Topological phases of topological insulator thin films

We study the properties of a thin film of topological insulator material. We treat the coupling between helical states at opposite surfaces of the film in the properly-adapted tunneling approximation, and show that the tunneling matrix element oscillates as function of both the film thickness and the momentum in the plane of the film for Bi$_2$Se$_3$ and Bi$_2$Te$_3$. As a result, while the magnitude of the matrix element at the center of the surface Brillouin Zone gives the gap in the energy spectrum, the sign of the matrix element uniquely determines the topological properties of the film, as demonstrated by explicitly computing the pseudospin textures and the Chern number. We find a sequence of transitions between topological and non-topological phases, separated by semimetallic states, as the film thickness varies. In the topological phase the edge states of the film always exist but only carry a spin current if the edge potentials break particle-hole symmetry. The edge states decay very slowly away from the boundary in Bi$_2$Se$_3$, making Bi$_{2}$Te$_{3}$, where this scale is shorter, a more promising candidate for the observation of these states. Our results hold for free-standing films as well as heterostructures with large-gap insulators

Bound states and controllable currents on Topological Insulator surfaces with extended magnetic defects

We show that a magnetic line defect on the surface of a topological insulator generically supports two distinct branches of spin-polarized and current carrying one-dimensional bound states. We identify the components of magnetic scattering that lead to the bound states. The velocity, and hence spin texture, of each of those branches can be independently tuned by a magnetic field rotated in the plane of the surface. We compute the local net and spin-resolved density of states as well as spin accumulation and charge currents. The net spin polarization and current due to both bound and scattering states vary stepwise as a function of the electrostatic and magnetic components of the scattering potential, and can be tuned by an applied field. We discuss stability of the bound states with respect to impurity scattering

Manipulation of a two-photon pump in superconductor - semiconductor heterostructures

We investigate the photon statistics, entanglement and squeezing of a pn-junction sandwiched between two superconducting leads, and show that such an electrically-driven photon pump generates correlated and entangled pairs of photons. In particular, we demonstrate that the squeezing of the fluctuations in the quadrature amplitudes of the emitted light can be manipulated by changing the relative phase of the order parameters of the superconductors. This reveals how macroscopic coherence of the superconducting state can be used to tailor the properties of a two-photon state.Comment: 4+ pages, 3 figures; includes Supplemental Material (9 pages, 1 figure). Published versio

Proximity-Induced Superconductivity at Non-Helical Topological Insulator Interfaces

We study how non-helical spin textures at the boundary between a topological insulator (TI) and a superconductor (SC) affect the proximity-induced superconductivity of the TI interface state. We consider TIs coupled to both spin-singlet and spin-triplet SCs, and show that for the spin-triplet parent SCs the resulting order parameter induced onto the interface state sensitively depends on the symmetries which are broken at the TI-SC boundary. For chiral spin-triplet parent SCs, we find that nodal proximity-induced superconductivity emerges when there is broken twofold rotational symmetry which forces the spins of the non-helical topological states to tilt away from the interface plane. We furthermore show that the Andreev conductance of lateral heterostructures joining TI-vacuum and TI-SC interfaces yields experimental signatures of the reduced symmetries of the interface states.Comment: 5 pages, 2 figure

Inter-quintuple layer coupling and topological phase transitions in the chalcogenide topological insulators

Driving quantum phase transitions in the 3D topological insulators offers pathways to tuning the topological states and their properties. We use DFT-based calculations to systematically investigate topological phase transitions in Bi$_2$Se$_3$, Sb$_2$Se$_3$, Bi$_2$Te$_3$ and Sb$_2$Te$_3$ by varying the $c/a$ ratio of lattice constants. This ensures no net hydrostatic pressure under anisotropic stress and strain and allows a clear identification of the physics leading to the transition. As a function of $c/a$, all of these materials exhibit structural and electronic stability of the quintuple layers (QLs), and quasi-linear behavior of both the inter-quintuple layer distance and the energy gap near the topological transition. Our results show that the transition is predominantly controlled by the inter-QL physics, namely by competing Coulomb and van der Waals interactions between the outer atomic sheets in neighboring quintuple layers. We discuss the implications of our results for topological tuning by alloying.Comment: 10 pages, 7 figure

Conductance of gated junctions as a probe of topological interface states

Energy dispersion and spin orientation of the protected states at interfaces between topological insulators (TIs) and non-topological materials depend on the charge redistribution, strain, and atomic displacement at the interface. Knowledge of these properties is essential for applications of topological compounds, but direct access to them in the interface geometry is difficult. We show that conductance of a gated double junction at the surface of a topological insulator exhibits oscillations and a quasi-linear decay as a function of gate voltage in different regimes. These give the values for the quasiparticle velocities along and normal to the junction in the interface region, and determine the symmetry of the topological interface states. The results are insensitive to the boundary conditions at the junction

Interface symmetry and spin control in topological-insulator-semiconductor heterostructures

Heterostructures combining topological and nontopological materials constitute the next frontier in the effort to incorporate topological insulators (TIs) into electronic devices. We show that the properties of the interface states appearing at the boundary between a topologically trivial semiconductor (SE) and a TI are controlled by the lowering of the interface symmetry due to the presence of the SE. For the [111]-grown heterostructure, SE-TI interface states exhibit elliptical contours of constant energy and complex spin textures with broken helicity, in contrast to the well-studied helical Dirac surface states. We derive a general effective Hamiltonian for SE-TI junctions, and propose experimental signatures such as an out of plane spin accumulation under a transport current and the opening of a spectral gap that depends on the direction of an applied in-plane magnetic field