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Andreev reflection at the CeCoIn 5 Heavy Fermion Superconductor Interface

Andreev reflection at the CeCoIn 5 Heavy Fermion Superconductor Interface. Wan Kyu Park and Laura H. Greene UIUC John L. Sarrao and Joe D. Thompson LANL Theoretical support: Justin E. Elenewski UIUC, Greene group Vladimir Lukic UIUC, Leggett group Anthony J. Leggett UIUC

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Andreev reflection at the CeCoIn 5 Heavy Fermion Superconductor Interface

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  1. Andreev reflection at the CeCoIn5Heavy Fermion Superconductor Interface Wan Kyu ParkandLaura H. GreeneUIUC John L. Sarrao and Joe D. Thompson LANL Theoretical support: Justin E. Elenewski UIUC, Greene group Vladimir Lukic UIUC, Leggett group Anthony J. Leggett UIUC David Pines LANL & UIUC Experimental support Karen Parkinson UIUC, Undergraduate Thesis Student Caitlin Jo Ramsey UIUC, Undergraduate B. Florian Wilken UIUC, German exchange student, 03-04 Alex N. Thaler UIUC, REU 2003 Patrick J. Hentges UIUC, PhD, 2004, now at Intel William L. Feldman UIUC, Lab Tech, retired 2003 Funding support: US DoE, DEFG02-91ER45439 through FSMRL and CMM RTS Workshop, June 10-11, 2005, Notre Dame, IN

  2. Conditions ~10ms after Big Bang: • 10 GeV/fm3 or ~1016gm/cm3 • T ~ 170 MeV or ~ 2 x 1012 K Same physics as superconductivity, (strongly-correlated electron systems) but 1016 different in energy !

  3. Outline • Definition of Issues • Andreev reflection between a heavy-fermion superconductor (HFS) and a normal (N) metal: • Point Contact Spectroscopy (PCS): • The HF superconductor CeCoIn5 • Some Basics of Andreev Reflection and PCS • Experiment: Cantilever-Andreev-Tunneling (CAT) • Data & Analysis (extended BTK model) • Known theories cannot explain AR at the N/HFS interface: • Some analysis consistent with d-wave and strong-coupling • New data on (110) may show spectroscopic evidence for d-wave • Conclusions

  4. Definition of the issues 1. Understanding charge transport across HF interface Existing models cannot account for Andreev reflection at the HFS/N interface 2. Spectroscopic studies of CeCoIn5 (OP symmetry, mechanism, etc.,…)

  5. The Heavy-Fermion Superconductor CeCoIn5 C. Petrovic et al., J. Phys.: Condens. Matter 13, L337 (2001)

  6. Tc = 2.3K (record high for HFS) • 0ab = 82Å, 0c = 53Å, ab ~ 1900Å, c ~ 2700Å, Hc2ab(0) = 12T, Hc2c(0) = 5T • Superconductivity in clean limit (l >> 0, l = 810Å) • Non-Fermi liquid:  ~ T 1.0 ± 0.1, Cen / T ~ -lnT, 1 / T1T ~ T –3/4 • Heavy-fermion liquid - n = Cen / T = 0.35J/mol K2,  meff = 83m0“heavy-fermion” • -(0) ~ 10 -2 emu/mol • - ( - 0) / T 2~ 0.1cm/K2 (under high pressure) • - Transition from Kondo impurity fluid to coherent heavy electron fluid at T * • TK ~ 1.7K (single ion Kondo temperature) • T * ~ 45K (intersite coupling energy of Kondo lattice) • CEF splitting~120K (Nakatsuji, Pines, Fisk, PRL 92, 016401 (2004)) • Anisotropic type-II superconductor • d-wave pairing symmetry? (Spectroscopic evidence is still lacking) • FFLO phase transition?- Power-law dependence: Cen / T ~ T,  ~ T 3.37, 1/T1 ~ T 3+,  ~ T 1.5

  7. Layered-tetragonal Crystal Structure Quasi-2D Fermi Surfaces T = Co, Rh, Ir a = 4.62Å, c = 7.55Å, c/a = 1.63 H. Shishido et al., JPSJ. 71, 162 (2002) Ce

  8. ANDREEV REFLECTION (no insulator): Normal Metal/Superconductor (N/S) In N: Electrons retro-reflected as holes e In S: Cooper Pairs Broken near interface h+ NS Probability of finding Cooper Pairs Pair Breaking N S

  9. Δ(few mV) ≈ ≈ Energy Scales for Andreev Reflection E EF (few V) N S k Particle conversion process that conserves charge, energy and momentum!

