1. P. Szabó, V. Hašková, T. Samuely, M. Kopčík, P. Samuely
SZUPRAVEZETÉS ERŐSEN RENDEZETLEN RENDSZEREKBEN. SZUPRAVEZETŐ-SZIGETELŐ ÁTMENTET
MoC VÉKONYRÉTEGEKBEN.
P. Szabó, V. Hašková, T. Samuely, M. Kopčík, P. Samuely
Centre of Low Temperature Physics, Košice
@ Slovak Academy of Sciences & P.J.Šafárik University, Slovakia
M. Grajcar and M. Žemlička
Comenius University, Bratislava, Slovakia
Sss

2. Démokritosz, Kis diakozmosz
"Ha ezt az almát kettõbe vágom, két fél alma marad a kezemben, ha az egyik fél almát ismét két részre vágom, két negyed alma marad, de ha az osztást tovább folytatom, vajon mindig marad-e a kezemben az alma 1/8, 1/16 stb. része? Vagy pedig egy adott pillanatban a következõ osztás eredményeként a megmaradt rész már nem rendelkezik az alma tulajdonságaival?"
Démokritosz, Kis diakozmosz
Διογένης Λαέρτιος. Βίοι καὶ γνῶμαι τῶν ἐν φιλοσοφίᾳ εὐδοκιμησάντων, σελ. Βιβλίο Θ', 41.

3. P. Szabó, V. Hašková, T. Samuely, M. Kopčík, P. Samuely
SZUPRAVEZETÉS ERŐSEN RENDEZETLEN RENDSZEREKBEN. SZUPRAVEZETŐ-SZIGETELŐ ÁTMENTET
MoC VÉKONYRÉTEGEKBEN.
P. Szabó, V. Hašková, T. Samuely, M. Kopčík, P. Samuely
Centre of Low Temperature Physics, Košice
@ Slovak Academy of Sciences & P.J.Šafárik University, Slovakia
M. Grajcar and M. Žemlička
Comenius University, Bratislava, Slovakia
Sss

4. Very dirty superconductors
S – I transition – study of the increased
disorder for the superconductivity
Disorder can be introduced -
physical/chemical doping,
reduced carrier concentration,
sample dimension/thickness
In superconductors
Anderson’s theory – non magnetic
impurities – no influence on Tc
- at low disorder
At high disorder – Tc is suppressed
the normal state resistance increases
In metals
at l < a (above a critical resistance)
transition to the insulating state

5. Minimum metallic conductivity (maximum sheet resistance)
Metal - insulator transition (MIT) in 2d
Ioffe-Regel criterion, Prog. Semicond. 1960
When lmin ~ a , electrons localize
(l - electron’s mean free path & a - lattice constant)
Ioffe
Regel
Minimum metallic conductivity (maximum sheet resistance)

6. Superconductor - insulator transition (SIT) in 2d
localization of Cooper pairs q=2e
insulating films
Rs ~ 6.45 kW
superconducting films
SIT tuned by chem. & phys. disorder, thickness,
carrier concentration, magnetic field

7. How S-I-T is achieved ? Superconductivity - macroscopic wave function
amplitude D and phase j
Suppressing of sc: amplitude D or phase breaking
Bosonic mechanism
Phase fluctuations
Superconductor goes directly to insulator
Cooper pairs survive with finite D
without long range phase coherence
SC droplets – Bose insulator
Fermionic mechanism
Amplitude
Disorder-enhanced Coulomb interaction destroys Copper pairs, D = 0
Poor metal goes to Fermi insulator
via MIT at higher disorder
Local studies of superconductivity: DOS, D by STM - important
S.M. Hollen, PRB 2013
Recent STM studies strongly support the bosonic picture
Understanding SIT important for amorphous superconductors, sc nanowires, HTc’s,
ultracold atomic gases, SIT – prototype of disorder driven QPT

8. Scanning Tunneling Spectroscopy (STS)
S-I-N junction with Au tip
At low T dI/dV is proportional
to the LDOS of SC
Low temperatures are important !!
Finite lifetime effect (Dynes formula):
Parameter G can account for broadening if necessary
via substitution of complex E’ = E- iG instead of E in NSBCS

9. Scanning tunneling spectroscopy in ultrathin TiN films
Film thickness 3-5 nm, coherence length x=10 nm
Disorder driven:
decrease of Tc
inhomogeneity of gap D
increased coupling ratio 2D/ kTc
Sacepé et al., PRL2008

10. Scanning tunneling spectroscopy in ultrathin TiN films
reduced DOS without coherence peaks
Tc=1.0 K
Tc=0.45 K
Tc=1.3 K
Pseudogap exists in ultrathin TiN up to 14 Tc
due fluctuations, 2D, proximity to SIT, enhanced e-e int.
Sacépé, Nature Comm. 2010

