereas higher magnetic field leads to lower Hall conductance plateaus in the IQHE, higher magnetic moment leads to higher Hall conductance plateaus in the QAH effect.In this Letter, we present a general theory for QAH effect with higher plateaus. Based on the first-principles calculations, we predict that thin films of Cr-doped Bi 2 (Se x Te 1−x ) 3 TI is a candidate for the C = 2 QAH insulator. The tunable magnetic ordering and SOC in t...

Topological insulators in the Bi 2 Se 3 family have an energy gap in the bulk and a gapless surface state consisting of a single Dirac cone. Low frequency optical absorption due to the surface state is universally determined by the fine structure constant. When the thickness of these three dimensional topological insulators is reduced, they become quasi-two dimensional insulators with enhanced absorbance. The two dimensional insulators can be topologically trivial or non-trivial depending on the thickness, and we predict that the optical absorption is larger for topological non-trivial case compared with the trivial case. Since the three dimensional topological insulator surface state is intrinsically gapless, we propose its potential application in wide bandwidth, high performance photo-detection covering a broad spectrum ranging from terahertz to infrared. The performance of photodetection can be dramatically enhanced when the thickness is reduced to several quintuple layers, with a widely tunable band gap depending on the thickness. PACS numbers: 78.68.+m 78.20.Bh, 78.20.Ci, Topological insulators (TIs) are a new state of quantum matter with an insulating bulk gap and gapless edge or surface states interesting for condensed matter physics, material science and electrical engineering [1][2][3][4][5][6][7][8] . The two-dimensional (2D) TI, with quantum spin Hall (QSH) effect has been predicted and observed in HgTe/CdTe quantum well 2,3 . Recently, 3D TI such as Bi 2 Se 3 and Bi 2 Te 3 were theoretically predicted to have bulk energy gap as large as 0.3eV, and gapless surface states consisting of a single Dirac cone 6,7 . The angle-resolved photoemission spectroscopy (ARPES) observed such linear Dirac spectrum dispersing from the Γ point in both of these materials 7,8 . Bi 2 Se 3 and Bi 2 Te 3 are stoichiometric rhombohedral crystals with layered structure consisting of stacked quintuple layers (QLs), with relatively weak Van der waals coupling between QLs (each QL is about 1nm thick). Therefore high quality thin films have been successfully grown on silicon and silicon carbide substrates via molecular beam epitaxy 9-11 , layer by layer, which enables further scientific study and applications integratable with today's electronics. These materials have also been grown by Au-catalyzed vaporliquid-solid 12 and catalyst-free vapor-solid chemical vapor deposition methods 13 on silicon, silicon dioxide and silicon nitride substrates. The surface states of such thin film have been predicted 6,14,15 and observed to open a gap when they are thinner than 6 QLs 9 . Up to now, few study on optical properties of the topological surface states has been reported. On the other hand, the single Dirac cone on the Bi 2 Se 3 surface can be imagined as 1/4 of graphene 16 , it is straightforward to study the optical properties and relevant applications of TI in analogy to the optoelectronics applications of graphene [17][18][19] .Starting from an effective k · p Hamiltonian and ignoring intra-unit cell dipole contribution to absorban...