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In this paper, we evaluate the transport properties of a Thue-Morse AB-stacked bilayer graphene superlattice with different interlayer potential biases. Based on the transfer matrix method, the transmission coefficient, the conductance, and the Fano factor are numerically calculated and discussed. We find that the symmetry of the transmission coefficient with respect to normal incidence depends on the structural symmetry of the system and the new transmission peak appears in the energy band gap opening region. The conductance and the Fano factor can be greatly modulated not only by the Fermi energy and the interlayer potential bias but also by the generation number. Interestingly, the conductance exhibits the plateau of almost zero conductance and the Fano factor plateaus with Poisson value occur in the energy band gap opening region for large interlayer potential bias.quantum Hall effect, 6 the Klein paradox, 7 the ballistic charge transport, 8 and the special Andreev reflection. 9,10 Natural bilayer graphene (BG) can be formed by two coupled graphene monolayers in the usual AB (or Bernal) stacking. 11,12 In contrast to the charge carriers in the monolayer graphene, the low-energy excitations in the BG behave as massive chiral Fermions with a finite density of states at zero energy and possess a parabolic dispersion close to the Dirac points. This leads to some different transport properties from those in the monolayer graphene, including the new type of integer quantum Hall effect, 3 the perfect reflection instead of the perfect transmission, 4 and the different Berry phase factor of 2π instead of π. 3,13 Also, the controllable energy band gap is an intriguing feature of the BG. It has been shown that a tunable interlayer potential bias, which can be induced by applying the external electric field vertically to the graphene sheet or by attaching some materials on one of the layers, can open a sizable energy band gap with values larger than 200 meV between the valence and conduction bands and can strongly modify the energy bands of the BG. 14-19 Therefore, the electrical conduction can be fully switched off by tuning the gate voltage, which is necessary for applications in nanoelectronics.Since superlattices are very successful in controlling the electronic band structures of many conventional semiconducting materials, 20 the electronic transport in BG superlattices has attracted much attention. 21-25 Bai and Zhang 21 have studied the transport properties of charge carriers through a BG superlattice by using the transfer matrix method based on the two-band Hamiltonian and found that the transmission of the BG superlattice system exhibits similar properties to those in the semiconductor superlattice, and the angularly averaged conductance can be controlled by changing the structure parameters even if Klein tunneling exists. Also, the transmission coefficient and the angularly averaged conductance in a Fibonacci BG superlattice have been investigated in detail. 22 It is shown that the transmission spectra are frag...

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