We discuss optical absorption in topological insulators and study possible photoelectric effects theoretically. We found that absorption of circularly polarized electromagnetic waves in twodimensional topological insulators results in electric current in the conducting 1D edge channels, the direction of the current being determined by the light polarization. We suggest two ways of inducing such a current: due to magnetic dipole electron transitions stimulated by irradiation of frequency below the bulk energy gap, and due to electric dipole transitions in the bulk at frequencies larger than the energy gap with subsequent capture of the photogenerated carriers on conducting edge states. PACS numbers: 73.25.+i,72.25.Fe, 72.40.+w The rich new physics and unusual properties of topological insulators (TI) attract much attention in recent years, for review see [1][2][3]. The spectrum of TI in the bulk has a finite energy gap E G , while there are topologically protected conductive surface states inside the gap. The states with somewhat similar properties were predicted also long ago at the surface of a conventional narrow-gap semiconductor [4] and at the interface of heterojunctions made of two insulators with inverted energy bands [5] without appealing to topological reasons. The chiral states studied in recent works on TI [1-3] and the chiral states considered in old papers [4,5] were derived using different theoretical models and the states have different spin structure. Derivation of the surface state of TI was essentially based on quadratic dispersion relation of the mass term in a Dirac-type Hamiltonian which is valid for materials like Bi 2 Se 3 [2, 3] or HgTe/CdTe semiconductor quantum wells [1,6], and the wave functions of the surface states are formed from the states of bulk bands with the same spin directions. Therefore, the electron surface states in TI can be characterized by spin oriented perpendicular to the momentum. While in Refs. [4,5] the mass dispersion is not needed to derive the surface states, and the surface states are formed from the bulk band states of the opposite spin directions.Experimental study of transport properties related to the surface states is typically complicated by residual electrons and holes in the bulk. In this respect it would be interesting to study the possibility to induce the current in the surface state by absorption of circularly polarized light. As the left/right circular polarization of the light is associated with the angular momentum projection ±1, the absorption of polarized light can vary the number of electrons with definite spin. Since the directions of the spin and momentum of electrons in the chiral states are related, variation of the spin distribution may affect the symmetry of the momentum distribution, and, hence, excite the current. As these effects are related only to the chiral surface state, the bulk contribution to the current should be absent.Below we set e,h and k B to unity, restoring dimensional units in final expressions when necessary.Semicon...

We study theoretically 2D HgTe/CdTe quantum well topological insulator (TI) illuminated by circularly polarized light with frequencies higher than the difference between the equilibrium Fermi level and the bottom of the conduction band (THz range). We show that electron-hole asymmetry results in spin-dependent electric dipole transitions between edge and bulk states, and we predict an occurrence of a circular photocurrent. If the edge state is tunnel-coupled to a conductor, then the photocurrent can be detected by measuring an electromotive force (EMF) in the conductor, which is proportional to the photocurrent.

Cooper pairs in two-dimensional unconventional superconductors with broken inversion symmetry are in a mixture of an even-parity spin-singlet pairing state with an odd-parity spin-triplet pairing state. We study the magnetic properties of the impurity bound states in such superconductors and find striking signatures in their spin polarization which allow to unambiguously discriminate a nontopological superconducting phase from a topological one. Moreover, we show how these properties, which could be measured using spin-polarized scanning tunneling microscopy (STM), also enable to determine the direction of the spin-triplet pairing vector of the host material and thus to distinguish between different types of unconventional pairing.