Bloch state with energy . Within first-order perturbation theory in k2, one obtains the energy . Now, will exhibit a larger probability in the well, so that it seems reasonable to replace the second term by where is the effective mass of the quantum well. Wannier functions By definition the Bloch functions are delocalized over the whole superlattice. This may provide difficulties if electric fields are applied or effects due to the superlattice's finite length are considered. Therefore, it is often helpful to use different sets of basis states that are better localized. A tempting choice would be the use of eigenstates of single quantum wells. Nevertheless, such a choice has a severe shortcoming: the corresponding states are solutions of two different Hamiltonians, each neglecting the presence of the other well. Thus these states are not orthogonal, creating complications. Typically, the coupling is estimated by the transfer Hamiltonian within this approach. For these reasons, it is more convenient to use the set of Wannier functions. Wannier–Stark ladder Applying an electric field F to the superlattice structure causes the Hamiltonian to exhibit an additional scalar potential eφ(z) = −eFz that destroys the translational invariance. In this case, given an eigenstate with wavefunction and energy , then the set of states corresponding to wavefunctions are eigenstates of the Hamiltonian with energies Ej = E0 − jeFd. These states are equally spaced both in energy and real space and form the so-called Wannier–Stark ladder. The potential is not bounded for the infinite crystal, which implies a continuous energy spectrum. Nevertheless, the characteristic energy spectrum of these Wannier–Stark ladders could be resolved experimentally. Transport The motion of charge carriers in a superlattice is different from that in the individual layers: mobility of charge carriers can be enhanced, which is beneficial for high-frequency devices, and specific optical properties are used in semiconductor lasers. If an external bias is applied to a conductor, such as a metal or a semiconductor, typically an electric current is generated. The magnitude of this current is determined by the band structure of the material, scattering processes, the applied field strength and the equilibrium carrier distribution of the conductor. A particular case of superlattices called superstripes are made of superconducting units separated by spacers. In each miniband the superconducting order parameter, called the superconducting gap, takes different values, producing a multi-gap, or two-gap or multiband superconductivity. Recently, Felix and Pereira investigated