Fermi surface of underdoped high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>superconducting cuprates

The coexistence of a $\ensuremath{\pi}$-flux state and a $d$-wave resonant-valance-bond (RVB) state is considered in this paper within the slave-boson approach. A critical value of doping concentration ${\ensuremath{\delta}}_{c}$ is found, below which the coexisting $\ensuremath{\pi}$-flux and $d$-wave RVB state is favored in energy. The pseudo-Fermi surface of spinons and the physical electron spectral function are calculated. A clear Fermi-level crossing is found along the (0,0) to $(\ensuremath{\pi}$, $\ensuremath{\pi})$ direction, but no such crossing is detected along the $(\ensuremath{\pi}$, 0) to $(\ensuremath{\pi}$, $\ensuremath{\pi})$ direction. Also, an energy gap of $d$-wave symmetry appears at the Fermi level in our calculation. The above results are in agreement with the angle-resolved photoemission experiments which indicate at a $d$-wave pseudogap and a half-pocket-like Fermi surface in underdoped cuprates.

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