Fermi surfaces in general co-dimension and a new controlled non-trivial fixed point

Details Fermi surfaces in general co-dimension and a new controlled non-trivial fixed point Fermi surfaces in general co-dimension and a new controlled non-trivial fixed point

2008-06-30

arxiv.org/abs/0807.0032v1

Phys. Rev. Lett. 102, 046406 (2009)

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages

Scientific paper

10.1103/PhysRevLett.102.046406

Traditionally Fermi surfaces for problems in $d$ spatial dimensions have dimensionality $d-1$, i.e., codimension $d_c=1$ along which energy varies. Situations with $d_c >1$ arise when the gapless fermionic excitations live at isolated nodal points or lines. For $d_c > 1$ weak short range interactions are irrelevant at the non-interacting fixed point. Increasing interaction strength can lead to phase transitions out of this Fermi liquid. We illustrate this by studying the transition to superconductivity in a controlled $\epsilon$ expansion near $d_c = 1$. The resulting non-trivial fixed point is shown to describe a scale invariant theory that lives in effective space-time dimension $D=d_c + 1$. Remarkably, the results can be reproduced by the more familiar Hertz-Millis action for the bosonic superconducting order parameter even though it lives in different space-time dimensions.

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