11. STS on SIT phenomenology
On approach to SIT (TiN, InO, NbN,...)
Tc decrease
D decrease smaller or not at all, 2D / kBTc increase
D inhomogeneity on scale of x
pseudogap appearance
V-shape background appearance
coherence peaks in SC DOS suppression
bosonic scenario?
Last decade experiments strongly suggest - bosonic picture of the SIT is universal - motivation
N. Trivedi, in book Conductor Insulator Quantum Phase Transitions (Oxford University Press 2012).
The most current theories of the disorder-driven SIT predict the formation of puddles of CPs
that become phase incoherent with one another with increasing disorder.
V. L. Pokrovsky, G. M. Falco, and T. Nattermann, Phys. Rev. Lett. 105, (2010).

12. SIT TiN vs. MoC thin film - MOTIVATION
Extremely sharp transition SIT @ Rs ~ 3 kW < h/4e2
SIT t <1.3 nm & Dt < 0.1 nm
WL + EEI
Sacepé et al., PRL2008
MoC – week increase of R(T), week QS
NS of tunneling spectra not affected by
Strong quantum effects
Increase R(T) – strong Quantum States
in insulating/metallic normal state
e.g. - strong EEI – Altshurer - Aronov effect
reduced tunnelling backround in Normal State
L. Bartosch et al., EPL 2001

13. MoC ultra thin film prepared by the reactive magnetron sputtering
on single-crystal sapphire substrates ( at 200 oC)
in a mixture of Ar and acetylene gas
t = 10 nm Rs (10 K) = 344 W, Tc = 6.7 K, kFl = 2
t = 5 nm Rs (10 K) = 850 W, Tc = 3.3 K, kFl = 1.8
t = 3 nm Rs (10 K) = 1227W, Tc = 1.3 K, kFl = 1.3
Disorder - characterized by the sheet resistance, Rs
- lowering of thickness leads to higher disorder & lower Tc
After sputtering - the surface passivated with photoresist
optimization of acetylene pressure
to have high Rs and still SC
Sheet resistance Rs vs. thickenss
@ optimal acetylene pressure

14. STM - experimental setup in Košice Experimental setup in Košice
home made STM head (collaboration with J.G.Rodrigo - UAM Madrid)
Dulcinea SPM controller by Nanotec
300mK: Janis SSV 3He refrigerator - acoustic reducer + operation without pumping the 1K pot
8T Janis cryomagnetic system
no UHV – samles are at the air during installation - cca. 10 min.
Experimental setup in Košice

15. Scanning Tunneling Spectroscopy (STS)
S-I-N junction with Au tip
At low T dI/dV is proportional
to the LDOS of SC
Low temperatures are important !!
Finite lifetime effect (Dynes formula):
Parameter G can account for broadening if necessary
via substitution of complex E’ = E- iG instead of E in NSBCS

16. deviations 5% - in the range of device noice
STM results – 450 mK
10 nm nm nm
Homogeneous gap
deviations 5% - in the range of device noice

17. The gapmap fits the surface
Topography at 0.5 K
Gapmap at 0.5 K
small 7-10% variation of D observed in thicker areas with corrugation ~ 1 nm

18. D = 0.62 meV , G/D = 0.3 D , Tc = 3.5 K, 2D/kBTc = 3.87
10 nm nm nm
D = 1.1 meV, G/D = 0.1D ,
Tc = 6.5 K, 2D/kBTc = 3.85
D = 0.62 meV , G/D = 0.3 D , Tc = 3.5 K, 2D/kBTc = 3.87
D = 0.2 meV , G/D = 0.9 D
Tc = 1.35 K, 2D/kBTc = 3.7-4

19. 5 nm strongly disordered MoC films – vortex lattice
CITS conductance map at V = 0 mV, 400 nm x 400 nm, T = 0.5 K, H = 1 Tesla
CITS
Hc2 = 5.4 Tesla, x = 7.5 nm
at H = 1 Tesla a = 49 nm
Vortices are manifestation of the quantum coherence of the superconducting state
– no (strong) phase fluctuations

20. Summary Fermionic scenario: Bosonic insulator scenario:
Tc and D decrease together
2D / kBTc almost not changing
No D fluctuations
no pseudogap
the bosonic picture is not universal
Bosonic insulator scenario:
Tc and D decrease
2 D / kBTc increase
D inhomogeneity on scale of x
pseudogap appearance
increased disorder – increased Dynes G- increase of ingap states
disorder leads to pair-breaking or interface effect (new theory?)
[1] P. Szabó, et al., Phys. Rev. B 93, (2016).
[2] M. Žemlička, et al., Phys. Rev. B 92, (2015.)