Functional renormalization group for multi-orbital Fermi surface instabilities

Abstract. A highly unconventional superconducting state with a spin-singlet d x 2 −y 2 ± 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 Hamiltonians to angle-resolved renormalization group calculations. We further discuss multiple distinctive properties of the chiral d-wave superconducting state in graphene, as well as its stability in the presence of disorder. We also review means of enhancing the chiral d-wave state using proximity-induced superconductivity. The appearance of chiral d-wave superconductivity is intimately linked to the hexagonal crystal lattice and we also offer a brief overview of other materials which have also been proposed to be chiral d-wave superconductors.

show abstract

“…For this, the reader is referred to recent reviews by e.g. Metzner et al [94] and Platt et al [95]. We instead just sketch the main ingredients.…”

Section: Renormalization Group Results For Graphenementioning

confidence: 99%

“…Most studies, see e.g. the reviews [94] and [95], use a band energy cutoff, such that modes with |ε b (k)| ≥ Λ in band b are integrated out for cutoff Λ. However, at least one work on the honeycomb lattice has employed a cutoff in Matsubara frequency space [44].…”

Section: Renormalization Group Results For Graphenementioning

confidence: 99%

Chirald-wave superconductivity in doped graphene

Black‐Schaffer

Honerkamp

2014

J. Phys.: Condens. Matter

175

176

View full text Add to dashboard Cite

show abstract

“…All these estimates are orders of magnitude at best, therefore we turn again to a quantitative treatment in terms of multi-sublattice fRG 27,28 . Since superconductivity is an itinerant effect, the inherent fRG assumption of weak coupling should be acceptable.…”

Section: Article Nature Communications | Doi: 101038/ncomms5261mentioning

confidence: 99%

“…We employed multi-sublattice functional RG 27,28 to investigate the superconducting instability for a herbertsmithite Fermiology interpolating from the Zn limit at half filling to the hole-doped Ga limit. For the calculations we considered the effective two-dimensional band structure obtained from our ab initio calculations.…”

Section: Dca(risb)mentioning

confidence: 99%

Theoretical prediction of a strongly correlated Dirac metal

et al. 2014

View full text Add to dashboard Cite

Recently, the most intensely studied objects in the electronic theory of solids have been strongly correlated systems and graphene. However, the fact that the Dirac bands in graphene are made up of $sp^{2}$-electrons, which are subject to neither strong Hubbard repulsion $U$ nor strong Hund's rule coupling $J$ creates certain limitations in terms of novel, interaction-induced physics that could be derived from Dirac points. Here we propose GaCu$_{3}$(OH)$_{6}$Cl$_{2}$ (Ga-substituted herbertsmithite) as a correlated Dirac-Kagome metal combining Dirac electrons, strong interactions and frustrated magnetism. Using density functional theory (DFT), we calculate its crystallographic and electronic properties, and observe that it has symmetry-protected Dirac points at the Fermi level. Its many-body physics is excitingly rich, with possible charge, magnetic and superconducting instabilities. Through a combination of various many-body methods we study possible symmetry-lowering phase transitions such as Mott-Hubbard, charge or magnetic ordering, and unconventional superconductivity, which in this compound assumes an $f$-wave symmetry

show abstract

“…The couplings U 1 and U 2 do not participate in SC pairing, but U 1 contributes to the coupling in the SDW channel U 1 + U 3 > 0, which for U i > 0 is larger than in SC channels, i.e., the system first develops SDW order upon lowering T , and superconductivity emerges from a pre-existing SDW state. RG studies found that the SC interaction gets larger as energy decreases in the RG flow 46,47,50,51 . Yet, at low dopings, the SDW order comes first and SC develops in the coexistence region with magnetism.…”

Section: Introductionmentioning

confidence: 99%

Time-Reversal Symmetry Breaking Superconductivity in the Coexistence Phase with Magnetism in Fe Pnictides

2014

View full text Add to dashboard Cite

We argue that superconductivity in the coexistence region with spin-density-wave (SDW) order in weakly doped Fe-pnictides differs qualitatively from the ordinary s +− state outside the coexistence region, as it develops an additional gap component which is a mixture of intra-pocket singlet (s ++ ) and inter-pocket spin-triplet pairings (the t−state). The coupling constant for the t−channel is proportional to the SDW order and involves interactions that do not contribute to superconductivity outside of the SDW region. We argue that the s +− and t−type superconducting orders coexist at low temperatures, and the relative phase between the two is in general different than 0 or π, manifesting explicitly the breaking of the time-reversal symmetry promoted by long-range SDW order. We show that this exotic state emerges already in the simplest model of Fe-pnictides, with one hole pocket and two symmetry-related electron pockets. We argue that in some parameter range time-reversal gets broken even before long-range superconducting order develops. IntroductionIron-based superconductors (FeSCs) have been the subject of intense study since 20081 . Their rich phase diagram includes the regions of superconductivity (SC), spin density wave (SDW), nematic order, and a region where SDW, SC, and nematic order coexist 2 . Outside the SDW/nematic region, SC develops in the spin-singlet channel and in most of Fe-based superconductors has s−wave symmetry with a π phase shift between the SC order parameters on hole and on electron pockets ( s +− gap structure) 3,4 . It has been recently argued by several groups that the multiband structure of FeSCs allows for superconducting states with more exotic properties 5-11,14-21 . Of particular interest are SC states that break time-reversal symmetry (TRS), as such states have a plethora of interesting properties like, e.g., novel collective modes 12,13,15,20 . TRS-broken states emerge when the phase differences ψ i between SC order parameters on different Fermi surfaces (FS) are not multiples of π.The two current proposals for TRS breaking in FeSCs are s + id 5,[9][10][11]19 and s + is states 6,15,20,21 . The first emerges when attractions in the d−wave and s−wave channels are of near-equal strength. The second emerges when there is a competition between different s +− states favored by inter-pocket and intra-pocket interactions. Both of these proposals were, however, argued to be applicable only to strongly hole or electron-doped FeSCc. For weakly/moderately doped FeSCs the common belief is that s +− superconductivity is robust. In this communication we argue that an exotic state which breaks TRS can emerge already at low doping, in a range where SC is known [22][23][24][25][26][27][28][29][30] to emerge from a pre-existing SDW state. Previous works on SC in the coexistence region focused on the SDW-induced modification of the form of s +− gap 31-37 . We argue that there is another effect -SDW order also induces attraction in another pairing channel, for which the order parameter is an admix...

show abstract

Functional renormalization group for multi-orbital Fermi surface instabilities

Cited by 196 publications

References 233 publications

Chirald-wave superconductivity in doped graphene

Chirald-wave superconductivity in doped graphene

Theoretical prediction of a strongly correlated Dirac metal

Time-Reversal Symmetry Breaking Superconductivity in the Coexistence Phase with Magnetism in Fe Pnictides

Contact Info

Product

Resources

About