Entering the Quantum Griffiths Phase of a Disordered Superconductor - PowerPoint PPT Presentation

Entering the Quantum Griffiths Phase of a Disordered Superconductor Jérôme Lesueur Physics and Materials Laboratory (LPEM) ESPCI – CNRS – UPMC Paris SIT 2018 Villars de Lans

People PhD & PDF : A. Jouan �� G. Singh - J. Biscaras – S. Hurand Collaborators : N. Bergeal, C. Feuillet-Palma, LPEM (Paris) A. Rastogi, ITT Kanpur (India) R. C. Budhani, A. Dogra, NPL Dehli (India) A. Barthelemy, M. Bibes, J. Villegas, N. Reyren, E Lesne UMR Thales-CNRS (Palaiseau) M. Grilli, S. Caprara, L. Benfatto, La Sapienza (Rome)

Quantum Phase Transition and fluctuations Spatial correlation length − ν ξ ≈ δ − δ c Critical exponents Dynamical correlation length − z ν ξ τ ≈ δ − δ c Universality class QCP Parameter in the Hamiltonian

Quantum Phase Transition and fluctuations in 2D ■ Phase diagram Correlation length − ν ξ ≈ B − B × LTO/STO Dynamical correlation length − z ν ξ τ ≈ B − B × QCP QCP Perpendicular Caviglia et al, Nature 2008 Gate Voltage V G magnetic field B Biscaras et al, PRL 108, 247004 (2012)

Complex phase diagrams ■ Large varieties Xing et al, Science (2015) Saito et al, Nat Com (2018) Sun et al, Nat Com (2018) Biscaras et al, Nat Mat (2013)

Critical exponents ■ Large varieties z = 1 ν = 0.66 ν = 7/4 ν = 4/3 ν = ... ν = 3/2 ■ Non universal exponents Thin Ga films InOx films Xing et al, Science (2015) Lewellyn et al, arXiv 2018

Quantum Phase Transition in oxide interfaces ? Point #1 SC Normal ■ Role of the mesoscopic disorder ... Feigel'man et al, PRL 2001 - Intrinsic inhomogeneity builts up Spivak et al, PRB 2008 - Quasi-1D filamentary structure appears Ioffe-Mezard PRL 2010, Goetz-Benfatto-Castellani PRL 2012 Multiple Quantum Criticalities ? ? Point #2 ■ Role of the Griffiths singularities ? - Rare events matter - Consequence on the observables Evidence for a Griffiths phase ?

Outline Tunable superconductivity in oxide 2DEG Quantum phase transition in magnetic field Quantum phase transition in gate voltage

2 DEG at oxides interfaces LaXO 3 /SrTiO 3 (X=Al or Ti) ■ Thin layer of LaAlO 3 or LaTiO 3 deposited by PLD on a SrTiO 3 substrate SrTiO 3 LaAlO 3 or LaTiO 3 O Ohtomo et al, Nature 2002 O Ti Hwang et al, Physica E 2004 Ti Sr La 2 DEG at the interface n S ~ 10 14 e/cm 2 LaAlO 3 10 u.c. a few nanometers Substrate SrTiO 3 Herranz et al, Nature Comm. 2015 Reyren et al, Science 2007 2D SC Physics Superconductivity Biscaras et al, Nature Com. 1, 89 (2010)

Electric field effect ■ Control of the 2-DEG by electrostatic back gate LaTiO 3 /SrTiO 3 remove e- R s decrease with Vg T c goes through a maximum add e - Caviglia et al, Nature 2008 Biscaras et al, PRL 108, 247004 (2012) ■ Superconductor-insulator transition induced by field effect

Electric field effect ■ Control of the 2-DEG by electrostatic back gate LaTiO 3 /SrTiO 3 remove e- R s decrease with Vg T c goes through a maximum add e - Caviglia et al, Nature 2008 Biscaras et al, PRL 108, 247004 (2012) ■ Superconductor-insulator transition induced by field effect

