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We clarify universal critical properties of delocalization-localizationtransitions in three-dimensional (3D) unitary and orthogonal classes withparticle-hole and/or chiral symmetries (classes AIII, BDI, D, C and CI). Wefirst introduce tight-binding models on cubic lattice that belong to these fivenonstandard symmetry classes respectively. Unlike the Bogoliubov-de GennesHamiltonian for superconductors, all the five models have finite areas of Fermisurfaces in the momentum space in the clean limit. Thereby, the scaling theoryof the Anderson transition guarantees the presence of thedelocalization-localization transitions at finite disorder strength in thesemodels. Based on this expectation, we carry out extensive transfer matrixcalculations of the Lyapunov exponents for zero-energy eigenstates of thedisordered tight-binding models with quasi-one-dimensional geometry. Near theAnderson transition point, the correlation length diverges with a universalcritical exponent $\nu$. Using finite-size scaling analysis of the localizationlength, we determine the critical exponent of the transitions and scalingfunction of the (normalized) localization length in the three non-standardunitary symmetry classes: $\nu_{\text{AIII}}=1.06\pm0.02$,$\nu_{\text{D}}=0.87\pm0.03$, and $\nu_{\text{C}}=0.996\pm0.012$. Our result ofthe class C is consistent with a previous study of classical network model [M.Ortu\~no et al, Phys. Rev. Lett. 102, 070603 (2009)]. The critical exponents ofthe two non-standard orthogonal classes are estimated as $\nu_{\text{CI}}=1.17\pm 0.02$ and $\nu_{\text{BDI}}=1.12 \pm 0.06$. Our result of the class CI isconsistent with another previous study of a lattice model, while the exponentof the class BDI is at variance with the previous evaluation of nodal Diracring model [X. L. Luo et al, Phys. Rev. B. 101, 020202(R) (2020)].

Universality classes of the Anderson transition in three-dimensional symmetry classes AIII, BDI, C, D and CI