Symmetry not required

Superconductivity is a complex phenomenon. And now there's something else to think about: a magnetic material whose structure is not mirror symmetric and yet, unexpectedly, superconducts.

Symmetry is central to our understanding and description of natural phenomena. The fundamental conservation laws of physics, such as the conservation of momentum and energy, are the consequences of symmetries in space and time; also, our understanding of the forces of nature is based on a local symmetry known as gauge symmetry. However, the world we observe is often unsymmetrical: in the process of nuclear β-decay, there is an absence of inversion or mirror symmetry, known as parity violation; the structure of DNA is not mirror symmetric.

The consequences of broken symmetries can be dramatic. The breaking of gauge invariance, for example, is associated with the onset of superconductivity — the resistanceless flow of current, usually at very low temperatures. In Physical Review Letters, Bauer et al.1 present a material in which space and time inversion symmetries and gauge symmetry are broken: a compound of cerium, platinum and silicon (CePt3Si) is the first example of a magnetic superconductor that has no mirror symmetry, an observation that will lead to a re-examination of our current understanding of these phenomena.

In 1957, Bardeen, Cooper and Schrieffer (BCS) explained the origin of superconductivity in simple metals such as aluminium. In BCS theory, electrons joined into Cooper pairs are the mediators of the supercurrent flow. The quantum wavefunction (or description) of the superconductor is a coherent superposition of paired-electron states. The Cooper states of lowest energy have overall zero momentum and so there must be pairing of electrons of momenta equal in magnitude, but opposite in direction (Fig. 1a). Moreover, the pair states depend not only on the coordinates of the electrons but also on their spin orientation. Because the electrons in the Cooper-pair state are fermions (with one half-unit of spin each), the pair-state wavefunction must be anti-symmetric under interchange of the two electrons. This is the origin of the familiar Pauli exclusion principle.

Figure 1: Superconductivity without space inversion symmetry.

a, The inner and outer rings (separated for clarity) enclose occupied electron states in momentum space, typical of a normal superconductor. b, When space inversion symmetry is lacking, spins might rotate around the momentum-space surface, clockwise on one side and anticlockwise on the other.

In simple metals such as aluminium, the Cooper-state wavefunction can be separated into two parts, one that depends only on the spatial coordinates and the other only on the spin coordinates. In crystals with space-inversion symmetry, an interchange of the spatial coordinates of the electrons leads to a state that is indistinguishable from the original. Hence, the probability distribution of the electrons in the Cooper state must be unchanged. The Cooper-state wavefunction can only change by a phase factor under this transformation. Because a second interchange must lead back to the original quantum state, the phase factor must be +1 or −1. This simply means that the spatial part of the Cooper state must be either symmetric or anti-symmetric.

For the complete Cooper state to be anti-symmetric, the other part of the wavefunction, the spin part, must have opposite symmetry under electron interchange. Thus, when the spatial wavefunction is symmetric, the spin wavefunction must be anti-symmetric. This arrangement (corresponding to what is known as the ‘spin-singlet’ state) is realized in many metals, such as aluminium. On the other hand, when the spatial wavefunction is anti-symmetric, the spin wavefunction must be symmetric (corresponding to the ‘spin-triplet’ state). This particular case is realized in liquid helium-3, which has a superfluid state with intricate properties that arise from the orbital and spin angular momentum of the Cooper-pair states.

Now CePt3Si, as Bauer et al.1 report, has no space inversion symmetry (Fig. 1), so the spatial part of the wavefunction cannot simply be taken to be symmetric or anti-symmetric. The same applies to the spin part of the wavefunction, if the overall anti-symmetry of the Cooper-pair state is to be preserved. In other words, the Cooper pair in crystals like CePt3Si is a mixture of spin-singlet and spin-triplet states.

A new way of thinking about the spin configuration of the possible Cooper-pair states for such a parity-violating superconductor is needed (Fig. 1b). In contrast to the previous example of aluminium, where the spin orientation of the fermion is the same over the whole Fermi surface, in this model for a system with broken inversion symmetry the spin orientation would rotate around the surface. The consequences of such a state are not yet fully understood but have been examined in several recent papers2,3,4.

To progress, it would be desirable to have many examples of such parity-violating superconductors. So it is encouraging that a second example has already been found: Akazawa et al.5 have reported that the magnetic compound UIr, which also lacks inversion symmetry, becomes superconducting under pressure. Although magnetically mediated pairing is thought to be relevant in such systems, it has thus far only been studied in detail for parity-conserving materials. The discoveries of superconductivity in CePt3Si and UIr promise to open up entirely new avenues for theoretical and experimental research, and not only in the field of superconductivity.


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Saxena, S., Monthoux, P. Symmetry not required. Nature 427, 799 (2004).

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