Theory of the Luttinger surface in doped Mott insulators
Abstract
We prove that the Mott insulating state is characterized by a divergence of the electron self-energy at well-defined values of momenta in the first Brillouin zone. When particle-hole symmetry is present, the divergence obtains at the momenta of the Fermi surface for the corresponding noninteracting system. Such a divergence gives rise to a surface of zeros (the Luttinger surface) of the single-particle Green function and offers a single unifying principle of Mottness from which pseudogap phenomena, spectral weight transfer, and broad spectral features emerge in doped Mott insulators. We also show that only when particle-hole symmetry is present does the volume of the zero surface equal the particle density. We identify that the general breakdown of Luttinger’s theorem in a Mott insulator arises from the breakdown of a perturbative expansion for the self-energy in the single-particle Green function around the noninteracting limit. A modified version of Luttinger’s theorem is derived for special cases.
- Publication:
-
Physical Review B
- Pub Date:
- March 2007
- DOI:
- 10.1103/PhysRevB.75.104503
- arXiv:
- arXiv:cond-mat/0602280
- Bibcode:
- 2007PhRvB..75j4503S
- Keywords:
-
- 71.27.+a;
- 74.72.-h;
- Strongly correlated electron systems;
- heavy fermions;
- Cuprate superconductors;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- New version proves explicitly that only when particle-hole symmetry is present does the volume of the surface of zeros equal the particle density thereby generalising recent perturbative arguments