We investigate the effect of edges on the intrinsic electron-electron interaction driven d-wave superconducting state in graphene doped close to the van Hove singularity. While the bulk is in a chiral $d_{x^2-y^2}+id_{xy}$ state, the order parameter at any edge is enhanced and has $d_{x^2-y^2}$-symmetry, with a decay length strongly increasing with weakening superconductivity. No graphene edge is pair breaking for the $d_{x^2-y^2}$ state and we never find any localized zero-energy edge states. We find two chiral edge modes which carry a spontaneous, but not quantized, quasiparticle current related to the zero-energy momentum. Moreover, for realistic values of the Rashba spin-orbit coupling, a Majorana fermion appears at the edge when tuning a Zeeman field.
Two-gap superconductivity in heavily n-doped graphene: ab initio Migdal-Eliashberg theory
石墨烯是从零维到三维材料的碳家族中唯一尚未观察到超导性的成员。目前尚不清楚对超导石墨烯的探索是否受到技术挑战的阻碍，或者是二维序参量的波动。在这一领域，从头计算是有用的，以指导实验工作，缩小搜索空间。本着这种精神，我们从第一原理研究了使用由Wannier-Fourier插值提供动力的完全各向异性Migdal-Eliashberg理论在掺杂石墨烯中诱导超导性的可能性。为了解决最好的情况下，我们考虑在高载流子密度的电子和空穴掺杂，以便对准费米能级的范霍夫奇点。在这些条件下，我们发现超导间隙的$s$波对称性，与轻微的各向异性引起的三角形翘曲，并在$n$掺杂的石墨烯的情况下，一个意想不到的两个间隙结构联想到MgB $_2$。我们的Migdal-Eliashberg计算表明，对于载流子密度超过$10^{15}$ cm $^{-2}$的$n$掺杂的石墨烯，在低温下观察到超导性应该是可能的。
We present a new way to enhance the electron-phonon coupling constant and the critical superconducting temperature of graphene, significantly beyond all reported values. Using density functional theory, we explore the application effects of the tensile biaxial strain on the lithium intercalated graphene. Both effects together, the presence of adatom and the strain, trigger enhancement of critical temperature, up to 300\%, compared to non-strained lithium intercalated graphene.
We theoretically study exotic superconducting phases in graphenelike single-sheet material BC$_3$ doped to its type-II Van Hove singularity whose saddle point momenta are {\it not} time-reversal-invariant. From combined renormalization group analysis and RPA calculations, we show that the dominant superconducting instability induced by weak repulsive interactions is in the time-reversal-invariant $p+ip$ pairing channel because of the interplay among dominant ferromagnetic fluctuations, subleading spin fluctuations at finite momentum, and spin-orbit coupling. Such time-reversal-invariant $p+ip$…
A highly unconventional superconducting state with a spin-singlet $d_{x^2-y^2}\pm id_{xy}$-wave, or chiral d-wave, symmetry has recently been proposed to emerge from electron-electron interactions in doped graphene. Especially graphene doped to the van Hove singularity at 1/4 doping, where the density of states diverges, has been argued to likely be a chiral d-wave superconductor. In this review we summarize the currently mounting theoretical evidence for the existence of a chiral d-wave superconducting state in graphene, obtained with methods ranging from mean-field studies of effective Hamil…
Electron pairing in the vast majority of superconductors follows the Bardeen-Cooper-Schrieffer theory of superconductivity, which describes the condensation of electrons into pairs with antiparallel spins in a singlet state with an s-wave symmetry. Unconventional superconductivity is predicted in single layer graphene where the electrons pair with a p-wave or chiral d-wave symmetry, depending on the position of the Fermi energy with respect to the Dirac point. By placing single layer graphene on an electron-doped (non-chiral) d-wave superconductor and performing local scanning tunnelling micro…
Graphene, a zero-gap semimetal, can be transformed into a metallic, semiconducting or insulating state by either physical or chemical modification. Superconductivity is conspicuously missing among these states despite considerable experimental efforts as well as many theoretical proposals. Here, we report superconductivity in calcium-decorated graphene achieved by intercalation of graphene laminates that consist of well separated and electronically decoupled graphene crystals. In contrast to intercalated graphite, we find that Ca is the only dopant that induces superconductivity in graphene la…
It is shown that the gap solution and critical transition temperature are significantly enhanced by doping in a recently developed BCS formalism for graphene superconductivity in such a way that positive gap and transition temperature both occur in arbitrary pairing coupling as far as doping is present. The analytic construction of the BCS gap and transition temperature offers highly effective globally convergent iterative methods for the computation of these quantities. A series of numerical examples are presented as illustrations consolidating the analytic understanding achieved.
