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金兹堡-朗道理论

1950
  • Vitaly Ginzburg
  • Lev Landau
Laboratory experiment on superconductors illustrating Ginzburg-Landau Theory applications.

(图片仅供参考)

Developed in 1950 by Vitaly Ginzburg and Lev Landau, this is a phenomenological theory that describes superconductivity near the phase transition. It introduces a complex order parameter, [latex]\Psi[/latex], to represent the density of superconducting electrons. The theory successfully describes effects like the Meissner effect and predicts the distinction between Type I and Type II superconductors based on a single parameter, [latex]\kappa[/latex].

The Ginzburg-Landau theory is a macroscopic theory, meaning it does not explain the microscopic origin of superconductivity (which was later done by BCS theory), but it brilliantly describes the behavior of superconductors. It is based on Landau’s general theory of second-order phase transitions. The central idea is to write the free energy of the system as an expansion in powers of the order parameter [latex]\Psi[/latex] and its gradient. The order parameter is zero in the normal state and non-zero in the superconducting state. The free energy density is given by [latex]f = f_n + \alpha|\Psi|^2 + \frac{\beta}{2}|\Psi|^4 + \frac{1}{2m^*}|(-i\hbar\nabla – e^*\mathbf{A})\Psi|^2 + \frac{|\mathbf{B}|^2}{2\mu_0}[/latex], where [latex]\alpha[/latex] and [latex]\beta[/latex] are phenomenological parameters, [latex]\mathbf{A}[/latex] is the magnetic vector potential, and [latex]e^*[/latex] and [latex]m^*[/latex] are the effective charge and mass of the superconducting charge carriers. Minimizing this free energy yields the Ginzburg-Landau equations, which describe the spatial variation of [latex]\Psi[/latex] and the supercurrents. The theory defines two characteristic length scales: the coherence length [latex]\xi[/latex], over which [latex]\Psi[/latex] can vary significantly, and the London penetration depth [latex]\lambda[/latex]. Their ratio, the Ginzburg-Landau parameter [latex]\kappa = \lambda/\xi[/latex], determines the type of superconductor. If [latex]\kappa 1/\sqrt{2}[/latex], it’s Type II. This prediction of a second type of superconductor, which allows partial magnetic field penetration in a vortex lattice, was a major success of the theory, confirmed experimentally by Abrikosov in 1957.

UNESCO Nomenclature: 2211
– Solid state physics

类型

Theoretical Model

中断

Substancial

用法

广泛使用

前体

  • Landau’s theory of second-order phase transitions
  • 伦敦方程式
  • discovery of the Meissner effect
  • 热力学和统计力学

应用程序

  • 超导体的分类(i 型与 ii 型)
  • 临界场和电流的计算
  • modeling of vortices in type ii superconductors
  • theoretical framework for phase transitions in other fields (e.g., 粒子物理学, cosmology)

专利:

NA

潜在创新理念

  • 高临界场超导材料的计算设计
  • modeling of domain walls in ferroelectric and ferromagnetic 材料
  • 模拟早期宇宙中宇宙弦的形成
  • 发展拓扑量子计算理论
  • 预测玻色-爱因斯坦凝聚态的行为
  • 设计具有特定几何形状的超导器件以实现磁通钉扎
  • 模拟生物模式形成
  • 分析流体动力学中的不稳定性
  • 为材料科学中的相场建模创建先进的算法
  • 理解粒子物理学中的希格斯机制(相对论类似物)
Related to: Ginzburg-Landau theory, order parameter, phase transition, Type I superconductor, Type II superconductor, coherence length, penetration depth, Abrikosov vortex, phenomenological theory, free energy.

历史背景

金兹堡-朗道理论

1950
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1957
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1957
1958

(如果日期未知或不相关,例如“流体力学”,则提供其显著出现的近似估计)

第十年 周年纪念日

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