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

the setup

CNT

Vg

400nm

CN

T

back gate

Niobium: Bcrit, Tcrit, ∆Nb ⟶ much larger parameter space

• “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

• tunnel probe “senses” local

density of states

• A. Kumar et al., PRB 89, 075428 (2014)

differential conductance — overview

0.0 0.0 2.5 2.5 5.0 5.0

• 2.5

4.5

• 2.5

V (mV)

sd

V (mV)

sd

V (V)

g

5.0 5.5 6.0 6.5

0.00 dI/dV (e²/h) 0.02 0.04 0.06

B=0T B=2T

• 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)

detail analysis of ABS features (I)

0.5

• 0.5

0.0 4.60 4.65 V

sd (mV)

2∆Nb+2∆Al

Vg (V)

0.06 0.00

• 0.06

4.55 E

F

Δ

Nb

• ε

abs

+εab

s

ΔAl

ε

abs+

=

Δ

Al eVsd

E (probe)

F

Nb Q-dot Al lower ABS:

(fork) (probe) DOS DOS

• “non-crossing” ABS

εabs(Vg) ≥ 0

• 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 probe electrode]

• second resonance (◇): second

ABS, aligned as (⭐)!

• A. Kumar et al., PRB 89, 075428 (2014)

detail analysis of ABS features (I)

0.5

• 0.5

0.0 4.60 4.65 V

sd (mV)

2∆Nb+2∆Al

Vg (V)

0.06 0.00

• 0.06

4.55 E

F

Δ

Nb

• ε

abs

+εab

s

ΔAl

ε

abs

eVsd

E (probe)

F

Nb Q-dot Al

(fork) (probe) DOS DOS

= replica:

• “non-crossing” ABS

εabs(Vg) ≥ 0

• 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 probe electrode]

• second resonance (◇): second

ABS, aligned as (⭐)!

• A. Kumar et al., PRB 89, 075428 (2014)

detail analysis of ABS features (I)

0.5

• 0.5

0.0 4.60 4.65 V

sd (mV)

2∆Nb+2∆Al

Vg (V)

0.06 0.00

• 0.06

4.55 E

F

Δ

Nb

• ε

abs,2

+εab

s,2

ΔAl

ε

abs,2

+ =

Δ

Al eVsd

E (probe)

F

Nb Q-dot Al 2nd ABS:

(fork) (probe) DOS DOS

• “non-crossing” ABS

εabs(Vg) ≥ 0

• 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 probe electrode]

• second resonance (◇): second

ABS, aligned as (⭐)!

• A. Kumar et al., PRB 89, 075428 (2014)

detail analysis of ABS features (II)

5.40 5.44 0.5

• 0.5

0.0 Vg (V)

0.05 0.05 0.00

• V

sd (mV)

E

F

Δ

Nb

• ε

abs

+εab

s

ΔAl

ε

abs+

=

Δ

Al eVsd

E (probe)

F

Nb Q-dot Al lower ABS:

(fork) (probe) DOS DOS

• “crossing” ABS: 0-π phase

transition εabs(Vg) passes through zero

• 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 probe electrode]

• second resonance (◇): second

ABS, aligned as (⭐)!

• A. Kumar et al., PRB 89, 075428 (2014)

detail analysis of ABS features (II)

5.40 5.44 0.5

• 0.5

0.0 Vg (V)

0.05 0.05 0.00

• V

sd (mV)

E

F

Δ

Nb

• ε

abs

+εab

s

ΔAl

ε

abs

eVsd

E (probe)

F

Nb Q-dot Al

(fork) (probe) DOS DOS

= replica:

• “crossing” ABS: 0-π phase

transition εabs(Vg) passes through zero

• 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 probe electrode]

• second resonance (◇): second

ABS, aligned as (⭐)!

• A. Kumar et al., PRB 89, 075428 (2014)

detail analysis of ABS features (II)

5.40 5.44 0.5

• 0.5

0.0 Vg (V)

0.05 0.05 0.00

• V

sd (mV)

E

F

Δ

Nb

• ε

abs,2

+εab

s,2

ΔAl

ε

abs,2

+ =

Δ

Al eVsd

E (probe)

F

Nb Q-dot Al 2nd ABS:

(fork) (probe) DOS DOS

• “crossing” ABS: 0-π phase

transition εabs(Vg) passes through zero

• 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 probe electrode]

• second resonance (◇): second

ABS, aligned as (⭐)!