  10. Probabilities Blonder-Tinkham-Klapwijk (BTK) Model for charge transport across the N/S interfacePRB 25, 4515 (1982)Assumes (among other things) Ballistic transport A : Andreev reflection B : Normal reflection C : Transmission without branch- crossing (electron-like) D : Transmission with branch- crossing (hole-like) A(E)+B(E)+C(E)+D(E)=1

  11. s-wave BTK Conductance • Describes transitional behavior from AR to tunneling • Effective barrier strength

  12. Extended BTK theory S. Kashiwaya et al., PRB 53, 2667 (1996)

  13. d-wave BTK Conductance along c-axis

  14. BTK model has worked well for a wide range of materials, but NOT for HFS/N interfaces: The Fermi velocity mismatch is so great at the HFS/N interface that Andreev reflection (AR) should never occur(Z>5, extreme tunneling limit). Recall the effective barrier strength: However, AR is routinely measured at the N/HFS interface (many reports), albeit suppressed.

  15. Our Experiment: Cantilever-Andreev-Tunneling (CAT) rig Gold tip - sharpened by electrochemical etching CeCoIn5 single crystal - c-axis oriented - etch-cleaned using H3PO4 Coarse approach - done before inserting probe Fine approach - done during cool down - piezo driven by computer control Operation range - Temperature : down to 300mK - Magnetic Field : up to 12T

  16. Basics of PCS: Contact Regimes Length scales 2a: contact size lel: elastic mean free path lin: inelastic mean free path x: coherence length For our experiment: * Upper limit of 2a = 46 nm * lel at Tc= is 81 nm (from thermal conductivity), and increases with decreasing T, to 4-5 µm at 400mK. Therefore, our experiments are in the ballistic, Sharvin Limit, required for good spectroscopy

  17. DATA: Dynamic Conductance of Au/CeCoIn5 Background develops an asymmetry at the heavy-fermion liquid coherence temperature, T* ~45 K, gradually increasing with decreasing temperature to the onset of superconducting coherence, Tc=2.3 K. T* Tc

  18. Background Normalization Normalization by dividing each G-V data by normal state (2.6K) G-V data

  19. s-wave fit Z=0.346 Strong Coupling Γ(T)Δ(T) BUT: Decreasing  with decreasing T: Not physically meaningful

  20. d-wave fit Fitting Parameters s-wave d-wave Z 0.346 0.215 (eV) 384 460 (eV) 305 220  strong coupling BUT AGAIN, decreasing  with decreasing T (like s-wave case): So again, Not physically meaningful

  21. Zero-bias Conductance Fit (one point) Fitting Parameters s-wave d-wave Z 0.346 0.365 D D(0) = 349 meV, D(T): BCS energy gap D(T, f) = D(T)cos(2f), D(T) = 2.35kBTc x tanh(2.06(Tc/T-1)1/2) G G(t) = 0.86D(0) x (1-t3/3) 218 meV Constant Γ : Supportive of d-wave pairing symmetry, consistent with literature

  22. Similar AR magnitudes: Common in N/HFS G. Goll et al., PRL 70, 2008 (1993) URu2Si2-Pt Yu. G. Naidyukv et al., Europhys Lett. 33, 557 (95).

  23. VERY NEW DATA: PCS on 110-orientation: Spectroscopic proof of d-wave ??? (work in progress):

  24. Temperature Dependence: Can normalize as the c-axis data

  25. Note magnitude of Andreev signal is the SAME as for the (001) PCS! This supports:A) Intrinsic property (reproducibility indicates not a “barrier” effect)B) Sharvin limit Shape supports d-wave: May be 1st spectroscopic evidence.

  26. BTK Conductance: s-wave vs. d-wavework in progress… s-wave d-wave: ab-plane d-wave: c-axis a = /4

  27. Models which address the observation of AR at HFS/N Interface 3-Dimensional System 1. Deutscher and Nozières, PRB 50, 13577 (1994) From PCS of N/HFS, it has been common to obtain conductance curves corresponding to low Zeff value. Deutscher and Nozières’ argument: “The boundary condition at the interface involves Fermi velocities without mass-enhancement factors.” 2. N. A. Mortensen et al., PRB 59, 10176 (2000) Mismatch of Fermi Momenta combined with the two-fluid model of Nakatsuji, Pines & Fisk causes strong effect on tunneling cone. Zeff must be calculated for each component. This effect can explain ZBC normalized to normal state conductance, but not to high-bias conductance.

