observe a trend that the Dirac operator acquires a zero mode in the large-$N$ limit. We also confirm that the wave function of the zero mode is localized at a point, which is consistent with the picture of intersecting D-branes.

In this scenario, the Dirac zero modes appear in pairs with opposite chirality. As simple ways to obtain chiral fermions from classical solutions in the type IIB matrix model, one can either compactify the model on a non-commutative torus [@Aoki:2008ik; @Aoki:2010gv] or one can replace the matrices by operators [@Honda:2019bdi] assuming $N=\infty$. However, it is still an open question whether the original type IIB matrix model can give rise to chiral fermions at low energy starting from finite $N$ and taking the large-$N$ limit.

The rest of this paper is organized as follows. In section \[sec:classicalsolution\], we explain how we generate classical solutions of the type IIB matrix model assuming a quasi direct-product structure for the (3+1) dimensions and the extra six dimensions. In section \[Sec:analysis\_X\], we investigate the space-time structure in the (3+1) dimensions and show that the expanding behavior with a smooth structure appears in typical solutions. In section \[sec: results\_chiralzeromode\], we show that the block-diagonal structure in 