Consider the Lindhard response function:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\chi(\vec{q})=\int\frac{d\vec{k}}{(2\pi)^d}\frac{f_\vec{k}-f_{\vec{k}+\vec{q}}}{\epsilon_\vec{k}-\epsilon_{\vec{k}+\vec{q}}}[/tex]

where ##\vec{q}## is the wavevector, ##\epsilon## is the free electron energy and ##f## is Fermi-Dirac distribution function. For 1D near ##2k_F##, this reduces to:

[tex]\chi(q)=-e^2n(\epsilon_F)\ln\frac{q+2\vec{k}_F}{q-2\vec{k}_F}[/tex]

where ##n(\epsilon_\vec{F})## is the density of states. Clearly ##\chi(\vec{q})## diverges near ##\vec{q}=2\vec{k}_F##.

It is argued (see the picture below) that this divergence is due to Fermi surface nesting, which is represented by the arrows in the picture. What I do not understand is that why, in the 2D case, the arrows are restricted to be horizontal? I can still draw an arrow in any direction since this is a Fermi surface and all points have the same energy and are thus identical...

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Instability of a 1D material due to Fermi surface nesting

Loading...

Similar Threads - Instability material Fermi | Date |
---|---|

I Discharge voltage of materials for Li-Ion batteries | Apr 8, 2017 |

I Material phase in Cu-Zr alloy | Mar 3, 2017 |

Snake instability and vortex pair | Dec 9, 2014 |

Superconducting instability? | Feb 17, 2011 |

Instability of Fermi surface | Apr 28, 2010 |

**Physics Forums - The Fusion of Science and Community**