Unconventional Superconductivity in Systems with Annular Fermi Surfaces: Application to Rhombohedral Trilayer Graphene

Evolution of superconductivity in twisted graphene multilayers

The group of moiré graphene superconductors keeps growing, and by now it contains twisted graphene multilayers as well as untwisted stacks. We analyze here the contribution of long-range charge fluctuations in the superconductivity of twisted double bilayers and helical trilayers, and compare the results to twisted bilayer graphene. A diagrammatic approach which depends on a few, well-known parameters is used. We find that the critical temperature and the order parameter differ significantly between twisted double bilayers and helical trilayers on one hand, and twisted bilayer graphene on the other. This trend, consistent with experiments, can be associated with the role played by moiré Umklapp processes in the different systems.

Emergent Correlated Phases in Rhombohedral Trilayer Graphene Induced by Proximity Spin-Orbit and Exchange Coupling

The impact of proximity-induced spin-orbit and exchange coupling on the correlated phase diagram of rhombohedral trilayer graphene (RTG) is investigated theoretically. By employing ab initio-fitted effective models of RTG encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic Cr_{2}Ge_{2}Te_{6} (exchange proximity effect), we incorporate the Coulomb interactions within the random-phase approximation to explore potential correlated phases at different displacement fields and doping. We find a rich spectrum of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin-orbit proximity effects, such as the emergence of a spin-valley-coherent phase due to the presence of valley-Zeeman coupling. Similarly, proximity exchange removes the phase degeneracies by biasing the spin direction, enabling a magnetocorrelation effect-strong sensitivity of the correlated phases to the relative magnetization orientations (parallel or antiparallel) of the encapsulating ferromagnetic layers.

Honeycomb Electron Lattice Induced Dirac Fermion with Trigonal Warping in Bilayer Electrides

Emergent fermions arising from the excess electrons of electrides provide a new perspective for exploring semimetal states with unique Fermi surface geometries. In this study, a class of unique two-dimensional (2D) highly anisotropic Dirac fermions is designed using a sandwich structure. Based on the structural design and first-principles calculations, 2D electride MB (M = Ca/Sr, B = Cl/Br/I) is an ideal candidate material. The excess electrons of the bilayer MB could be stably localized in the interstitial cavities, constructing a natural zigzag honeycomb electron sublattice that further forms a Dirac fermion. Compared with traditional Dirac semimetals, 2D Dirac electrides exhibited rich physical properties: i) The Fermi surface shows trigonal warping in low-energy regions. In particular, the geometry of the Fermi surface determines the high anisotropy of the Fermi velocity. ii) A pair of Dirac fermions are protected by three-fold rotational symmetry and exhibit strong robustness. iii) Electride MB possesses a lower work function that strongly correlates with the surface area of the emission channel. Based on these properties, an electron-emitting device with multifunctional applications is fabricated. Therefore, this study provides an ideal platform for studying potential entanglement between structures, electrides, and topological states.

Stoner Ferromagnetism in a Momentum-Confined Interacting 2D Electron Gas

In this work we investigate the ground state of a momentum-confined interacting 2D electron gas, a momentum-space analog of an infinite quantum well. The study is performed by combining analytical results with a numerical exact diagonalization procedure. We find a ferromagnetic ground state near a particular electron density and for a range of effective electron (or hole) masses. We argue that this observation may be relevant to the generalized Stoner ferromagnetism recently observed in multilayer graphene systems. The collective magnon excitations exhibit a linear dispersion, which originates from a diverging spin stiffness.

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

Gate-Defined Topological Josephson Junctions in Bernal Bilayer Graphene

Recent experiments on Bernal bilayer graphene (BLG) deposited on monolayer WSe_{2} revealed robust, ultraclean superconductivity coexisting with sizable induced spin-orbit coupling. Here, we propose BLG/WSe_{2} as a platform to engineer gate-defined planar topological Josephson junctions, where the normal and superconducting regions descend from a common material. More precisely, we show that if superconductivity in BLG/WSe_{2} is gapped and emerges from a parent state with intervalley coherence, then Majorana zero-energy modes can form in the barrier region upon applying weak in-plane magnetic fields. Our results spotlight a potential pathway for "internally engineered" topological superconductivity that minimizes detrimental disorder and orbital-magnetic-field effects.

