TY - JOUR

T1 - Mottness

AU - Phillips, Philip

N1 - Funding Information:
I wish to acknowledge several of my students who have worked assiduously on the ideas presented in this review: Tudor D. Stanescu, whose thesis was entitled “Mottness,” Ting-Pong Choy, and Dimitrios Galanakis. I also acknowledge the collaboration with Claudio Chamon which led to the proof on T-linear resistivity. I also thank E. Fradkin whose insistence that zeros did not exist forced us to construct the proof on zeros in Section 4 and A. Tsvelik for an e-mail exchange on the 1D zero problem. This work was funded by the NSF Grant No. DMR-0305864. The Workshop on Mottness and Quantum Criticality was made possible by a Grant from NSF and the DOE.

PY - 2006/7

Y1 - 2006/7

N2 - We review several of the normal state properties of the cuprates in an attempt to establish an organizing principle from which pseudogap phenomena, broad spectral features, T-linear resistivity, and spectral weight transfer emerge. We first show that standard field theories with a single critical length scale cannot capture the T-linear resistivity as long as the charge carriers are critical. What seems to be missing is an additional length scale, which may or may not be critical. Second, we prove a generalised version of Luttinger's theorem for a Mott insulator. In particular, we show that for Mott insulators, regardless of the spatial dimension, the Fermi surface of the non-interacting system is converted into a surface of zeros of the single-particle Green function when the underlying band structure has particle-hole symmetry. Only in the presence of particle-hole symmetry does the volume of the surface of zeros equal the particle density. The surface of zeros persists at finite doping and is shown to provide a framework from which pseudogaps, broad spectral features, spectral weight transfer on the Mott gap scale, and the additional length scale required to capture T-linear resistivity can be understood.

AB - We review several of the normal state properties of the cuprates in an attempt to establish an organizing principle from which pseudogap phenomena, broad spectral features, T-linear resistivity, and spectral weight transfer emerge. We first show that standard field theories with a single critical length scale cannot capture the T-linear resistivity as long as the charge carriers are critical. What seems to be missing is an additional length scale, which may or may not be critical. Second, we prove a generalised version of Luttinger's theorem for a Mott insulator. In particular, we show that for Mott insulators, regardless of the spatial dimension, the Fermi surface of the non-interacting system is converted into a surface of zeros of the single-particle Green function when the underlying band structure has particle-hole symmetry. Only in the presence of particle-hole symmetry does the volume of the surface of zeros equal the particle density. The surface of zeros persists at finite doping and is shown to provide a framework from which pseudogaps, broad spectral features, spectral weight transfer on the Mott gap scale, and the additional length scale required to capture T-linear resistivity can be understood.

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U2 - 10.1016/j.aop.2006.04.003

DO - 10.1016/j.aop.2006.04.003

M3 - Article

AN - SCOPUS:33744968668

VL - 321

SP - 1634

EP - 1650

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 7

ER -