Florian Loder

Magnetic flux periodicity of h / e in superconducting loops

1 ar X iv :0 70 9. 41 11 v1 [ co nd -m at .s up rco n] 2 6 Se p 20 07 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 of 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 h/2e. Here, the ratio of Planck’s constant and the elementary charge defines the magnetic flux quantum h/e. The well-known 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 h/e periodicity. These superconductors include the high-Tc cuprates, Sr2RuO4, 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 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. Currents of electrons moving on multiply connected paths are modulated by an applied magnetic flux with a period of h/e , as predicted by Aharonov and Bohm . In superconducting rings the order parameter responds also periodically to a magnetic flux, as Fritz London recognized when he analyzed the implications of a single-valued superconducting wave function; different condensate states, which differ by integer flux quanta, are related by a gauge transformation. London concluded that the flux periodicity in superconducting rings is h/e . He missed, however, a class of supercurrent carrying wave functions, which were identified years later, and allowed to explain the experimentally observed h/2e flux quantization. Indeed, according to the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity the electronic condensate is formed by Cooper pairs, which carry

Crossover from h c / e to h c / 2 e current oscillations in rings of s -wave superconductors

We analyze the crossover from an

Superconductivity with Rashba spin?orbit coupling and magnetic field

hc/e

Superconductivity and local noncentrosymmetricity in crystal lattices

periodicity of the persistent current in flux-threaded clean metallic rings toward an

Flux periodicities in loops of nodal superconductors

hc/2e

Mean-field pairing theory for the charge-stripe phase of high-temperature cuprate superconductors.

-flux periodicity of the supercurrent upon entering the superconducting state. On the basis of a model calculation for a one-dimensional ring we identify the underlying mechanism, which balances the

Superconducting state with a finite-momentum pairing mechanism in zero external magnetic field

hc/e

Superconductors with Staggered Non-centrosymmetricity

versus the

Route to Topological Superconductivity via Magnetic Field Rotation.

hc/2e

Supercurrent through grain boundaries of cuprate superconductors in the presence of strong correlations.

periodic components of the current density. When the ring circumference exceeds the coherence length of the superconductor, the flux dependence is strictly