Topological Majorana and Dirac Zero Modes in Superconducting Vortex Cores

Roy, Rahul

doi:10.1103/physrevlett.105.186401

Cited by 43 publications

(34 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Experimentally, this topological invariant manifests itself in universal signatures of thermal and spin Hall conductivity due to N low-energy edge modes of the superconducting droplet [198][199][200]. Note that while an N = 1 Chern Bogoliubov band suggests the existence of a single Majorana mode in a vortex core at zero energy protected by particle-hole symmetry [198,[201][202][203], this vortex core profile of a chiral d-wave superconductor is less revealing, as the two Chern modes can recombine and gap out. However, Sato et al [204] pointed out that the addition of Rashba spin-orbit coupling and Zeeman field in a (d + id)-superconductor effectively realizes the spinless (p + ip)-pairing state and therefore could lead to the very same non-Abelian properties sought after.…”

Section: Chiral (D + Id)-pairing Phasementioning

confidence: 99%

Functional renormalization group for multi-orbital Fermi surface instabilities

Platt

Hanke

Thomale

2013

Advances in Physics

192

253

View full text Add to dashboard Cite

Technological progress in material synthesis, as well as artificial realization of condensed matter scenarios via ultra-cold atomic gases in optical lattices or epitaxial growth of thin films, is opening the gate to investigate a plethora of unprecedented strongly correlated electron systems. In a large subclass thereof, a metallic state of layered electrons undergoes an ordering transition below some temperature into unconventional states of matter driven by electronic correlations, such as magnetism, superconductivity, or other Fermi surface instabilities. While this type of phenomena has been a well-established direction of research in condensed matter for decades, the variety of today's accessible scenarios pose fundamental new challenges to describe them. A core complication is the multi-orbital nature of the low-energy electronic structure of these systems, such as the multi-d orbital nature of electrons in iron pnictides and transition-metal oxides in general, but also electronic states of matter on lattices with multiple sites per unit cell such as the honeycomb or kagome lattice. In this review, we propagate the functional renormalization group (FRG) as a suited approach to investigate multi-orbital Fermi surface instabilities. The primary goal of the review is to describe the FRG in explicit detail and render it accessible to everyone both at a technical and intuitive level. Summarizing recent progress in the field of multi-orbital Fermi surface instabilities, we illustrate how the unbiased fashion by which the FRG treats all kinds of ordering tendencies guarantees an adequate description of electronic phase diagrams and often allows to obtain parameter trends of sufficient accuracy to make qualitative predictions for experiments. This review includes detailed and illustrative illustrations of magnetism and, in particular, superconductivity for the iron pnictides from the viewpoint of FRG. Furthermore, it discusses candidate scenarios for topological bulk singlet superconductivity and exotic particle-hole condensates on hexagonal lattices such as sodium-doped cobaltates, graphene doped to van Hove filling, and the kagome Hubbard model. In total, the FRG promises to be one of the most versatile and revealing numerical approaches to address unconventional Fermi surface instabilities in future fields of condensed matter research.

show abstract

Section: Chiral (D + Id)-pairing Phasementioning

confidence: 99%

Functional renormalization group for multi-orbital Fermi surface instabilities

Platt

Hanke

Thomale

2013

Advances in Physics

192

253

View full text Add to dashboard Cite

show abstract

“…The nontrivial bulk topology in Hermitian systems can * wuyajie@xatu.edu.cn † Junpeng.Hou@utdallas.edu be detected by defects, such as edges, π-flux, dislocations and vortices [48][49][50][51][52][53]. When it comes to non-Hermitian systems, stable edge states could also exist at the interface between topological and trivial phases [54][55][56][57][58][59][60][61][62].…”

Section: Non-hermitian Hamiltonian Captures Essentials Of Open Systemmentioning

confidence: 99%

Symmetry-protected localized states at defects in non-Hermitian systems

Hou

2019

Phys. Rev. A

View full text Add to dashboard Cite

Understanding how local potentials affect system eigenmodes is crucial for experimental studies of nontrivial bulk topology. Recent studies have discovered many exotic and highly non-trivial topological states in non-Hermitian systems. As such, it would be interesting to see how non-Hermitian systems respond to local perturbations. In this work, we consider chiral and particlehole -symmetric non-Hermitian systems on a bipartite lattice, including SSH model and photonic graphene, and find that a disordered local potential could induce bound states evolving from the bulk. When the local potential on a single site becomes infinite, which renders a lattice vacancy, chiral-symmetry-protected zero-energy mode and particle-hole symmetry-protected bound states with purely imaginary eigenvalues emerge near the vacancy. These modes are robust against any symmetry-preserved perturbations. Our work generalizes the symmetry-protected localized states to non-Hermitian systems.

show abstract

“…where D t and D s are the triplet and singlet pairing strength, respectively, and q k is the angle between k and k x -axis. To search for Majorana fermions, instead of solving the Bogoliubov-de Gennes equations in the presence of vortices, we apply an index theorem proved in [28] that superconductors with an odd Chern number can support Majorana zero modes. In [17,18], the Chern number C of this state has been shown to be 2j…”

Section: Topological Phase Diagram With Zeeman Fieldmentioning

confidence: 99%