  Bound states in the continuum (BICs) and Fano resonances in planar photonic
lattices, including metasurfaces and photonic crystal slabs, have been studied
extensively in recent years. Typically, the BICs and Fano resonances are
associated with the second stop bands open at the second-order Gamma ($\Gamma$)
point. This paper address the fundamental properties of the fourth stop band
accompanied by BICs at the third-order $\Gamma$ point in one-dimensional (1D)
leaky-mode photonic lattices. At the fourth stop band, one band edge mode
suffers radiation loss, thereby generating a Fano resonance, while the other
band edge mode becomes a nonleaky BIC. The fourth stop band is controlled
primarily by the Bragg processes associated with the first, second, and fourth
Fourier harmonic components of the periodic dielectric constant modulation. The
interplay between these three major processes closes the fourth band gap and
induces a band flip whereby the leaky and BIC edges transit across the fourth
band gap. At the fourth stop band, a new type of BIC is formed owing to the
destructive interplay between the first and second Fourier harmonics. When the
fourth band gap closes with strongly enhanced $Q$ factors, Dirac cone
dispersions can appear at the third-order $\Gamma$ point. Our results
demonstrate a method for manipulating electromagnetic waves by utilizing the
high-$Q$ Bloch modes at the fourth stop band.