Signatures of Cooper pair dynamics and quantum-critical superconductivity in tunable carrier bands

Different superconducting pairing mechanisms are markedly distinct in the underlying Cooper pair kinematics. Quantum-critical soft modes drive pairing interactions in which the pair scattering processes are highly collinear and can be classified into two categories: forward scattering and backscattering. Conversely, in conventional phonon mechanisms, Cooper pair scattering is of a generic noncollinear character. In this study, we present a method to discern the kinematic type by observing the evolution of superconductivity while adjusting the Fermi surface geometry. To demonstrate our approach, we utilize the recently reported phase diagrams of untwisted graphene multilayers. Our analysis connects the emergence of superconductivity at "ghost crossings" of Fermi surfaces in distinct valleys to the pair kinematics of a backscattering type. Together with the observed nonmonotonic behavior of superconductivity near its onset (sharp rise followed by a drop), it lends strong support to a particular quantum-critical superconductivity scenario in which pairing is driven by intervalley coherence fluctuations. These findings offer direct insights into the genesis of pairing in these systems, providing compelling evidence for the electron-electron interactions driving superconductivity. More broadly, our work highlights the potential of tuning bands via ghost crossings as a promising means of boosting superconductivity.

Ising superconductivity induced from spin-selective valley symmetry breaking in twisted trilayer graphene

We show that the e-e interaction induces a strong breakdown of valley symmetry for each spin channel in twisted trilayer graphene, leading to a ground state where the two spin projections have opposite sign of the valley symmetry breaking order parameter. This leads to a spin-valley locking in which the electrons of a Cooper pair are forced to live on different Fermi lines attached to opposite valleys. Furthermore, we find an effective intrinsic spin-orbit coupling explaining the protection of the superconductivity against in-plane magnetic fields. The effect of spin-selective valley symmetry breaking is validated as it reproduces the experimental observation of the reset of the Hall density at 2-hole doping. It also implies a breakdown of the symmetry of the bands from C₆ to C₃, with an enhancement of the anisotropy of the Fermi lines which is at the origin of a Kohn-Luttinger (pairing) instability. The isotropy of the bands is gradually recovered, however, when the Fermi level approaches the bottom of the second valence band, explaining why the superconductivity fades away in the doping range beyond 3 holes per moiré unit cell in twisted trilayer graphene.

Functional Renormalization Group Study of Superconductivity in Rhombohedral Trilayer Graphene

We employ a functional renormalization group approach to ascertain the pairing mechanism and symmetry of the superconducting phase observed in rhombohedral trilayer graphene. Superconductivity in this system occurs in a regime of carrier density and displacement field with a weakly distorted annular Fermi sea. We find that repulsive Coulomb interactions can induce electron pairing on the Fermi surface by taking advantage of momentum-space structure associated with the finite width of the Fermi sea annulus. The degeneracy between spin-singlet and spin-triplet pairing is lifted by valley-exchange interactions that strengthen under the RG flow and develop nontrivial momentum-space structure. We find that the leading pairing instability is d-wave-like and spin singlet, and that the theoretical phase diagram versus carrier density and displacement field agrees qualitatively with experiment.

Enhanced superconductivity in spin-orbit proximitized bilayer graphene

In the presence of a large perpendicular electric field, Bernal-stacked bilayer graphene (BLG) features several broken-symmetry metallic phases^1-3 as well as magnetic-field-induced superconductivity¹. The superconducting state is quite fragile, however, appearing only in a narrow window of density and with a maximum critical temperature T_c≈ 30 mK. Here we show that placing monolayer tungsten diselenide (WSe₂) on BLG promotes Cooper pairing to an extraordinary degree: superconductivity appears at zero magnetic field, exhibits an order of magnitude enhancement in T_c and occurs over a density range that is wider by a factor of eight. By mapping quantum oscillations in BLG-WSe₂ as a function of electric field and doping, we establish that superconductivity emerges throughout a region for which the normal state is polarized, with two out of four spin-valley flavours predominantly populated. In-plane magnetic field measurements further reveal that superconductivity in BLG-WSe₂ can exhibit striking dependence of the critical field on doping, with the Chandrasekhar-Clogston (Pauli) limit roughly obeyed on one end of the superconducting dome, yet sharply violated on the other. Moreover, the superconductivity arises only for perpendicular electric fields that push BLG hole wavefunctions towards WSe₂, indicating that proximity-induced (Ising) spin-orbit coupling plays a key role in stabilizing the pairing. Our results pave the way for engineering robust, highly tunable and ultra-clean graphene-based superconductors.

