# Fractionally Quantized Hall Effect: Liquid-Crystal Ground-State and it Excitations - Condensed Matter > Mesoscale and Nanoscale Physics

Abstract: It is shown that the ground-state and the lowest excited-states oftwo-dimensional electron system 2DES, with ion jellium background, correspondto partial crystal-like with the period $L {x}^{\square}=\sqrt{2 m \pi}\ell {0}$ correlation order among $N$ electrons of the main region MR; $L {x}\times L {y}$. Many-body variational ground-state wave function of 2DES ispresented at the fractional and the integral filling factors $u=1-m$;$m=2\ell+1$ and $\ell=0, 1, 2, .$. The ground-state manifests the brokensymmetry liquid-crystal state with 2DES density that is periodic along the $y-$direction, with the period $L {x}^{\square}-m$, and independent of $x$. At$m=3, 5$, the ground-state has essentially lower energy per electron than theLaughlin, uniform liquid, ground-state; the same holds at $m=1$. At $m \geq 3$,the compound form of the many-body ground-state wave function leads to thecompound structure of each electron within the main strip MS; $L {x}^{\square}\times L {y}$. Obtained compound exciton and compound spin-exciton states showfinite excitation gaps. The excited compound electron hole is composed,within MS, from $m$ strongly correlated quasielectrons quasiholes of thetotal charge $e-m$ $-e-m$ each. The activation gap is obtained: it is givenby the excitation gap of relevant compound exciton, at $m \geq 3$, and by thegap of pertinent compound spin-exciton, at $m=1$. Quantized Hall conductance$\sigma {H}=e^{2}-2 m \pi \hbar$ is obtained. The theory is in good agreementwith experiments.

Author: O. G. Balev

Source: https://arxiv.org/