Inducing chiral superconductivity on honeycomb lattice systems

Abstract

Superconductivity in graphene-based systems has recently attracted much attention, as either intrinsic behavior or induced by proximity to a superconductor may lead to interesting topological phases and symmetries of the pairing function. A prominent system considers the pairing to have chiral symmetry. The question arises as to the effect of possible spin-orbit coupling on the resulting superconducting quasiparticle spectrum. Utilizing a Bogolyubov-de Gennes (BdG) Hamiltonian, we explore the interplay of different interaction terms in the system, and their role in generating complex Berry curvatures in the quasiparticle spectrum, as well as non-trivial topological behavior. We demonstrate that the topology of the BdG Hamiltonian in these systems may result in the appearance of edge states along the zigzag edges of nanoribbons in the appropriate regime. For suitable chemical potential and superconducting pairing strength, we find the appearance of robust midgap states at zigzag edges, well protected by large excitation gaps and momentum transfer.

Chiral Josephson effect in double layers: The role of particle–hole duality

“…In conclusion, we studied pairing in the EEDL and in the EHDL on the basis of the BdG equation. Both systems are connected by the duality relation (6). Although the systems have different quasiparticle modes in the presence of a domain wall, they have the same Josephson currents.…”

“…Recent research on layered chiral materials has revived the interest in this approach, in particular, for the special properties of zero‐energy (or mid‐gap) modes. [ 3–9 ]…”

“…Recent research on layered chiral materials has revived the interest in this approach, in particular, for the special properties of zero-energy (or mid-gap) modes. [3][4][5][6][7][8][9] An interesting phenomenon related to pairing is the Josephson effect [10] that originates in the coupling between the macroscopic superfluid or superconducting order parameter with the quasiparticle modes induced by a Josephson junction. [11][12][13][14][15][16] It has been discussed for different systems, including electron-electron graphene bilayers, [17,18] systems with spin-orbit coupling, [19] electron-hole bilayers, [20,21] electron-hole double layers [22][23][24] and electron-hole double-bilayers.…”

Long-range pairing in monolayer NbSe2 facilitates the emergence of topological superconducting states

“…Two-dimensional TSCs with nontrivial properties exhibit topological edge states (TESs) along their edges, as dictated by the well-established bulk-boundary correspondence (BBC) principle, which associates the topological invariant with the number of TESs [2,18]. However, recent research progress on topological materials has revealed the sensitivity and richness of the CN phase diagram to variations in the chemical potential (µ), magnetic field (V z ), and superconducting order parameter amplitude [19][20][21][22][23]. Furthermore, there is evidence of a mismatch between the CN and the number of TESs, indicating a deviation from the BBC principle [19,[21][22][23][24][25][26][27][28][29][30].…”

“…However, recent research progress on topological materials has revealed the sensitivity and richness of the CN phase diagram to variations in the chemical potential (µ), magnetic field (V z ), and superconducting order parameter amplitude [19][20][21][22][23]. Furthermore, there is evidence of a mismatch between the CN and the number of TESs, indicating a deviation from the BBC principle [19,[21][22][23][24][25][26][27][28][29][30]. For example, 2 H b -stacked bilayer transition metal dichalcogenides and bilayer bismuth lattice considering on-site s-wave pairing with Kane-Mele type SOC strength 0.0075 eV or without SOC show the TSC phases with rich and high CNs up to 4 under various µ and superconducting order parameters, which do not strictly always contain the same number of TESs as the CNs [19,25,29].…”