Effective potentials in the integral quantum Hall effect
Effective potentials in the integral quantum Hall effect
复制标题
积分量子霍尔效应中的有效势
DOI：
10.1103/physrevb.67.245322
复制
发表时间：
2003
影响因子：
3.7
通讯作者：
F. Lado
中科院分区：
文献类型：
--
作者：
F. Lado
精确的n体分布函数计算的二维，无相互作用的量子电子气在外部磁场中的任何温度和密度。在低温和填充的最低朗道水平下，这些函数与Jancovici [Phys. Rev. Lett. 46，386（1981）]对于特殊等离子体参数Γ=2的经典二维单组分等离子体（2DOCP）。这就建立了与积分量子霍尔效应相关的填充因子v=1的量子态可以精确地用有效经典势Φ（r）=-2 In r来描述，因此2DOCP形式的经典玻尔兹曼因子可以代替量子斯莱特和。此外，该玻尔兹曼因子与Laughlin [Phys. Rev. Lett. 50，1395（1983）]来解释分数量子霍尔效应。更高填充因子v= 2，3，.半解析地从精确的Yvon-Born-绿色积分方程得到，数值地从近似的超网链积分方程得到。它们有渐近形式Φ（r）∈-（2/v）ln r。
The exact n-body distribution functions are calculated for a two-dimensional, noninteracting quantum electron gas in an external magnetic field for any temperature and density. At low temperature and filled lowest Landau level, these functions are identical to the exact distribution functions obtained by Jancovici [Phys. Rev. Lett. 46, 386 (1981)] for the classical two-dimensional one-component plasma (2DOCP) at the special plasma parameter Γ=2. This establishes that the quantum state with filling factor v=1, associated with the integral quantum Hall effect, is precisely described by an effective classical potential Φ(r)=-2 In r, so that a classical Boltzmann factor of 2DOCP form can replace the quantum Slater sum. Further, this Boltzmann factor exactly matches that constructed by Laughlin [Phys. Rev. Lett. 50, 1395 (1983)] to account for the fractional quantum Hall effect. Additional effective potentials for higher filling factors v= 2,3,... are obtained semianalytically from the exact Yvon-Born-Green integral equation and numerically from the approximate hypernetted-chain integral equation. They have the asymptotic form Φ(r)∼-(2/v)ln r.