Atoms

2-D Superconductivity

		Substances in 1 or 2 dimension were considered to be incapable of generating superconductive current because there is not enough connection between different particles to overcome thermal agitation. It was subsequently shown in the 1980s (by the 2016 Nobel Prize winners) that 2-D superconductivity (SC) is possible under certain conditions. The transition to such phase is recapped briefly in the followings.
Figure 13-08f 2-D SC, Phase Diagram	Figure 13-08g 2-D Superconductivity, Vortices [view large image]

• As shown in Figure 13-08f in region D (the Meissner state in 3-D material), superconductivity is destroyed by high magnetic field (up to H_c1) and temperature (up to T_2D).


• Vortices of current start to appear as the external magnetic field (applied perpendicular to the 2-D surface) increases to beyond :
  See "Quantized Magnetic Flux" in SC.
  The GL parameter k turns out to be critical in determining the type of superconductor. For the normal (classical) type I, k < 1/, while for the type II 2-D superconductor k > 1/. Anyway, there is no superconductive current at this stage (region P in Figure 13-08f) as the vortices move in a dis-organized way (similar to the atoms or molecules in liquid) destroying the zero-resistance state (Figures 13-08g,h).



With further decreasing temperature, the system enters the hexatic phase (region H in Figure 13-08f, also see Figure 13-08h) with the vortices arrange themselves in hexagonal patterns. This phase has orientational order but is only one step closer to superconductive state. Such configuration is sometimes referred to as topological order to mimic the discrete change between geometric classes to phase change between matter states (see more in "Topological Interpretation").

Figure 13-08h Hexatic Phase [view large image]




As the temperature drops below the critical value of TM (see Figure 13-08f), = 1.9 K for NbSe2, the vortices with opposite spin pair up into a composite entity behaving like a spin 0 particle. This phase has a structure with both translational and orientational orders (Figures 13-08h,i). The pairs of vortices are the basic component of the superconductive current similar to the Cooper pairs in type I superconductor. The separation of the electrons in the Cooper pair and the pair of vortices are both of the order 10-5 cm. The type II superconductivity disappear beyond the upper magnetic field limit (see Figure 13-08f). The vortices are sometimes called topological defects as they are different kind of objects in the crystal lattices.

Figure 13-08i Vortices in 2-D Superconductor [view large image]




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