In a lot of semimetalic and nanow-gap semiconductors Bi l-xSbx, Pb1_xSnx Te, Bii Te3, Hg Te, TlBiTe2 spin-orbit interaction (SOI) has an impo1iant pattern on the electronic structure in the fo1m of the band inversion and this attr·ibute leads to the new solid state - topological insulator. This state is fundamentally distinguished from a regular band insulator by a nontr·ivial time-reversal topological invariant, which characterizes its band str11cture, and non-u-ivial inte1play of charge and spin degree of freedom of band elecu-ons. In results new physics and phenomena related to this states have greatly emerged. Paii of interest in Tis stems from the fact that they represent a new topological phase of noninteracting electr·ons: the TI character of a material is its bulk prope1iy, nontr·ivially encoded in the wavefunctions of the occupied (valence band) states. However, it is the presence of the helical edge/surface states which leads to observable consequences. The gapless helical surface states with lineai· dispersion is similai· to photons. Therefore, when two different Tis or TI and band insulator (BI) are attached together, the refraction phenomenon similai· to optics is expected at the junction as well as this open new ways in nanoscale prope1iies tailoring based on its heterostructure engineering and design of new type of nandevice structures. Some aspects of emergent multifunctional materials and nanodevices based on topological insulator heterostr11ctures ai·e highlighted in the present paper. The elecu-onic states of such materials are described by the low­energy effective 3D Hamiltonian which has the 4x4 matr·ix fo1m and can be expressed in general fonn as H = ( 6(z) + V(z) fonn as H = ( 6(z) + V(z) where cr ai·e the Pauli man-ices,  Δ=Eg/2 Mlk2z +M2k2, p = -in(v.1.. v' vy,v11v z), vi I , V.1 are the electr·on Fe1mi velocities, and V(z) is the potential, which inco1porates the change in the work function in the structure and applied gate voltage. Following the results of our early works we intr·oduced the vector paraineters u which describes the elecu-ical polai·ization and the scalar L to describe the antifenomagnetic ordering along z-axis. We fnTst analyze topological states bound to the inteface of TI and BI like PbTe/SnTe. This helical nature of surface topological states of TI leads to new interface physics of heterojunction of two TI. In the case of two Tis, at the junction we establish a coupling between two surface states belonging to different Tis. Fmiher we analyse on the basis of the above Hamiltonian the TIS for topological insulator heterostr11ctures with inco1porated electr·ical polai·ization u. Using the metod of supersymmetr·ic quantmn mechanics we obtaine the energy spectr11m of the TIS. The proposed TI heterostr11ctures driven by electr·ical polarization has many unique advantages, including: I) it can be realized based on commonly used semiconductors and be integrated into vai·ious devices; 2) it is driven by lai·ge intr·insic polarization fields; 3) the TI state can be manipulated by applying external fields or injecting chai·ge caiTiers and can be adjusted by standai·d semiconductor techniques, including doping, alloying and va1ying the QW thickness. Another oppo1iunity to tailor the TIS is offered by the antiferromagnetic ordering of the materials, which constituted heterostructure. Using again the anzatz of the supersymmetr·ic quantmn mechanics we obtaine the solution of the TIS in such structure.Exploring the prope1iies of nanoscale topological insulators is a growing ai·ea of reseai·ch and the last of the paper paper reveals some aspects of interface device physics of such materials. The spectrum and chai·acteristics of topological interfaceface states (TIS) depending on geometr·ical configuration can be manipulates by different factors: electrical and magnetic fields, str·ain and defo1mation ets. For this reason TI are being explored with a view towai·ds applications, as a potential platfo1m for tailoring nanostructures and nanomaterials prope1iies. This topics cover the main paii of the paper. Thennoelecu-ic aspect of TSS are discussed in the context of TI materials Bi2Se3 and BhTe3 knowing as the best thermoelectric.