ABSTRACT - DRUM - University of Maryland
ABSTRACT - DRUM - University of Maryland
ABSTRACT - DRUM - University of Maryland
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Chapter 7<br />
Majorana Zero Modes Beyond BCS Mean-Field<br />
Theory<br />
The BCS theory <strong>of</strong> superconductivity [149], which all our theoretical study<br />
<strong>of</strong> topological superconductors is based on, is a mean-field theory <strong>of</strong> the manybody<br />
effect originating from four-fermion interaction. Although it has been proved<br />
to be enormously successful in describing superconductivity, fluctuation effects beyond<br />
the mean-field theory do arise in certain circumstances. For example, in the<br />
neighborhood <strong>of</strong> the superconducting phase transition where the mean-field order<br />
parameter is very small, the fluctuation effect can be dominant in various thermodynamical<br />
quantities. Another scenario where fluctuations can not be neglected is<br />
low-dimensional systems, where fluctuation effects are actually most prominent. A<br />
celebrated theorem proved by Mermin and Wagner [150], states that under very<br />
generic conditions (e.g. short-range interactions) no spontaneous continuous symmetry<br />
breaking can occur in one dimension (1 + 1 space-time dimension) even at<br />
zero temperature. The same is true in two dimensions at any finite temperature. In<br />
both cases, the <strong>of</strong>f-diagonal long-range order [151], which defines the spontaneous<br />
symmetry breaking, is smeared out by strong quantum or thermal fluctuations and<br />
becomes quasi-long-range order characterized by the algebraic decay <strong>of</strong> order pa-<br />
127