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Superconductivity in a graphene system survives a strong magnetic field

Quantum phases of matter known as superconductors transmit electrical current with zero resistance. Microscopically, this phenomenon arises from the fact that it is energetically favourable for electrons to bind into two-electron states, dubbed Cooper pairs, that move collectively and cooperatively without energy loss. A Cooper pair is said to be spin-singlet when its two electron spins (intrinsic angular momenta) point in opposite directions and the pair has a total spin of zero, whereas spin-triplet Cooper pairs have a total spin of 1, and the two electron spins can be aligned in the same direction. Most experimentally known superconductors have spin-singlet Cooper pairs; these include metals (such as lead and niobium) that demonstrate conventional superconductivity, and cuprates (layered copper oxide compounds) that exhibit unconventional superconductivity. Writing in Nature, Cao et al.1 report evidence for unconventional superconductivity associated with spin-triplet Cooper pairs.

Two-dimensional spin-triplet superconductors have attracted widespread attention because many of them are predicted to host exotic zero-energy excitations called Majorana zero modes. A well-studied example of such a superconductor is a 2D chiral p-wave superconductor2. This system breaks time-reversal symmetry (its physical properties would change if the direction of time were reversed), and Majorana zero modes are expected to exist in the cores of vortices (threads of magnetic flux) when a magnetic field is applied perpendicular to the system. Majorana zero modes are promising candidates for topological qubits — the building blocks of a type of ‘fault-tolerant’ quantum computation known as topological quantum computation3,4. Therefore, given that most known spin-triplet superconductors are 3D, experimentally established 2D spin-triplet superconductors are much desired.

In the past four years, experimentalists have started to probe quasi-2D systems consisting of stacked but slightly misaligned layers of graphene — single sheets of hexagonally arranged carbon atoms (see refs 5 and 6, for example). Such systems have rapidly gained attention because they can be easily tuned experimentally and host a rich variety of correlated quantum phases. Earlier this year, superconductivity was reported in twisted trilayer graphene7,8, which comprises three stacked graphene layers in which the top and bottom layers are rotated at angles of θ and – θ, respectively, relative to the middle layer (Fig. 1). By tuning the value of θ, the physics in twisted trilayer graphene can be investigated in regimes ranging from one in which the electrons are essentially weakly coupled to each other to one in which they are strongly coupled.

Figure 1

Figure 1 | Superconductivity in twisted trilayer graphene. a, Magic-angle twisted trilayer graphene (MATTG) is a system of three sheets of hexagonally arranged carbon atoms, stacked with a relative rotation angle θ of approximately 1.6°. b, Superconductivity results from electrons binding into two-electron states called Cooper pairs. In a spin-singlet Cooper pair, the electron spins (intrinsic angular momenta) point in opposite directions; in a spin-triplet Cooper pair, they can be aligned in the same direction. c, In the presence of a strong magnetic field in the plane of the material, a spin-singlet Cooper pair breaks apart because a phenomenon known as the Zeeman effect causes the spins to align in the same direction. By contrast, a spin-triplet Cooper pair can survive such a field. Cao et al.1 found that superconductivity in MATTG persists under a strong in-plane magnetic field, and suggest that this observation is evidence for spin-triplet Cooper pairs.

Cao et al. studied twisted trilayer graphene when θ is equal to the ‘magic’ angle of approximately 1.6° — the angle at which the system is expected to enter the strong-coupling regime. They observed superconductivity in such magic-angle twisted trilayer graphene (MATTG), and studied the spin properties of this superconductivity. Specifically, they measured the electrical resistance of MATTG at low temperatures (down to below 1 kelvin) and discovered a zero-resistance phase. They then applied a magnetic field to MATTG in the plane of the graphene layers and identified the critical field strength at which the observed superconductivity vanishes. They found that the superconductivity survives up to a surprisingly high critical field strength of nearly 10 tesla, which is not expected for spin-singlet superconductors.

Magnetic fields couple to the orbital angular momentum and spin of Cooper pairs in a superconductor. When a strong in-plane field is applied to a quasi-2D superconductor, the orbital effect is negligible. However, above a field strength called the Pauli limit, the spin effect tends to cause spin-singlet Cooper pairs, which have oppositely aligned electron spins, to break apart, because a phenomenon known as the Zeeman effect causes the spins to point in the same direction (Fig. 1). By contrast, spin-triplet Cooper pairs that have electron spins aligned in a single direction parallel to the field are compatible with such a spin effect and are not bound by the Pauli limit. The in-plane critical field strength measured by Cao et al. in MATTG is two to three times the Pauli limit and is therefore considered evidence of spin-triplet superconductivity.

Cao and colleagues also detected a second superconducting phase that exists at even higher in-plane magnetic field strengths than does the first one, persisting above 10 tesla. On the basis of the resistance behaviour of MATTG when the field strength is increased compared with when it is decreased, the authors suggest that the two phases might be connected by a type of phase transition called a first-order phase transition. Such ‘re-entrant’ superconductivity is reminiscent of that observed in some 3D spin-triplet superconductors, such as uranium rhodium germanium9 and uranium telluride10, and in the spin-triplet superfluid (zero-viscosity liquid) helium-311. This similarity might provide hints about the nature of the two superconducting phases in MATTG.

The evidence reported by the authors for quasi-2D spin-triplet superconductivity in MATTG paves the way for unconventional superconductors that can be manipulated experimentally. High in-plane critical field strengths can typically develop in various ways other than in spin-triplet Cooper pairs. But these sources are unlikely to occur in MATTG owing to the negligible coupling between the spin and orbital angular momentum of electrons in graphene. Nevertheless, further measurements are needed to show whether the orbital structure of the Cooper pairs in MATTG is consistent with spin-triplet superconductivity.

Crucially, being spin-triplet does not imply that the observed superconductivity would be useful for topological quantum computation. Future work needs to study the topological properties of the superconductivity. For instance, researchers should determine whether it breaks time-reversal symmetry — an indication of possible chiral p-wave superconductivity. They should also look for direct evidence of zero-energy states in vortex cores, which would signal the presence of Majorana zero modes. The understanding gained from such studies could help physicists to develop promising platforms for topological quantum computation.

Nature 595, 495-496 (2021)

doi: https://doi.org/10.1038/d41586-021-01890-3

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Competing Interests

The author declares no competing interests.

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