$|F = 2, m_F = 2 \rangle$ and $|F = 1, m_F = -1 \rangle$ of $^{87}$Rb atom [@myatt_97]. The TBECs, in the weakly interacting continuum systems, have been used to investigate novel phenomena such as pattern formation [@sasaki_09; @gautam_10_1; @gautam_10_2; @ronen_08; @hoefer_11; @hamner_11; @de_14], phase separation [@ho_96; @ao_98; @gautam_11; @roy_15_2; @bandyopadhyay_17; @papp_08; @tojo_10; @mccarron_11; @wacker_15; @wang_16], nonlinear dynamical excitations [@gautam_12; @gautam_13; @roy_14_2; @kuopanportti_19; @mertes_07; @eto_16a; @eto_16], collective excitations [@roy_14_1; @suthar_15; @roy_15_1; @suthar_16; @suthar_17; @pal_17; @pal_18], Kibble-Zurek mechanism [@nicklas_15], and the production of dipolar molecules [@molony_14; @guo_16; @will_16]. The phase separation, among all the phenomena is a unique property of TBECs. In this work we study the TBECs trapped in the optical lattices, and can be described by the BHM with appropriate modifications. The experimental realization of TBECs in optical lattices are reported in Ref. [@catani_08; @gadway_10] and early theoretical studies are presented in Ref. [@altman_03; @chen_03; @kuklov_03; @kuklov_04]. A remarkable recent achievement related to TBECs is the experimental realization of TBEC with dipolar quantum mixtures of Er-Dy was reported in a recent work [@trautmann_18].

The physics of the two-species BHM (TBHM), the lattice counterpart of TBEC, in 1D has been investigated in detail [@mishra_07; @zhan_14; @wang_14]. And, there has 