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Register a new userPairing in graphene-based moire superlattices
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Added by
Mathias S. Scheurer
Publication date
2019
fields
Physics
and research's language is
English
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We present a systematic classification and analysis of possible pairing instabilities in graphene-based moire superlattices. Motivated by recent experiments on twisted double-bilayer graphene showing signs of triplet superconductivity, we analyze both singlet and triplet pairing separately, and describe how these two channels behave close to the limit where the system is invariant under separate spin rotations in the two valleys, realizing an SU(2)$_+$ $times$ SU(2)$_-$ symmetry. Further, we discuss the conditions under which singlet and triplet can mix via two nearly degenerate transitions, and how the different pairing states behave when an external magnetic field is applied. The consequences of the additional microscopic or emergent approximate symmetries relevant for superconductivity in twisted bilayer graphene and ABC trilayer graphene on hexagonal boron nitride are described in detail. We also analyze which of the pairing states can arise in mean-field theory and study the impact of corrections coming from ferromagnetic fluctuations. For instance, we show that, close to the parameters of mean-field theory, a nematic mixed singlet-triplet state emerges. Our study illustrates that graphene superlattices provide a rich platform for exotic superconducting states, and allow for the admixture of singlet and triplet pairing even in the absence of spin-orbit coupling.
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Motivated by the possible non-spin-singlet superconductivity in the magic-angle twisted trilayer graphene experiment, we investigate the triplet-pairing superconductivity arising from a correlation-induced spin-fermion model on a honeycomb lattice. We find that the $f$-wave pairing is favored due to the valley-sublattice structure, and the superconducting state is time-reversal symmetric, fully gapped, and non-topological. With a small in-plane magnetic field, the superconducting state becomes partially polarized, and the transition temperature can be slightly enhanced. Our results apply qualitatively for the triplet-pairing superconductivity in graphene-based moire systems, which is fundamentally distinct from triplet superconductivity in $^3$He and ferromagnetic superconductors.
Identifying the microscopic mechanism for superconductivity in magic-angle twisted bilayer graphene (MATBG) is an outstanding open problem. While MATBG exhibits a rich phase-diagram, driven partly by the strong interactions relative to the electronic bandwidth, its single-particle properties are unique and likely play an important role in some of the phenomenological complexity. Some of the salient features include an electronic bandwidth smaller than the characteristic phonon bandwidth and a non-trivial structure of the underlying Bloch wavefunctions. We perform a theoretical study of the cooperative effects due to phonons and plasmons on pairing in order to disentangle the distinct role played by these modes on superconductivity. We consider a variant of MATBG with an enlarged number of fermion flavors, $N gg 1$, where the study of pairing instabilities reduces to the conventional (weak-coupling) Eliashberg framework. In particular, we show that certain umklapp processes involving mini-optical phonon modes, which arise physically as a result of the folding of the original acoustic branch of graphene due to the moire superlattice structure, contribute significantly towards enhancing pairing. We also investigate the role played by the dynamics of the screened Coulomb interaction on pairing, which leads to an enhancement in a narrow window of fillings, and study the effect of external screening due to a metallic gate on superconductivity. At strong coupling the dynamical pairing interaction leaves a spectral mark in the single particle tunneling density of states. We thus predict such features will appear at specific frequencies of the umklapp phonons corresponding to the sound velocity of graphene times an integer multiple of the Brillouin zone size.
We theoretically demonstrate that moire phonons at the lowest-energy bands can become chiral. A general symmetry analysis reveals that they originate from stacking configurations leading to an asymmetric interlayer binding energy that breaks the $C_{2z}$ symmetry on the moire length scale. Within elastic theory, we provide a complete classification of van der Waals heterostructures in respect to hosting moire chiral phonons and discuss their emergence in twisted bilayer MoS$_2$ as an example. The formation of the chiral phonons can be qualitatively understood using an effective model, which emphasizes their origin in the energy difference between stacking domains. Since moire chiral phonons are highly tunable, with excitation energies in only a few meV, and moire scale wavelengths, they might find potential applications in phononic twistronic devices.
Twisted van der Waals materials open up novel avenues to control electronic correlation and topological effects. These systems contain the unprecedented possibility to precisely tune strong correlations, topology, magnetism, nematicity, and superconductivity with an external non-invasive electrostatic doping. By doing so, rich phase diagrams featuring an interplay of different states of correlated quantum matter can be unveiled. The nature of the superconducting order presents a recurring overarching open question in this context. In this work, we quantitatively assess the case of spin-fluctuation-mediated pairing for $Gamma$-valley twisted transition metal dichalcogenide homobilayers. We construct a low-energy honeycomb model on which basis we self-consistently and dynamically calculate a doping dependent phase diagram for the superconducting transition temperature $T_{mathrm{c}}$. A superconducting dome emerges with a maximal $T_{mathrm{c}}approx$ 0.1-1 K depending on twist angle. We qualitatively compare our results with conventional phonon-mediated superconductivity and discern clear fingerprints which are detectable in doping-dependent measurements of the superconducting transition temperature, providing direct access to probing the superconducting pairing mechanism in twisted Van der Waals materials.
We investigate the interplay of magnetic fluctuations and Cooper pairing in twisted bilayer graphene from a purely microscopic model within a large-scale tight-binding approach resolving the AA ngstrom scale. For local onsite repulsive interactions and using the random-phase approximation for spin fluctuations, we derive a microscopic effective pairing interaction that we use for self-consistent solutions of the Bogoliubov-de-Gennes equations of superconductivity. We study the predominant pairing types as function of interaction strength, temperature and band filling. For large regions of this parameter space, we find chiral $d$-wave pairing regimes, spontaneously breaking time-reversal symmetry, separated by magnetic instabilities at integer band fillings. Interestingly, the $d$-wave pairing is strongly concentrated in the AA regions of the moire unit cell and exhibits phase windings of integer multiples of $2pi$ around these superconducting islands, i.e. pinned vortices. The spontaneous circulating current creates a distinctive magnetic field pattern. This signature of the chiral pairing should be measurable by state-of-the-art experimental techniques.
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