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We present a study of the thermoelectric (Seebeck and Nernst) response inheavily overdoped, non-superconducting La$_{1.67}$Sr$_{0.33}$CuO$_4$. In spiteof the electron-like curvature of the Fermi surface, the Seebeck coefficient ispositive at low temperatures. Such a feature, previously observed in copper,silver, gold and lithium, is caused by a non-trivial energy dependence of thescattering time. We argue that this feature implies a strong asymmetry betweenthe lifetime of occupied and unoccupied states along the zone diagonals andsuch an electron-hole asymmetry impedes formation of Cooper pairs along thenodal direction in the superconducting ground state emerging at lower dopinglevels.

Positive Seebeck coefficient in highly doped La$_{2-x}$Sr$_x$CuO$_4$ ($x$=0.33); its origin and implication