Superconductivity ... inhomogeneous medium Bert et al, PRB (2012) Resistance Superfluid density ■ Effective Medium Theory ■ Random Resistance Network ■ Filamentary structure S. Caprara et al, Phys Rev B (R) 88, 020504 (2013) D. Bucheli et al, New J. of Phys. 15, 023014 (2013) Ioffe-Mezard PRL 2010, Goetz-Benfatto-Castellani PRL 2012

Superconductivity ... inhomogeneous medium ■ Josephson Junctions (JJ) ■ Hysteretic characteristics ■ Stochastic Critical Current ■ RCSJ model for the JJ ■ Thermal vs Quantum SC G SC D S. Hurand et al. unpublished results

Superconductivity ... inhomogeneous medium ■ Statistical analysis : 10 000 switching events ■ Evolution with temperature σ sw ■ Compatible with MQT behavior ■ σ sw saturates at low temperature ■ σ sw follows Ic at high temperature ■ σ sw � I c 2/3 ■ RCSJ model T cr ≈ 478mK S. Hurand et al. unpublished results

Superconductivity ... inhomogeneous medium ■ Josephson Junctions (JJ) network ■ Typical scale : 200 nm 200 nm Prawiroatmodjo et al. Phys Rev B 93 , 184504 (2016)

Outline Tunable superconductivity in oxide 2DEG Quantum phase transition in magnetic field Quantum phase transition in gate voltage

Magnetic field driven Quantum Phase Transition ■ Suppression of superconductivity by a perpendicular magnetic field at V G =80V V G =80V 400 B = 0.3 T B = 0 T 300 R (k Ω ) Tc (K) R S ( Ω / � ) 200 V G = + 80 V 100 0 0.1 0.2 0.3 0.4 T (K) ➨ Transition from superconducting to weakly localized metallic state

Magnetic field driven Quantum Phase Transition ■ Suppression of superconductivity by a perpendicular magnetic field at V G =80V V G =80V 400 B = 0.3 T 380 B = 0 T 375 0.2 K 300 370 R X R (k Ω ) Tc (K) B X B � R S ( Ω / � ) R S ( Ω / � ) 0.1 K R S ( Ω / � ) 370 360 200 V G = + 80 V 350 365 100 340 0.12 0.14 0.16 0.18 0.20 0.22 0.12 0.16 0.20 0.24 T (K) B (T) 0 0.1 0.2 0.3 0.4 T (K) ➨ Crossing point at B ✕ : a first signature of a quantum phase transition ➨ transition from superconducting to weakly localized metallic state

Scaling and critical exponents ■ Finite size scaling analysis Correlation length − ν ξ ≈ B − B × R = F B − B ×     Dynamical correlation length T z ν R c   − z ν ξ τ ≈ B − B × − 1/ z υ ( ) t = T / T 0 Biscaras et al, Nature Mat. 12, 542 (2013) B-B × t N. Markovic et al. PRL 1998 Scaling Behaviour with z ν = 2/3 (as in a-Bi, NbSi, … ) H. Aubin et al. PRB 2006 M Fisher PRL 1990 Superfluid transition in charged system : z=1 I F Herbut et al. PRL 2001 Universality Class : (2+1)D XY in the clean limit : ν = 2/3 (Quantum Phase Fluctuations)

A true quantum Phase Transition ? 375 R X R S ( Ω / � ) 370 380 365 R C R S ( Ω / � ) 0.12 0.14 0.16 0.18 0.20 0.22 375 T (K) 370 0.06 0.08 0.10 T (K) ➨ Scaling does not work at low temperature !