Optical Conductivity as a Probe of the Interaction-Driven Metal in Rhombohedral Trilayer Graphene

Study of the strongly correlated states in van der Waals heterostructures is one of the central topics in modern condensed matter physics. Among these, the rhombohedral trilayer graphene (RTG) occupies a prominent place since it hosts a variety of interaction-driven phases, with the metallic ones yielding exotic superconducting orders upon doping. Motivated by these experimental findings, we show within the framework of the low-energy Dirac theory that the optical conductivity can distinguish different candidates for a paramagnetic metallic ground state in this system. In particular, this observable shows a single peak in the fully gapped valence-bond state. On the other hand, the bond-current state features two pronounced peaks in the optical conductivity as the probing frequency increases. Finally, the rotational symmetry breaking charge-density wave exhibits a minimal conductivity with the value independent of the amplitude of the order parameter, which corresponds precisely to the splitting of the two cubic nodal points at the two valleys into two triplets of the band touching points featuring linearly dispersing quasiparticles. These features represent the smoking gun signatures of different candidate order parameters for the paramagnetic metallic ground state, which should motivate further experimental studies of the RTG.

Inter-valley coherent order and isospin fluctuation mediated superconductivity in rhombohedral trilayer graphene

Superconductivity was recently discovered in rhombohedral trilayer graphene (RTG) in the absence of a moiré potential. Superconductivity is observed proximate to a metallic state with reduced isospin symmetry, but it remains unknown whether this is a coincidence or a key ingredient for superconductivity. Using a Hartree-Fock analysis and constraints from experiments, we argue that the symmetry breaking is inter-valley coherent (IVC) in nature. We evaluate IVC fluctuations as a possible pairing glue, and find that they lead to chiral unconventional superconductivity when the fluctuations are strong. We further elucidate how the inter-valley Hund’s coupling determines the spin-structure of the IVC ground state and breaks the degeneracy between spin-singlet and triplet superconductivity. Remarkably, if the normal state is spin-unpolarized, we find that a ferromagnetic Hund’s coupling favors spin-singlet superconductivity, in agreement with experiments. Instead, if the normal state is spin-polarized, then IVC fluctuations lead to spin-triplet pairing.

Trilayer graphene was recently shown to exhibit superconductivity without a Moire pattern that had proved important in tuning superconductivity in bilayer graphene. Here, the authors explore correlated metallic phases and the pairing mechanism of superconductivity in trilayer graphene, and show that intervalley coherent fluctuations can act as a pairing glue, giving rise to chiral unconventional superconductivity.

Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene

In conventional superconductors, Cooper pairing occurs between electrons of opposite spin. We observe spin-polarized superconductivity in Bernal bilayer graphene when doped to a saddle-point van Hove singularity generated by a large applied perpendicular electric field. We observe a cascade of electrostatic gate-tuned transitions between electronic phases distinguished by their polarization within the isospin space defined by the combination of the spin and momentum-space valley degrees of freedom. Although all of these phases are metallic at zero magnetic field, we observe a transition to a superconducting state at finite magnetic field B_‖ ≈ 150 milliteslas applied parallel to the two-dimensional sheet. Superconductivity occurs near a symmetry-breaking transition and exists exclusively above the B_‖ limit expected of a paramagnetic superconductor with the observed transition critical temperature T_C ≈ 30 millikelvins, consistent with a spin-triplet order parameter.

Surprising superconductivity of graphene

An ordinary graphene bilayer exhibits extraordinary superconductivity.