  28. Breakdown of the Andreev Approximation 3. A. Golubov and F. Tafuri, PRB 62, 15200 (2000) • Retro-reflection whenever D << EF (Andreev approximation). • If D/EF is non-negligible, the hole does not trace back the electron trajectory exactly (breakdown of Andreev approx.).

  29. Energy-Dependent QP Lifetime HT HL HR eV 2D S N 4. F. B. Anders and K. Gloos, Physica B 230-232 437 (1997) • Causes a reduction in gap energy (renormalization due to the strongly reduced QP spectral weight) • Causes asymmetry: with the emergence of coherent heavy quasi-particles

  30. Conclusions Clean dynamic conductance data are measured between 60 K and 400 mK across HFS/N (CeCoIn5/Au) nano-scale junctions Careful investigations show the contact is in the Sharvin limit. Existing models cannot adequately describe the particle-hole Andreev conversion process at the HFS/N interface. The low-temperature (400mK) conductance curve is consistent with strong coupling and the temperature-dependence of a single point, the zero-bias conductance, is consistent with a d-wave order parameter symmetry, both conclusions consistent with the literature for CeCoIn5. We propose that systematic corrections to the BTK model that go beyond the breakdown of the Andreev approximation and re-normalized Fermi momenta may provide a framework for our future understanding of Andreev reflection at the N/HFS interface. Recent (110) data may be spectroscopic evidence for d-wave

  31. Biscuits

  32. Is the Contact in Sharvin Limit? Thermal Conductivity R. Movshovich et al., PRL 86, 5152 (2001) Scattering Rate from Microwave Conductivity R. Ormeno et al., PRL 88, 047005 (2002) • Contact Size, d O ~ 500 Å using Wexler’s formula with RN=R0(1+Z2), RN ~ 1 , Z ~ 0.35, Tc ~ 3.1 cm • 0 ~ 82Å • lel ~ 4-5 mm, lin ~0.65 mm @400mK • 0 < d<<lel, lin  Contact is ballistic, even if considering reduced l in point contact

  33. How can we explain the background conductance? • f(T) = f(0)(1-T/T*), T* ~ 45 K Kondo impurity fluid  Coherent heavy-fermion fluid Saturating to 0.9 below ~ 2K • Enhanced asymmetry due to DOS change (shift of spectral weight toward Fermi energy) with increasing HF fluid? • Particle-hole asymmetry due to different kinetic energies in HFL? • “The pseudo-gap at T*, arising from the formation of the heavy quasi-particles in the coherent state, asymmetrically increases the resistance of the contact.” (K. Gloos et al., JLTP 105,37 (1996)) Relative weight of HF fluid Nakatsuji, Pines, Fisk, PRL 92, 016401 (2004)

  34. Heating Effect? • Local minima not intrinsic but caused due to incomplete match of BC • No minima in un-normalized data • No heating effect due to non-ballistic contact Sharvin contact!

  35. Non-Ballistic Point Contact Properties of Heavy-Fermion Superconductors HFS Tc(K) m*/m0 r0 (mWcm) l (Å) x(Å) l/ x URu2Si2 1.20 140 11 440 75//a, 130//c ~ 6 UBe13 0.87 260 43 165 95 ~ 2 UPt3 0.48 180 0.27//c 0.45//b 1600 120//a,b 140//c ~ 13 UNi2Al3 1 48 30 470 190 ~ 2 UPd2Al3 2 66 3.5, 36.3 720 77 ~ 10 CeCu2Si2 0.5 380 1.5-65 270 90 3 CeCoIn5 2.3 83 3.1 810 82//a,b 53//c ~ 10 K. Gloos et al., JLTP 105, 37 (1996) dR = dRA + dRMAX In N/HFS point contact, Maxwell resistance dominates since the resistivity of HFS is large. CeCoIn5 has relatively small resistivity ( ~ 3.1 cm) and extremely long electron mean free path at low temperatures. Sharvin(ballistic) point contact could be formed

