Superconducting proximity effect in flat band systems

Abstract

We study theoretically proximity-induced superconductivity and its inverse effect in dice lattice flat band model by considering Josephson junction with an s-wave pairing in the superconducting leads. Using self-consistent tight-binding Bogoliubov-de Gennes method, we show that there is a critical value for chemical potential of the superconductors depending on paring interaction strength over which for undoped normal region the proximity effect is enhanced. Whereas if the superconductor chemical potential is less than the critical one the proximity effect decreases regardless of normal region doping and in the meanwhile, the pairing amplitude of superconducting region increases significantly. Furthermore, we unveil that the supercurrent passing through the junction is large (vanishingly small) when the superconductor chemical potential is smaller (larger) than the critical value which increases as a function of normal region chemical potential.

Generalized WKB theory for electron tunneling in gapped $α-\mathcal{T}_3$ lattices

“…Therefore, from Eqs. ( 52) and (23) we are able to find explicitly the spatially-dependent longitudinal momentum π x (ξ, ∆ 0 | φ) as…”

“…Initially designed as a purely theoretical model, 11 α − T 3 , and especially the dice lattices, has recently been found in a number of existing and experimentally synthesized materials. 12 These include three-layer arrangement of SrTiO 3 /SrIrO 3 /SrTiO 3 lattices 13 , Lieb [14][15][16][17] and the Kagome 18-20 optical lattices and waveguides 21,22 , Josephson arrays, 23 , Hg 1−x Cd x quantum well 24 . A comprehensive review of all dice-like systems with a flat band can be found in Ref.…”

Revival of superconductivity in a one-dimensional dimerized diamond lattice

“…Because of the flat bands, highly correlated phases, e.g., superconductivity, would be established in flat-band systems. Superconductivity in 3D and 2D systems supporting flat [42][43][44][45][46][47][48][49][50][51] or partially flat [52][53][54][55][56][57][58][59] band has been studied extensively, with intrinsic [60] and extrinsic [61] origins. The pairings of fermions [62] and Cooper pairs [63,64] on a 1D diamond chains embedded in a magnetic field have been studied.…”

Developing a semiclassical Wentzel-Kramers-Brillouin theory for $α-\mathcal{T}_3$ model

“…At this moment, a large number of α − T 3 materials and dice lattices have been fabricated. These include a trilayer SrTiO 3 /SrIrO 3 /SrTiO 3 , 58,59 Hg 1−x Cd x quantum well, 30,60 Josephson arrays, 41,61 Leib and Kagome optical lattices and optical waveguides. [62][63][64][65][66][67][68][69][70] , In 0.53 Ga 0.47 As/InP semiconducting layers 71 and many-many other existing materials.…”