Luttinger-volume violating Fermi liquid in the pseudogap phase of the cuprate superconductors

Based on the NMR measurements on Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ (La-Bi2201) in strong magnetic fields, we identify the non-superconducting pseudogap phase in the cuprates as a Luttinger-volume violating Fermi liquid (LvvFL). This state is a zero temperature quantum liquid that does not break translational symmetry, and yet, the Fermi surface encloses a volume smaller than the large one given by the Luttinger theorem. The particle number enclosed by the small Fermi surface in the LvvFL equals the doping level $p$, not the total electron number $n_e=1-p$. Both the phase string theory and the dopon theory are introduced to describe the LvvFL. For the dopon theory, we can obtain a semi-quantitative agreement with the NMR experiments.Comment: The final version in PR

Crossover from Fermi Arc to Full Fermi Surface

The Fermi surface as a contour of the gapless quasiparticle excitation in momentum space is studied based on a mean-field theory of the doped Mott insulator, where the underlying pseudogap phase is characterized by a two-component resonating-valence-bond (RVB) order that vanishes in the overdoping at $\delta>\delta^*$. Here the quasiparticle emerges as a ``collective'' mode and a Fermi arc is naturally present in the pseudogap regime, while a full Fermi surface is recovered at $\delta>\delta^*$. The area enclosed by the gapless quasiparticle contour still satisfies the Luttinger volume in both cases, and the ``Fermi arc'' at $\delta<\delta^*$ is actually due to a significant reduction of the spectral weight caused by a quasiparticle fractionalization in the antinodal region. The endpoints of the Fermi arcs exhibit enhanced density of states or ``hotspots'', which can further give rise to a charge-density-wave-like quasiparticle interference pattern. At the critical doping $\delta^*$, the fractionalized spin excitations become gapless and incoherent which is signaled by a divergent specific heat. At $\delta>\delta^*$, the quasiparticle excitation restores the coherence over the full Fermi surface, but the fractionalization still persists at a higher energy/temperature which may be responsible for a strange metal behavior. Different mechanisms for the Fermi arc and experimental comparisons are briefly discussed.Comment: 20 pages, 13 figure

(Z)-5-Benzene­carbothioyl-1,11-dimethyl-6-phenyl-5H-dibenzo[d,f][1,3]diazepine

The seven-membered ring in the title compound, C28H22N2S, has a two-coordinate N atom as well as a three-coordinate N atom. The ring adopts a boat-shaped conformation with two C atoms of one methyl­phenyl ring as the stern and the three-coordinate N atom as the prow. The N,N-dimethyl­ethane­thio­amide fragment is nearly planar (r.m.s. deviation = 0.049 Å); the phenyl ring of the benzene­carbothioyl unit connected to the three-coordinate N atom is aligned at 83.72 (4)° with respect to the mean plane of this fragment. Weak inter­molecular C—H⋯S hydrogen bonding is present in the crystal structure