IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. Real space imaging of the superconducting vortex lattice: Recent results and prospects Hermann Suderow Laboratorio de Bajas Temperaturas Departamento de Física de la Materia Condensada Instituto de Ciencia de Materiales Nicolás Cabrera Center for Condensed Matter Physics (IFIMAC) Universidad Autónoma de Madrid (UAM) 1
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. Real space imaging of the superconducting vortex lattice: Recent results and prospects • Real space imaging and spectroscopy of the vortex lattice • Superconducting CaKFe4As4, bandstructure, vortex core, vortex lattice and pinning • Vortex lattice structure: interactions vs disorder • Observation of vortex creep on cooling • Josephson effect at atomic scale 2
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. The birth of scanning probe microscopy The invention of the scanning tunneling microscope Gerd Binnig and Heini Rohrer, Zurich, 1982 A x , y 20 V 1Å ~ 250 mV Tunneling Piezoelectrics 3
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. Tunneling Conduction through constrictions Imaging superconducting vortex cores and lattices with a STM H. Suderow, I. Guillamón, J.G. Rodrigo and S. Vieira Superc. Sci. Techn., 27, 063001 (2014) 4
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. Tunneling Conduction through constrictions 3.0 2.5 2.0 G/G 0 1.5 1.0 0.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 z (nm) Imaging superconducting vortex cores and lattices with a STM H. Suderow, I. Guillamón, J.G. Rodrigo and S. Vieira Superc. Sci. Techn., 27, 063001 (2014) 5
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. Tunneling The tunneling current: Bardeen’s formalism 2 e 2 I f E 1 f E eV M E E Energy F p F m 1 f ( E ) μ +eV E E E F,T F k T 1 e B E F,S E ; vacuum tip sample d E ; Distance 2 * * M dS Tunnelling from a Many-Particle Point of View 2 m J. Bardeen PRL, 6, 57 (1961) Energy Energy Empty states Filled states E F,T tip E F,S E F,S E F,T tip sample sample Distance Distance 6
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. Tunneling The tunneling current: Tersoff-Haman Theory and Application for the Scanning Tunneling Microscope J. Tersoff and D. R. Hamann PRL, 50, 1998 (1983) Ideal tip, low bias voltage (V=0) : d 0 Rubén Pérez UAM 2 I d E E d , E 0 F 0 F STM: Contour map of the local DOS E eV F I r , V dE d , E T d , E , eV 0 S 0 0 E F 7
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. Tunneling The tunneling current: Chen Directional tunneling Microscopic (C p , k , , … ) Empty + filled states (ARPES, dHvA) Bandstructure (ARPES) Real space (neutrons, x-ray) E eV F I r , V dE d , E T d , E , eV 0 S 0 0 E F Energy Energy Empty states Filled states E F,T tip E F,S E F,S E F,T tip sample sample Distance Distance 8
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. Imaging Working in real space Random Hyperuniform Vortex lattice ? 9
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. Tunneling Superconductor Microscopic theory J. Bardeen, L. Cooper, J. Schrieffer (BCS, 1957) Cooper pairs i e S=0 L=0 k ' V ' 2 k kk E k ' k ' Kohn, Luttinger (1965) E 𝜁 𝑙 2 + Δ 2 S=1 L=1 k -k F k F e (k) e (k) 10
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. STM Tunneling 1.5 normalized conductance 1.0 0.5 MgB 2 0.0 -1 0 1 Normalized bias voltage Bardeen ’ s formalism 2 I d E E N d , E 0 F 0 F E N (E) dI f ( E eV ) S i The local density of states Δ 2 2 E (k) N ( E ) dE i i dV V P. Martínez-Samper et al. Physica C 2003 11
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. The superconducting gap through scanning tunneling spectroscopy at very low temperatures dI f ( E eV ) N ( E ) dE dV V MgB 2 YNi 2 B 2 C ErNi 2 B 2 C NbS 2 1.5 1.4 1.5 1.2 normalized conductance 1.0 Normalized conductance Normalized conductance 1.0 1.0 0.8 0.5 0.6 0.5 0.4 MgB 2 ErNi 2 B 2 C 0.0 0.2 -1 0 1 T = 0.15 K T c =11K 0.0 Normalized bias voltage -3 -2 -1 0 1 2 3 0.0 -4 -3 -2 -1 0 1 2 3 4 Bias voltage (mV) Bias voltage (mV) NbSe 2 Uemura plot 2.5 2.0 Normalized conductance 2.0 1.5 Normalized conductance 100 1.5 1.0 Critical temperature T c MgB 2 0.5 1.0 PrOs 4 Sb 12 T c =1.85 K LuNi 2 B 2 C 0.0 0.5 -2 -1 0 1 2 Bias voltage / 0 ( = 1.73k B T c ) 10 NbSe 2 Elements 0.0 2.5 -3 -2 -1 0 1 2 3 T = 150 mK 200 G Bias voltage (mV) = 0.28 meV TaS 2 PrOs 4 Sb 12 Multiband 2.0 2.0 Normalized conductance 2H-TaS 2 Normalized conductance 1 1.5 1.5 Sr 2 RuO 4 TaS 2 Al 1.0 1.0 UPt 3 0.5 0.5 0.1 T = 0.1 K Sr 2 RuO 4 0.0 10 100 1000 10000 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 Voltage (mV) 0.0 -1.2 -0.9 -0.6 -0.3 0.0 0.3 0.6 0.9 1.2 Fermi temperature T F Bias voltage (mV) Madrid 12
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. Can we find atomic resolution in a metal ? Atomic resolution STM Quasiparticle interference Electronic standing waves 30 Height (pm) 20 10 0 0 1 2 3 4 5 6 Lateral Position (nm) 𝜍 𝑠 = 𝑑𝑝𝑡 2𝑙 𝐺 𝑠 𝑠 3 1.3nm Here: URu 2 Si 2 at 150 mK 2 I d E E N d , E 0 F 0 F l F a 13
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. Atomic resolution 1,5 1,5 2 2 2 2 Normalized conductance Normalized conductance 1,0 1,0 2 1 2 1 0,5 0,5 0,0 0,0 -15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 Bias voltage (mV) Bias voltage (mV) i i Δ i (k) Δ i (k) E N (E) S i Δ 2 2 E (k) i i K. Cho et al Phys Rev B, 95, 100502(R) (2017) 14
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. Can we find atomic resolution in a metal ? STM Atomic resolution Quasiparticle interference Electronic standing waves 30 Height (pm) 20 10 0 0 1 2 3 4 5 6 Lateral Position (nm) 𝜍 𝑠 = 𝑑𝑝𝑡 2𝑙 𝐺 𝑠 𝑠 3 1.3nm Here: URu 2 Si 2 at 150 mK 2 I d E E N d , E 0 F 0 F l F a 15
IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), February 2020. Plenary presentation PL1-INV given at ISS, 3-5 December 2019, Kyoto, Japan. QPI Quasiparticle interference Bandstructure of empty and filled states Real space conductance map Fourier transform Energy, bias voltage 2k F E F Wavevector Fermi surface Real space DOS Fermi surface Real space DOS 2k F ½ l F Direct imaging of the two-dimensional Fermi contour: Fourier-transform STM L. Petersen et al. Phys. Rev. B, R6858, 57 (1998) A phenomenological approach of joint density of states for the determination of bandstructure in the case of a semi-metal studied by FT-STS L. Simon, F. Vonau and D. Aubel J. Phys. Cond. Matt. 19 (2007) 355009 16
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