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+@Article{Yang_PhysRevB_2024_v110_p235410,
+    author =   {Shengguo Yang and Jiaxin Chen and Chao-Fei Liu and Mingxing Chen},
+    title =    {{Evolution of flat bands in  MoSe2/WSe2  moir{\'e} lattices: A study
+             combining machine learning and band unfolding methods}},
+    journal =  {Phys. Rev. B},
+    year =     2024,
+    volume =   110,
+    number =   23,
+    pages =    235410,
+    doi =      {10.1103/PhysRevB.110.235410},
+    abstract = {Moir{\textbackslash}'e lattices have served as the ideal quantum
+             simulation platform for exploring novel physics due to the flat
+             electronic bands resulting from the long wavelength
+             moir{\textbackslash}'e potentials. However, the large sizes of this
+             type of system challenge the first-principles methods for full
+             calculations of their electronic structures, thus bringing
+             difficulties in understanding the nature and evolution of the flat
+             bands. In this study, we investigate the electronic structures of
+             moir{\textbackslash}'e patterns of MoSe{\$}{\_}2{\$}/WSe{\$}{\_}2{\$}
+             by combining ab initio and machine learning methods. We find that a
+             flat band with a bandwidth of about 5 meV emerges below the valence
+             band edge at the K point for the H-stacking at a twist angle of
+             3.89{\$}{\textasciicircum}{\{}{\textbackslash}circ{\}}{\$} without
+             spin-orbit coupling effect. Then, it shifts dramatically as the twist
+             angle decreases and becomes about 20 meV higher than the valence band
+             maximum for the twist angle of
+             3.15{\$}{\textasciicircum}{\{}{\textbackslash}circ{\}}{\$}. Multiple
+             ultra-flat bands emerge as the twist angle is reduced to
+             1.7{\$}{\textasciicircum}{\{}{\textbackslash}circ{\}}{\$}. The spin-
+             orbit coupling leads to a giant spin splitting comparable to that
+             observed in the untwisted system (about 0.45 eV) and is nearly
+             independent of twisting and stacking. As a result, the K-valley flat
+             band remains the valence band maximum with the inclusion of spin-orbit
+             coupling. Band unfolding reveals that the ultra-flat bands formed by
+             the {\$}{\textbackslash}Gamma{\$} and K valleys show distinct
+             behaviors. The {\$}{\textbackslash}Gamma{\$}-valley flat bands are
+             sensitive to the interlayer coupling, thus experiencing dramatic
+             changes as the twist angle decreases. In contrast, the K-valley flat
+             band, which shows a weak dependence on the interlayer coupling, is
+             mainly modulated by structural reconstruction. Therefore, a relatively
+             small angle
+             (2.13{\$}{\textasciicircum}{\{}{\textbackslash}circ{\}}{\$}) is
+             required to generate the K-valley flat band, which experiences a
+             transition from the honeycomb to the triangular lattice as the twist
+             angle decreases.},
+}
+
 @Article{Tang_NatCommun_2024_v15_p8815,
     author =   {Zechen Tang and He Li and Peize Lin and Xiaoxun Gong and Gan Jin and
              Lixin He and Hong Jiang and Xinguo Ren and Wenhui Duan and Yong Xu},