Temperature dependence of Andreev spectra in a superconducting - PowerPoint PPT Presentation

Temperature dependence of Andreev spectra in a superconducting carbon nanotube quantum dot A. Kumar, M. Gaim, D. Steininger, A. Levy Yeyati, A. Mart´ ın-Rodero, A. K. H¨ uttel, and C. Strunk Phys. Rev. B 89 , 075428 (2014) (TT 73.5), 2. April 2014, DPG Fr¨ uhjahrstagung Dresden

CNT V g 400nm CN T back gate the setup • “traditional” nanotube device fabrication: metal on top • 3nm Pd / 60nm Nb “fork” electrode • 1nm Ti / 60nm Al tunnel probe, weakly coupled • Andreev bound states form between branches of Nb fork Niobium: B crit , T crit , ∆ Nb • tunnel probe “senses” local density of states ⟶ much larger parameter space A. Kumar et al. , PRB 89 , 075428 (2014)

6.5 V (V) 0.06 0.04 0.02 (e²/h) dI/dV 0.00 0.0 6.0 5.5 5.0 g sd B =2T V (mV) sd V (mV) -2.5 4.5 -2.5 5.0 5.0 2.5 2.5 0.0 B =0T differential conductance — overview • B = 0 T: supercond. energy gap and ABS features clearly visible around zero bias • B = 2 T: return to regular Coulomb blockade behaviour • disordered system, no clear indications of shell filling A. Kumar et al. , PRB 89 , 075428 (2014)

abs + Δ (probe) s Δ Al ε 0.5 = (fork) E (probe) F Nb abs - ε lower ABS: V g (V) -0.5 0.0 4.60 4.65 V DOS 2∆ Nb +2∆ Al 0.06 Nb 0.00 -0.06 4.55 DOS F Δ Q-dot Al detail analysis of ABS features (I) • “non-crossing” ABS ε abs ( V g ) ≥ 0 sd (mV) • main resonance ( ⭐ ): ABS aligned with BCS edge in Al tunnel probe • weak replica ( ○ ): ABS at Fermi edge of probe electrode [note: needs finite DOS in BCS gap of + ε ab E probe electrode] Al eV sd • second resonance ( ◇ ): second ABS, aligned as ( ⭐ )! A. Kumar et al. , PRB 89 , 075428 (2014)

eV sd DOS s Δ Al ε 0.5 abs E (probe) F Nb Q-dot Al (fork) abs - ε DOS V g (V) -0.5 0.0 4.60 4.65 V replica: 2∆ Nb +2∆ Al 0.06 Nb 0.00 -0.06 4.55 = F Δ (probe) detail analysis of ABS features (I) • “non-crossing” ABS ε abs ( V g ) ≥ 0 sd (mV) • main resonance ( ⭐ ): ABS aligned with BCS edge in Al tunnel probe • weak replica ( ○ ): ABS at Fermi edge of probe electrode [note: needs finite DOS in BCS gap of + ε ab E probe electrode] • second resonance ( ◇ ): second ABS, aligned as ( ⭐ )! A. Kumar et al. , PRB 89 , 075428 (2014)

abs,2 Δ s,2 Δ Al ε 0.5 + = + ε ab (probe) E (probe) F Nb Q-dot Al abs,2 (fork) 0.06 -0.5 0.0 4.60 4.65 V DOS 2∆ Nb +2∆ Al V g (V) 0.00 -0.06 4.55 DOS F Δ Nb - ε 2nd ABS: detail analysis of ABS features (I) • “non-crossing” ABS ε abs ( V g ) ≥ 0 sd (mV) • main resonance ( ⭐ ): ABS aligned with BCS edge in Al tunnel probe • weak replica ( ○ ): ABS at Fermi edge of probe electrode [note: needs finite DOS in BCS gap of E probe electrode] Al eV sd • second resonance ( ◇ ): second ABS, aligned as ( ⭐ )! A. Kumar et al. , PRB 89 , 075428 (2014)

= Δ s Δ Al ε abs + 5.40 abs (fork) E (probe) F Nb (probe) lower ABS: 0.00 5.44 0.5 -0.5 0.0 V g (V) 0.05 0.05 - - ε V DOS DOS F Δ Nb Q-dot Al detail analysis of ABS features (II) • “crossing” ABS: 0- π phase transition ε abs ( V g ) passes through zero sd (mV) • main resonance ( ⭐ ): ABS aligned with BCS edge in Al tunnel probe • weak replica ( ○ ): ABS at Fermi edge of probe electrode + ε ab [note: needs finite DOS in BCS gap of E probe electrode] Al eV sd • second resonance ( ◇ ): second ABS, aligned as ( ⭐ )! A. Kumar et al. , PRB 89 , 075428 (2014)

abs eV sd DOS s Δ Al ε 5.40 E (probe) F Nb Q-dot Al (fork) abs - ε DOS 0.05 5.44 0.5 -0.5 0.0 V g (V) 0.05 0.00 Nb - V replica: = F Δ (probe) detail analysis of ABS features (II) • “crossing” ABS: 0- π phase transition ε abs ( V g ) passes through zero sd (mV) • main resonance ( ⭐ ): ABS aligned with BCS edge in Al tunnel probe • weak replica ( ○ ): ABS at Fermi edge of probe electrode + ε ab [note: needs finite DOS in BCS gap of E probe electrode] • second resonance ( ◇ ): second ABS, aligned as ( ⭐ )! A. Kumar et al. , PRB 89 , 075428 (2014)

