Signatures of Andreev Blockade in a Double Quantum Dot Coupled to a Superconductor

Subgap Dynamics of Double Quantum Dot Coupled Between Superconducting and Normal Leads

“…In particular, for the singly occupied quantum dots (what can be assured by appropriate gating) the superconducting proximity effect could be blocked. Such triplet blockade effect has been recently reported in S-DQD-S 17 and N-DQD-S 18 nanostructures. As regards the Coulomb potential, its influence is indirectly manifested through the singlet-doublet transitions (related to variations between the even-odd occupancies of the quantum dots 17,18 ) and, under specific conditions, can lead to the subgap Kondo effect 22,23,30,38,44 .…”

“…Major features of two quantum dots coupled in series to the superconducting lead(s) originate from the ground state configuration which can vary its even-odd parity, depending on: the energy levels, hybridization with the external reservoirs, the inter-dot coupling, and the Coulomb potential 30,38 . Such parity changes are corroborated by crossings of the in-gap bound states and can be empirically detected by discontinuities of the Josephson current in S-DQD-S junctions [14][15][16] or the subgap Andreev current in N-DQD-S junctions 14,18,19 . The resulting zero-bias conductance as a function the quantum dot levels (tunable by the plunger gates) resembles a honeycomb structure [14][15][16] instead of a diamond shape, typical for the single quantum dot junctions.…”

“…We have solved numerically these coupled differential equations (10)(11)(12)(13)(14)(15)(16)(17)(18)(19) subject to the specific initial conditions. For convenience, we have assumed that at t = 0 both external reservoirs were isolated from the quantum dots.…”

“…So far the static properties of in-gap bound states have been throughly investigated for the single and multiple quantum dots 10,11 and recently also for nanoscopic length atomic chains, semiconducting nanowires, and magnetic islands proximitized to bulk superconductors 12 . Their particular realizations in the double quantum dots (DQDs) have been experimentally probed by the tunneling spectroscopy, using InAs [13][14][15][16][17][18] , InSb 19 , Ge/Si 20 and carbon nanotubes 21,22 and by the scanning tunneling microscopy applied to various di-molecules deposited on superconducting substrates [23][24][25][26][27] . Rich properties of such in-gap bound states of the DQDs have been analyzed theoretically by a number groups 11,19,[28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] .…”

Andreev reflection mediated by Majorana zero modes in T-shaped double quantum dots

“…Some interesting phenomena were then found, such as half of the quantum value of the electron conductance [19] and sign reversion of the thermopower [20 -22]. There were also some works concerning MZMs hybridized to QDs with metallic and superconductor leads [23][24][25]. It was found that in the absence of the intradot Coulomb interaction, there is destructive (constructive) interference for spin-up (spin-down) electrons at the in-gap states.…”