Chiral Surface States Research Articles

Edge states of integral quantum Hall states versus edge states of antiferromagnetic quantum spin chains.

Using the network model representation, it is shown that the edge states of finite-size integral quantum Hall liquid can be regarded as the edge states of an SU$(2N)$ open antiferromagnetic quantum spin chain in the $N \rightarrow 0$ limit. The structures of edge states in both cases of integer quantum Hall liquid and an SU$(2N)$ antiferromagnetic quantum spin chain are compared and the relations between them are pointed out. This correspondence is used to give qualitative arguments in favor of the recent results on two-dimensional electron systems coupled in layers with a large perpendicular magnetic field. In particular, it is shown that the absence of the localization in the two-dimensional chiral surface state of the integral quantum Hall liquid in the case of the finite-size coupled system can be explained by the absence of the gap in the excitation spectrum of an SU$(2N)$ ferromagnetic quantum spin chain in the $N \rightarrow 0$ limit.

Chiral surface states in the bulk quantum Hall effect.

In layered samples which exhibit a bulk quantum Hall effect (QHE), a two-dimensional (2D) surface ``sheath'' of gapless excitations is expected. These excitations comprise a novel 2D chiral quantum liquid which should dominate the low temperature transport along the field ( $z$ axis). For the integer QHE, we show that localization effects are completely absent in the ``sheath,'' giving a metallic $z$-axis conductivity. For fractional filling $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/3$, the sheath is a 2D non-Fermi-liquid, with incoherent $z$-axis transport and ${\ensuremath{\sigma}}_{\mathrm{zz}}\ensuremath{\sim}{T}^{3}$. Experimental implications for the Bechgaard salts are discussed.