Recovered minimal conductivity in 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
Jie Wang, Jun-Feng Liu, C. S. Ting
Abstract
Whether there is a minimal conductivity in the $\ensuremath{\alpha}\text{\ensuremath{-}}{T}_{3}$ model or not is still in debate. By considering the evanescent modes contributing to the zero-energy conductivity, we showed that the conductivity of a large sample vanishes in the clean limit but it can rise up swiftly to the same magnitude of order of ${\ensuremath{\sigma}}_{0}=4{e}^{2}/h\ensuremath{\pi}$ when either a mass term of Dirac electrons or a weak disorder is introduced into the system. Both methods can render a nonzero minimal conductivity that is continuous upon the parameter $\ensuremath{\alpha}$. The mass term can cause the conductivity smaller than ${\ensuremath{\sigma}}_{0}$ depending on $\ensuremath{\alpha}$, while the static disorder can make it approach to ${\ensuremath{\sigma}}_{0}$ for $\ensuremath{\alpha}\ensuremath{\rightarrow}0$ and be a little larger than ${\ensuremath{\sigma}}_{0}$ for $\ensuremath{\alpha}\ensuremath{\rightarrow}1$ in a mesoscopic sample. It is also found that the recovered minimal conductivity is quite stable against a moderate disorder strength.