Correlation-induced triplet superconductivity on the graphene lattice (original) (raw)

Unconventional Superconductivity in Semiconductor Artificial Graphene

arXiv: Superconductivity, 2019

Unconventional superconductivity featuring large pairing energies has attracted immense interest, yet tractable microscopic theories have proven elusive. A major breakthrough has been the advent of twisted bilayer graphene (TBG), which serves as a simple model system to 'look under the hood' of unconventional superconductivity. We propose a new model, within current experimental reach, to investigate the microscopics of strong-binding superconductivity. Our proposed device is semiconductor artificial graphene (AG), a two dimensional electron gas overlaid with a periodic potential (superlattice). We demonstrate a new mechanism for superconductivity that originates solely from the repulsive Coulomb interaction. The superlattice promotes certain interactions, which are antiscreened, cause attractive ppp-wave pairing and - in contrast to graphene - can be strongly enhanced through device engineering. The strength of the pairing energy is similar to TBG, and we find within the ac...

Cooper-pair propagation and superconducting correlations in graphene

Physical Review B, 2007

We investigate the Cooper-pair propagation and the proximity effect in graphene under conditions in which the distance L between superconducting electrodes is much larger than the width W of the contacts. In the case of undoped graphene, supercurrents may exist with a spatial decay proportional to W 2 /L 3 . This changes upon doping into a 1/L 2 behavior, opening the possibility to observe a supercurrent over length scales above 1 µm at suitable doping levels. We also show that there is in general a crossover temperature T * ∼ vF /kBL that marks the onset of the strong decay of the supercurrent, and that corresponds to the scale below which the Cooper pairs are not disrupted by thermal effects during their propagation.

Nonlocal superconducting correlations in graphene in the quantum Hall regime

We study Andreev processes and nonlocal transport in a three-terminal graphene-superconductor hybrid system under a quantizing perpendicular magnetic field [G.-H. Lee et al., Nature Phys. 13, 693 (2017)]. We find that the amplitude of the crossed Andreev reflection (CAR) processes crucially depends on the orientation of the lattice. By employing Landauer-Büttiker scattering theory, we find that CAR is generally very small for a zigzag edge, while for an armchair edge it can be larger than the normal transmission, thereby resulting in a negative nonlocal resistance. In the case of an armchair edge and with a wide superconducting region (as compared to the superconducting coherence length), CAR exhibits large oscillations as a function of the magnetic field due to interference effects. This results in sign changes of the nonlocal resistance.

Chiral triplet superconductivity on the graphene lattice

Physical Review B

Motivated by the possibility of superconductivity in doped graphene sheets, we investigate superconducting order in the extended Hubbard model on the two-dimensional graphene lattice using the variational cluster approximation (VCA) and the cellular dynamical mean-field theory (CDMFT) with an exact diagonalization solver at zero temperature. The nearest-neighbor interaction is treated using a mean-field decoupling between clusters. We compare different pairing symmetries, singlet and triplet, based on short-range pairing. VCA simulations show that the real (nonchiral), triplet p-wave symmetry is favored for small V , small on-site interaction U or large doping, whereas the chiral combination p + ip is favored for larger values of V , stronger on-site interaction U or smaller doping. CDMFT simulations confirm the stability of the p + ip solution, even at half-filling. Singlet superconductivity (extended s-wave or d-wave) is either absent or subdominant .

Quantum Hall Effect in Graphene with Superconducting Electrodes

Nano Letters, 2012

We have realized an integer quantum Hall system with superconducting contacts by connecting graphene to niobium electrodes. Below their upper critical field of 4 T, an integer quantum Hall effect coexists with superconductivity in the leads but with a plateau conductance that is larger than in the normal state. We ascribe this enhanced quantum Hall plateau conductance to Andreev processes at the graphene− superconductor interface leading to the formation of so-called Andreev edge-states. The enhancement depends strongly on the filling-factor and is less pronounced on the first plateau due to the special nature of the zero energy Landau level in monolayer graphene.

Superconductivity of electron–hole pairs in a bilayer graphene system in a quantizing magnetic field

Low Temperature Physics, 2009

A state with spontaneous interlayer phase coherence in a bilayer quantum Hall system based on graphene is studied. This state can be regarded as a gas of superfluid electron-hole pairs whose components belong to different layers. A superfluid flow of such pairs is equivalent to two electric supercurrents in the layers. It is shown that in a graphene system a state with interlayer phase coherence arises if a definite unbalance of the filling factors of the Landau levels in neighboring layers is created. The temperature of the transition into a superfluid state, the maximum interlayer distance for which phase coherence is possible, and the critical values of the supercurrent are found. The advantages of using graphene systems instead of GaAs heterostructures to realize bilayer electron-hole superconductivity are discussed.