Scaling at lower temperature 380 ■ Crossing point at B c 376 0.07 K R S ( Ω / � ) B c > B � B C B c 0.04 K 372 0.20 0.22 0.24 0.26 0.28 B (T) ■ Finite size scaling analysis ➨ Critical exponent z ν ≈ 3/2 Biscaras et al, Nature Mat. 12, 542 (2013)

Critical exponents as a function V G 0.25 0.25 0.20 0.20 0.15 0.15 T C (K) B (T) T C B X 0.10 0.10 B C 0.05 0.05 B d 0.00 0.00 -40 -20 0 20 40 60 80 100 V G (V) 2.5 2.0 z ν ≥ 3/2 B C 1.5 z ν z ν = 1 1.0 B X 0.5 z ν ≈ 2/3 0.0 -40 -20 0 20 40 60 80 100 V G (V) ➨ Multiple Critical Behavior (B x & B c ) associated to different critical exponents

Multiple Quantum Critical Behaviors in 2D SC ■ Superconducting puddles in a 2DEG matrix Spivak et al, PRB 2008 G 2DEG ■ Characteristic puddle size L d L d ~200 nm ■ Puddles coupled by Josephson through G 2DEG L Φ ■ Phases fluctuations in the SC puddles AND between puddles : two critical fields 2 DEG ■ Divergence of the thermal dephasing length L Φ � T -1/z if z=1 ➨ Low temperature T < T d L Φ > L d “disordered” system ν ≥ 3/2 Harris criteria ➨ High temperature T > T d L Φ < L d “clean” system ν ≈ 2/3

Multiple Quantum Critical Behaviors in 2D SC Biscaras et al, Nat Mat (2013) Sun et al, Nat Com (2018)

Outline Tunable superconductivity in oxide 2DEG Quantum phase transition in magnetic field Quantum phase transition in gate voltage

Gate voltage driven Quantum Phase Transition ■ Quantum Critical Point Critical resistance R c and Voltage V GC

Gate voltage driven Quantum Phase Transition ■ Critical exponents ■ Finite size scaling analysis z ν ≈ 3/2 ➨ also observed in LSCO Bollinger et al, Nature 2011 ■ Scaling function and parameters ➨ if z = 1, ν = 3/2 ( − 1 ) ⎛ ⎞ R S = F V G − VGc ⎛ ⎞ z ν t = T ⎜ ⎟ ➨ not classical ( ν = 4/3 ) nor ⎜ ⎟ ⎜ ⎟ R c T z ν T 0 ⎝ ⎠ ⎝ ⎠ quantum ( ν = 7/4) percolation ➨ possible electronic phase separation

Scaling for different magnetic fields ■ Conventional scaling 1.2 B = 50 mT 1.1 1.2 B = 100 mT B=50mT B=100mT 1.0 0.2 0.18 1.0 0.9 0.16 0.2 0.14 0.18 0.12 0.8 0.16 0.14 R/Rc R/Rc 0.1 0.12 0.8 0.7 T(K) 0.08 0.1 zn~4.3 T(K) 0.08 0.06 z ν = 4.3 0.6 0.06 z ν = 5.5 zn~ 5.5 0.6 0.04 0.5 0.04 0.75 0.8 0.85 0.9 0.95 1 0.4 0.8 1 t t 0.4 1 10 1 10 (Vg-Vgc)t (Vg-Vgc)t ■ Problems ➨ z ν varies with magnetic field ➨ Difficult to extract a single z ν value

Quantum Griffiths phase transition ■ Recent results in magnetic field driven transition Thin Ga films ZrNCl films MoS 2 films Ying Xing et al. Science (2015) Saito et al, Nat Com 2018 LAO / STO InOx films Pb films Lewellyn et al, arXiv 2018 Ying Xing et al. PRB (2016) Liu et al, arXiv 2018

Quantum Griffiths Phase ■ Rare events and the Griffiths phase Vojta AIP Proceedings (2013) Classical Quantum Mixing FM & non FM Random transverse field Ising chain ■ Smeared transition Hoyos et al PRL (2007) − νψ ■ Critical exponents vary : infinite randomness z ' ≈ V G − V GC

Griffiths Phases ■ Magnetic systems ■ Biological systems Ubaid-Kassis et al PRL (2010) ■ Superconducting systems