• A. Kumar et al., PRB 89, 075428 (2014)

gate voltage dependence of the bare εabs(Vg)

E / ∆

0.5

• 0.5

0.0

• 8
• 4

4

ε/∆

• 12

E / ∆

• 8
• 4

4

ε/∆

• 12

0.5

• 0.5

0.0

• 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 TK(EC, Γ)/∆
• A. Kumar et al., PRB 89, 075428 (2014)

temperature evolution — experiment

Vsd (mV)

V (V)

0.5 0.5 0.0

dI/dV (e2/h)

0.05

• 0.05

0.00 6.24 6.28 6.24 6.28 6.24 6.28 6.24 6.28

30 mK 800 mK

g

400 mK 1 K

• measurement: distinct change of satellite curvature above 400 mK
• thermal excitation?
• A. Kumar et al., PRB 89, 075428 (2014)

30mK, low-temperature replica

meV −0.1 0.1 eVsatellite eVmain eVsatellite eV

• Δ

main Al

• (eV
• Δ )

main Al

ΔAl eVmain eVsatellite eVsatellite ΔAl e Vsd (meV) −0.2 0.2 Vg (V) 6.24 6.28 Vg (V) 6.24 6.28 Vsd (mV) 0.5

• 0.5

6.24 6.28

• distance between main resonance and satellite constant, ∼ ∆Al
• “shift” ⟶ peak positions coincide
• eVmain − ∆Al = eVsatellite
• this reduces all gate dependence to εabs(Vg)
• A. Kumar et al., PRB 89, 075428 (2014)

800mK, high-temperature replica

e Vsd (meV) −0.2 0.2 Vg (V) 6.24 6.28 meV Vg (V) 6.24 6.28

• (2Δ - eV

)

Al satellite

eVsatellite eVmain eVmain eVsatellite eVmain 2Δ - eV

Al satellite

eVmain −0.2 0.2 6.24 6.28 Vsd (mV) 0.5

• 0.5
• “flip and shift” ⟶ again, peak positions coincide
• need a minus sign from somewhere!
• 2∆Al − eVsatellite = eVmain
• this reduces all gate dependence to εabs(Vg)
• why? ...
• A. Kumar et al., PRB 89, 075428 (2014)

detail analysis of ABS features (III)

0.5

• 0.5

0.0 V

sd (mV)

Vg (V) E

F

Δ

Nb

• ε

abs

+εab

s

ΔAl

ε

abs+

=

Δ

Al eVsd

E (probe)

F

Nb Q-dot Al lower ABS:

(fork) (probe) DOS DOS

6.24 6.28

• 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

• indeed,

2∆Al − eVsatellite = eVmain

• A. Kumar et al., PRB 89, 075428 (2014)

detail analysis of ABS features (III)

0.5

• 0.5

0.0 V

sd (mV)

Vg (V) E

F

Δ

Nb

• ε

abs

+εab

s

Nb Q-dot Al high-T sat.:

(fork) (probe) DOS DOS

6.24 6.28

• =

Δ

ε

eV Al abs sd

• 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

• indeed,

2∆Al − eVsatellite = eVmain

• A. Kumar et al., PRB 89, 075428 (2014)

temperature evolution — model calculation

E / ∆

dI/dV (e2/h)

0.05

• 0.05

0.00

30 mK 800 mK

0.5

• 0.5

0.0

• 0.5

0.5

• 0.5

0.5

• 0.5

0.5

• 0.5

0.5

ε/∆

400 mK 1 K

• 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)

Thank you! — Questions?

(a) (b) (c) Vsd (mV)

V (V)

E / ∆

0.5 0.5 0.0

dI/dV (e2/h)

0.05

• 0.05

0.00 6.24 6.28 6.24 6.28 6.24 6.28 6.24 6.28

30 mK 800 mK (e) (f) (h)

0.5

• 0.5

0.0

• 0.5

0.5

• 0.5

0.5

• 0.5

0.5

• 0.5

0.5

ε/∆

g

400 mK (d) 1 K (g)

Temperature dependence of Andreev spectra in a superconducting carbon nanotube quantum dot

• A. Kumar et al., Phys. Rev. B 89, 075428 (2014)