Symmetry of superconducting correlations in displaced bilayers of graphene

Physical Review B, 2019

Using a Green's function approach, we study phonon-mediated superconducting pairing symmetries that may arise in bilayer graphene where the monolayers are displaced in-plane with respect to each other. We consider a generic coupling potential between the displaced graphene monolayers, which is applicable to both shifted and commensurate twisted graphene layers; study intralayer and interlayer phonon-mediated BCS pairings; and investigate AA and AB(AC) stacking orders. Our findings demonstrate that at the charge neutrality point, the dominant pairings in both AA and AB stackings with intralayer and interlayer electron-electron couplings can have even-parity s-wave class and odd-parity p-wave class of symmetries with the possibility of invoking equal-pseudospin and odd-frequency pair correlations. At a finite doping, however, the AB (and equivalently AC) stacking can develop pseudospin-singlet and pseudospin-triplet d-wave symmetry, in addition to s-wave, p-wave, f-wave, and their combinations, while the AA stacking order, similar to the undoped case, is unable to host the d-wave symmetry. When we introduce a generic coupling potential, applicable to commensurate twisted and shifted bilayers of graphene, d-wave symmetry can also appear at the charge neutrality point. Inspired by a recent experiment where two phonon modes were observed in a twisted bilayer graphene, we also discuss the possibility of the existence of two-gap superconductivity, where the intralayer and interlayer phonon-mediated BCS picture is responsible for superconductivity. These analyses may provide a useful tool in determining the superconducting pairing symmetries and mechanism in bilayer graphene systems.

Possible triplet p+ i p superconductivity in graphene at low filling

We study the Hubbard model on the honeycomb lattice with nearest-neighbor hopping (t > 0) and next-nearest-neighbor one (t ′ < 0). When t ′ < −t/6, the single-particle spectrum is featured by the continuously distributed Van-Hove saddle points at the band bottom, where the density of states diverges in power-law. We investigate possible unconventional superconductivity in such system with Fermi level close to the band bottom by employing both random phase approximation and determinant quantum Monte-Carlo approaches. Our study reveals a possible triplet p + ip superconductivity in this system with appropriate interactions. Our results might provide a possible route to look for triplet superconductivity with relatively-high transition temperature in a low-filled graphene and other similar systems.

Spin Hall effect in triplet chiral superconductors and graphene

Physical Review B, 2006

We study spin-Hall effects in time-reversal symmetry (TRS) broken systems such as triplet chiral superconductors and TRS preserved ones such as graphene. For chiral triplet superconductors, we show that the edge states carry a quantized spin-Hall current in response to an applied Zeeman magnetic field B along the d vector 1 , whereas the edge spin-current for B ⊥ d is screened by the condensate. We also derive the bulk spin-Hall current for chiral triplet superconductors for arbitrary relative orientation of B and d and discuss its relation with the edge spin-current. For TRS invariant system graphene, we show that the bulk effective action, unlike its TRS broken counterparts, does not support a SU(2) Hopf term but allows a crossed Hopf term in the presence of an external electromagnetic field, which yields a quantized bulk spin-Hall current in response to an electric field. We also present an analytical solution of the edge problem for armchair edges of graphene and contrast the properties of these edge states with their time reversal symmetry broken counterparts in chiral superconductors. We propose possible experiments to test our results.

Spin-Controlled Superconductivity and Tunable Triplet Correlations in Graphene Nanostructures

Physical Review Letters, 2013

We study graphene ferromagnet/superconductor/ferromagnet (F/S/F) nanostructures via a microscopic selfconsistent Dirac Bogoliubov-de Gennes formalism. We show that as a result of proximity effects, experimentally accessible spin switching phenomena can occur as one tunes the Fermi level µF of the F regions or varies the angle θ between exchange field orientations. Superconductivity can then be switched on and off by varying either θ or µF (a spin-controlled superconducting graphene switch). The induced equal-spin triplet correlations in S can be controlled by tuning µF , effectively making a graphene based two-dimensional spin-triplet valve.