  36. The Four Questions Is the contact ballistic, diffusive, or thermal? (A: Ballistic: we have shown the Sharvin Limit) How can we explain the background conductance shape? We observe a change in asymmetry at T* What is the Pairing symmetry? (s-wave or d-wave) fit the data using extended BTK models Why is the enhancement of sub-gap conductance so small? (~13.3% @ 400mK, NOT 100% as in conventional SCs) explore various possibilities…

  37. Models to account for observaion of AR at HFS/’N Interface Deutscher and Nozières, PRB 50, 13577 (1994) From PCS of N/HFS, it has been common to obtain conductance curves corresponding to low Zeff value. Deutscher and Nozières’ argument: “The boundary condition at the interface involves Fermi velocities without mass-enhancement factors.”

  38. Quantum Critical Point & Phase Diagram Ce(Co,Rh,Ir)In5 P. G. Pagliuso et al., Physica B 312-313, 129 (2002) • Coexistence of AFM & SC • Similar to cuprates V. A. Sidorov et al., PRL 89, 157004 (2002)

  39. Calculated Resistance of Point-Contact Yu. G. Naidyuk and I. K. Yanson, J. Phys.: Condens. Matter 10, 8905 (1998) PCS in Sharvin limit - contact resistance independent of materials’ resistivities - in practical situation, heterogeneous contact  x <d < l1, l2

  40. Is the Contact in Sharvin Limit? Thermal Conductivity R. Movshovich et al., PRL 86, 5152 (2001) Scattering Rate from Microwave Conductivity R. Ormeno et al., PRL 88, 047005 (2002) • Contact Size, d O ~ 500 Å using Wexler’s formula with RN=R0(1+Z2), RN ~ 1 , Z ~ 0.35, Tc ~ 3.1 cm • 0 ~ 82Å • lel ~ 4-5 mm, lin ~0.65 mm @400mK • 0 < d<<lel, lin  Contact is ballistic, even if considering reduced l in point contact

  41. Andreev Reflection Thermal resistance of Sn in intermediate state A. F. Andreev, Sov. Phys. JETP 19, 1228 (1964)

  42. Bogoliubov-de Gennes Equations Excitations in a superconductor Assume m(x)=m, V(x)=0, D(x)=D Plane wave solutions Solving for E, u, v Four types of QP waves for given E (u0 > v0)

  43. Suggestions For Theoretical Study Successful model should explain the following experimental features. • Concomitance of asymmetry in background conductance with emergent heavy-fermion liquid • Suppressed Andreev reflection to quantify the full conductance curve • Possible shrinking(?) of the conductance curve The following issues need to be investigated carefully. • Mismatch in Fermi parameters: effective mass, momentum, velocity • Anisotropy: order parameter, layered structure, Fermi surface • Emergent heavy quasiparticles, two fluid model • Quasiparticle scattering rate in AR process across N/HFS interface • Length scales for electrostatic potential, order parameter, effective mass, etc., in terms of coherence lengths both in a normal metal and in a superconductor

  44. Mismatch of Fermi Momenta 3-Dimensional System N. A. Mortensen et al., PRB 59, 10176 (2000) • This effect can explain the suppression of ZBC normalized to normal state conductance, but not to high-bias conductance. • If the superconductor is inhomogeneous as in the two-fluid model (Nakatsuji, Pines & Fisk), we can define different Zeff for each component. We’re exploring this possibility.

  45. Breakdown of Andreev Approximation Ratio of Gap Energy to Fermi Energy of Superconductors SC type Example Tc(K) (meV) EF(eV) /EF (%) Elemental Al 1.18 0.175 11.7 0.015 Pb 7.20 1.35 9.47 0.14 Nb 9.25 1.5 5.32 0.28 5 0.4-0.6 Two-band MgB2  39 2.4 7.0 0.5 1.2 – 1.8 ~ 1 Cuprate YBCO 90 20 ~ 2.0 HFS CeCoIn5 2.3 0.46 ~ 0.022 ~ 2.1 Layered N / isotropic S A. Golubov and F. Tafuri, PRB 62, 15200 (2000) • Retroreflection whenever D << EF (Andreev approximation). • If D/EF is non-negligible, the hole does not trace back the electron trajectory exactly (breakdown of Andreev approx.). • This happens in layered structures, too.

  46. d-wave BTK Conductance along ab-plane along c-axis a = /4

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