Thermodynamics of the Double-Layer Quantum Hall Systems

Abstract

In this paper we apply the exact solution of the sine-Gordon model to describe thermodynamic properties of the soliton liquid in the incommensurate phase of the double-layer quantum Hall systems. In this way we include thermal fluctuations and extend to finite temperatures the results obtained by C.B. Hanna, A.H. MacDonald and S.M. Girvin [Phys. Rev. B {\bf 63}, 125305 (2001)]. In addition we calculate the specific heat of the system. While the results obtained for the sine-Gordon model are available in a temperature interval $(0,T_c)$, where $T_c=8\pi {\rho }_s$, ${\rho }_s$ the pseudospin stiffness, they can be applied in the bilayer system up to temperatures $3T_{\mathrm{BKT}}$, where $T_{\mathrm{BKT}}=\pi {\rho }_s/2$ is the vortex mediated Berezinskii-Kosterlitz-Thouless transition temperature. Above this temperature the operators $\cos \beta \varphi$ and $\cos (2\pi \vartheta /\beta )$ are both relevant and the system is in a phase with coexisting order parameters. $\vartheta$ is the dual field of $\varphi$ and $\beta$ is the sine-Gordon coupling constant. We provide numerical estimates for thermodynamic quantities for the range of parameters relevant for GaAs.

6 pages, 4 figures, final version as published

References in corpus (3)

• Incommensurate ground state of double-layer quantum Hall systems
• Scaling Exponents in the Incommensurate Phase of the Sine-Gordon and U(1) Thirring Models
• Exact Results for Thermodynamics of the Classical Field Theories: Sine- and Sinh-Gordon Models