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

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.

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

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

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)

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

How S-I-T is achieved ? Superconductivity - macroscopic wave function amplitude D and phase j Suppressing of sc: amplitude D 0 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 0 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

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

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

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

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, 267001 (2010).

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

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

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

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

deviations 5% - in the range of device noice STM results – 450 mK 10 nm 5 nm 3 nm Homogeneous gap deviations 5% - in the range of device noice

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

D = 0.62 meV , G/D = 0.3 D , Tc = 3.5 K, 2D/kBTc = 3.87 10 nm 5 nm 3 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

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

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, 014505 (2016). [2] M. Žemlička, et al., Phys. Rev. B 92, 224506 (2015.)