+ Δ s,2 Δ Al ε abs,2 5.40 = + ε ab (probe) E (probe) F Nb Q-dot Al abs,2 (fork) 0.00 5.44 0.5 -0.5 0.0 V g (V) 0.05 0.05 - V DOS DOS F Δ Nb - ε 2nd ABS: detail analysis of ABS features (II) • “crossing” ABS: 0- π phase transition ε abs ( V g ) passes through zero sd (mV) • main resonance ( ⭐ ): ABS aligned with BCS edge in Al tunnel probe • weak replica ( ○ ): ABS at Fermi edge of probe electrode [note: needs finite DOS in BCS gap of E probe electrode] Al eV sd • second resonance ( ◇ ): second ABS, aligned as ( ⭐ )! A. Kumar et al. , PRB 89 , 075428 (2014)

-8 E / ∆ 0.5 -12 ε /∆ 4 0 -4 E / ∆ -12 0.0 ε /∆ 4 0 -4 -8 0.0 -0.5 0.5 -0.5 gate voltage dependence of the bare ε abs ( V g ) • NRG calculations for a two-channel superconducting Anderson model • two local levels couple via two channels to the superconductor • crossing / non-crossing controlled by ratio T K ( E C , Γ )/ ∆ A. Kumar et al. , PRB 89 , 075428 (2014)

6.24 6.28 800 mK 30 mK 6.28 6.24 6.28 6.24 6.28 1 K 6.24 400 mK 0.00 -0.05 0.05 (e 2 /h) dI/dV 0.0 0.5 0.5 V (V) g temperature evolution — experiment V sd (mV) • measurement: distinct change of satellite curvature above 400 mK • thermal excitation? A. Kumar et al. , PRB 89 , 075428 (2014)

e V sd (meV) 6.24 Δ Al meV −0.2 0 0.2 V g (V) 6.28 eV satellite V g (V) 6.24 6.28 6.28 0.5 -0.5 eV satellite eV main 6.24 eV −0.1 0 0.1 eV satellite eV main eV satellite - Δ Δ Al main Al -(eV - Δ ) main Al 0 30mK, low-temperature replica V sd (mV) • distance between main resonance and satellite constant, ∼ ∆ Al • “shift” ⟶ peak positions coincide • eV main − ∆ Al = eV satellite • this reduces all gate dependence to ε abs ( V g ) A. Kumar et al. , PRB 89 , 075428 (2014)

eV main eV main 0 6.28 6.24 0.2 0 −0.2 eV main satellite Al 2 Δ - eV e V sd (meV) eV satellite eV main eV satellite -0.5 satellite Al ) -(2 Δ - eV 6.28 6.24 V g (V) meV 6.28 6.24 V g (V) 0.2 0 −0.2 0.5 800mK, high-temperature replica V sd (mV) • “flip and shift” ⟶ again, peak positions coincide • need a minus sign from somewhere! • 2∆ Al − eV satellite = eV main • this reduces all gate dependence to ε abs ( V g ) • why? ... A. Kumar et al. , PRB 89 , 075428 (2014)

Δ ε lower ABS: Q-dot Al Nb F E (probe) 0.5 DOS = abs + Δ Al (probe) F -0.5 0.0 V 6.28 V g (V) 6.24 Δ s Nb - ε abs DOS (fork) detail analysis of ABS features (III) sd (mV) • main resonance ( ⭐ ): ABS aligned with BCS edge in Al tunnel probe (same as before) • weak replica, high temperature ( □ ): excited ABS aligned at BCS edge in Al tunnel probe + ε ab E • indeed, Al eV sd 2∆ Al − eV satellite = eV main A. Kumar et al. , PRB 89 , 075428 (2014)

(fork) ε Δ = - 6.28 6.24 DOS DOS (probe) 0.5 high-T sat.: Q-dot Al Nb Al F -0.5 0.0 V V g (V) sd Δ s Nb - ε abs abs eV detail analysis of ABS features (III) sd (mV) • main resonance ( ⭐ ): ABS aligned with BCS edge in Al tunnel probe (same as before) • weak replica, high temperature ( □ ): excited ABS aligned at BCS edge in Al tunnel probe + ε ab E • indeed, 2∆ Al − eV satellite = eV main A. Kumar et al. , PRB 89 , 075428 (2014)

0.5 0 ε /∆ 0.5 0 - 0.5 0.5 0 - 0.5 1 K - 0.5 0.5 - 0.5 400 mK 0.0 -0.5 0.5 800 mK 30 mK 0.00 -0.05 0.05 (e 2 /h) dI/dV 0 temperature evolution — model calculation E / ∆ • mean field description of the superconducting Anderson model • two superconducting leads with two different gap parameters • only temperature-dependent parameter: ∆ Al ( T ) • change of satellite curvature above 400 mK nicely reproduced A. Kumar et al. , PRB 89 , 075428 (2014)

(f) - 0.5 (a) (h) 0.5 -0.5 0.0 - 0.5 0 0.5 0.5 800 mK - 0.5 0 0.5 - 0.5 0 0.5 ε /∆ g 0 (e) 30 mK (d) (e 2 /h) (b) (c) (g) V (V) 1 K 0.5 0.5 0.0 dI/dV 0.05 6.28 -0.05 0.00 6.24 6.28 6.24 6.28 6.24 6.28 6.24 400 mK Thank you! — Questions? V sd (mV) E / ∆ Temperature dependence of Andreev spectra in a superconducting carbon nanotube quantum dot A. Kumar et al. , Phys. Rev. B 89 , 075428 (2014)