Dependencies of the lattice parameters and the coefficient of thermal expansion of TlInTe2 crystals on temperature are studied at a wide range of temperatures by using XRD, dilatometer, differential thermal analysis, and impedance spectroscopy (IS) methods. The IS measurements of the dielectric function were done along the c-axis and normal to the (110)-plane. IS for E ⊥ (110)-plane was done for two values of the amplitudes, U0 = 0.04 V and 1 V, of ac-voltage with different frequencies; moreover, the measurements for E∥c were realized at U0 = 0.04 V only. IS measurements demonstrate a sequence of the phase transitions (PTs) to the ferroelectric and the ionic conductivity states, also to a structural phase transition. Tl+ ions are shown to shift in the direction of normal to c-axis in the ferroelectric PT, but they are activated along the c-axis in the ionic conductivity PT. The dielectric function in the ionic conductivity PT is shown to increase to a huge positive value and then to drop to a big negative value, reversing its sign. An explanation of this effect is provided as a competition of Drude and polarization contribution to the dielectric function under ac-electric field. Thermal effects of the phase transitions were determined.

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We calculate the Josephson current between two one-dimensional (1D) nanowires oriented along x with proximity induced s-wave superconducting pairing and separated by a narrow dielectric barrier in the presence of both Rashba spin-orbit interaction (SOI) characterized by strength α and Zeeman fields (h alongẑ and B in the x − y plane). We formulate a general method for computing the Andreev bound states energy which allows us to obtain analytical expressions for the energy of these states in several asymptotic cases. We find that in the absence of the magnetic fields the energy gap between the Andreev bound states decreases with increasing Rashba SOI constant leading eventually to touching of the levels. In the absence of Rashba SOI, the Andreev bound states depend on the magnetic fields and display oscillatory behavior with orientational angle of B leading to magneto-Josephson effect. We also present analytic expressions for the dc Josephson current charting out their dependence on B, h, and α. We demonstrate the existence of finite spin-Josephson current in these junctions in the presence of external magnetic fields and provide analytic expressions for its dependence on α, B and h. Finally, we study the AC Josephson effect in the presence of the SOI (for |B| = h = 0) and an external radiation and show that the width of the resulting Shapiro steps in such a system can be tuned by varying α. We discuss experiments which can test our theoretical results.