The magnetic flux periodicity of superconducting loops as well as flux quantization itself are a manifestation of macroscopic quantum phenomena with far reaching implications. They provide the key to the understanding of many fundamental properties o
f superconductors and are the basis for most bulk and device applications of these materials. In superconducting rings the electrical current has been known to periodically respond to a magnetic flux with a periodicity of $bm{h/2e}$. Here, the ratio of Plancks constant and the elementary charge defines the magnetic flux quantum $bm{h/e}$. The well-known $bm{h/2e}$ periodicity is viewed to be a hallmark for electronic pairing in superconductors and is considered evidence for the existence of Cooper pairs. Here we show that in contrast to this long-term belief, rings of many superconductor bear an $bm{h/e}$ periodicity. These superconductors include the high-$bm{T_c}$ cuprates, Sr$_2$RuO$_4$, the heavy-fermion superconductors, as well as all other unconventional superconductors with nodes in the energy gap functions, and s-wave superconductors with small gaps or states in the gap. As we show, the 50-year-old Bardeen--Cooper--Schrieffer theory of superconductivity implies that for multiply connected paths of such superconductors the ground-state energies and consequently also the supercurrents are generically $bm{h/e}$ periodic. The origin of this periodicity is a magnetic-field driven reconstruction of the condensate and a concomitant Doppler-shifted energy spectrum. The robust, flux induced reconstruction of the condensate will be an important aspect to understand the magnetic properties of mesoscopic unconventional superconductors.
