Two noncentrosymmetric ternary pnictides, CaAgP and CaAgAs, are reported as topological line-node semimetals protected solely by mirror-reflection symmetry. The band gap vanishes on a circle in momentum space, and surface states emerge within the circle. Extending this study to spin-orbit coupled systems reveals that, compared with CaAgP, a substantial band gap is induced in CaAgAs by large spin-orbit interaction. The resulting states are a topological insulator, in which the Z 2 topological invariant is given by 1; 000. To clarify the Z 2 topological invariants for time-reversal-invariant systems without spatial-inversion symmetry, we introduce an alternative way to calculate the invariants characterizing a line node and topological insulator for mirror-reflection-invariant systems.

We develop a theory of the tunneling spectroscopy for superconducting topological insulators (STIs), where the surface Andreev bound states (SABSs) appear as helical Majorana fermions. Based on the symmetry and topological nature of parent topological insulators, we find that the SABSs in the STIs have a profound structural transition in the energy dispersions. The transition results in a variety of Majorana fermions, by tuning the chemical potential and the effective mass of the energy band. We clarify that Majorana fermions in the vicinity of the transitions give rise to robust zero bias peaks in the tunneling conductance between normal metal/STI junctions.

Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in Sr2RuO4 hosts a topological phase transition to a topological crystalline SC, which accompanies a d-vector rotation under a magnetic field along the c axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the d-vector rotation in Sr2RuO4 expected from Knight shift measurements but not yet verified.

We self-consistently study surface states of superconducting topological insulators. We clarify that, if a topologically trivial bulk s-wave pairing symmetry is realized, parity mixing of pair potential near the surface is anomalously enhanced by surface Dirac fermions, opening an additional surface gap larger than the bulk one. In contrast to classical s-wave superconductors, the resulting surface density of state hosts an extra coherent peak at the induced gap besides a conventional peak at the bulk gap. We also find that no such extra peak appears for odd-parity superconductors with a cylindrical Fermi surface. Our calculation suggests that the simple U-shaped scanning tunneling microscope spectrum in CuxBi2Se3 does not originate from s-wave superconductivity, but can be explained by odd-parity superconductivity with a cylindrical Fermi surface.

We study the electronic properties of a superconducting topological insulator whose parent material is a topological insulator. We calculate the temperature dependence of the specific heat and spin susceptibility for four promising superconducting pairings proposed by L. Fu and E. Berg [Phys. Rev. Lett. 105 (2010) 097001]. Since the line shapes of the temperature dependence of specific heat are almost identical among three of the four pairings, it is difficult to identify them simply from the specific heat. On the other hand, we obtain wide variations of the temperature dependence of spin susceptibility for each pairing, reflecting the spin structure of the Cooper pair. We propose that the pairing symmetry of a superconducting topological insulator can be determined from measurement of the Knight shift by changing the direction of the applied magnetic field.

Effects of disorder on two-dimensional Z 2 topological insulator are studied numerically by the transfer matrix method. Based on the scaling analysis, the phase diagram is derived for a model of HgTe quantum well as a function of disorder strength and magnitude of the energy gap. In the presence of s z non-conserving spin-orbit coupling, a finite metallic region is found that partitions the two topologically distinct insulating phases. As disorder increases, a narrowgap topologically trivial insulator undergoes a series of transitions; first to metal, second to topological insulator, third to metal, and finally back to trivial insulator. We show that this multiple transition is a consequence of two disorder effects; renormalization of the band gap, and Anderson localization. The metallic region found in the scaling analysis corresponds roughly to the region of finite density of states at the Fermi level evaluated in the self-consistent Born approximation.

We study polycrystalline samples of the hexagonal pnictides, CaAgP and CaAgAs, both of which are ideal candidates for line-node Dirac semimetals. The polycrystalline samples of CaAgP and CaAgAs obtained in this study are low-carrier metals, where hole carriers are dominant. By combining the hole carrier densities estimated from Hall coefficients and the electronic structures calculated by first principles calculations, both samples are found to have a ring-torus Fermi surface, derived from a ring-shaped Dirac line node. In the phosphide sample, the Fermi energy E F is located at around the end of the linear dispersion region of the electronic bands, while the E F in the arsenide sample exists in the middle of this region, suggesting that the arsenide is a more promising system for uncovering the physics of line-node Dirac semimetals.

Superconductors hosting long-sought excitations called Majorana fermions may be ultimately used as qubits of fault-tolerant topological quantum computers. A crucial challenge toward the topological quantum computer is to implement quantum operation of nearly degenerate quantum states as a dynamical process of Majorana fermions. In this paper, we investigate the braiding dynamics of Majorana fermions on superconducting nanowires. In a finite size system, a nonadiabatic dynamical process dominates the non-Abelian braiding that operates qubits of Majorana fermions. Our simulations clarify how qubits behave in the real-time braiding process, and elucidate the optimum condition of superconducting nanowires for efficient topological quantum operation.