Integer quantum Hall effect of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mtext>−</mml:mtext><mml:msub><mml:mi>T</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> model with a broken flat band
Juan Juan Wang, S. Liu, Jing Wang, Jun-Feng Liu
Abstract
The nondispersive flat band in the $\ensuremath{\alpha}\text{\ensuremath{-}}{T}_{3}$ model leads to a conventional integer quantum Hall effect (IQHE) for Dirac particles as well as the existence of the zero Hall-conductivity plateau ($\ensuremath{\nu}=0$) at the band center. In this work, we study the broken-flat-band effect on the IQHE by introducing the disorder or staggered lattice potential in the system. It is found that the zero-Hall plateau is quite vulnerable and readily destroyed by weak disorders and even the neighboring plateaux $\ensuremath{\nu}=\ifmmode\pm\else\textpm\fi{}2$ are also smeared. When a uniform staggered lattice potential is turned on without disorder, a new serial of integer Hall plateaux with ${\ensuremath{\sigma}}_{xy}=\ensuremath{\nu}{e}^{2}/h$ ($\ensuremath{\nu}=\ifmmode\pm\else\textpm\fi{}2,\ifmmode\pm\else\textpm\fi{}4,\ensuremath{\cdots}$) grow out in the zero-Hall conductivity regime and show no relativistic properties. This emergent IQHE is independent of the strong magnetic field and even fully valley polarized. The findings indicate that the broken flat band in the $\ensuremath{\alpha}\text{\ensuremath{-}}{T}_{3}$ model shall make a great difference on the transport properties of Dirac particles.