Orbital Aspect of IronBased Superconductors WeiCheng Lee Department

Orbital Aspect of Iron-Based Superconductors Wei-Cheng Lee Department of Physics University of Illinois at Urbana-Champaign

More is Different Statistics !!! Degrees of freedom to specify a single electron Momentum k Brillouin zone Fermi surface Spin Magnetism Superconductivity Orbital ? Topological Insulator

d Orbitals

Crystal Field Effect d orbitals atom cubic symmetry (a=b=c) tetragonal symmetry (a=b≠c)

Chronicle of Superconductor Copper age Iron age

Iron Age of Superhero (2008)

Introduction to Iron Pnictides – Crystal Structure Ba(Fe. As)2 K, Sr, Ca P Co, Ni, Rh, Pd, Ir, Pt, Ru Fe-As layer is responsible for the most electronic properties.

Introduction to Iron Pnictides – Phase Diagram Doping-induced superconductivity Structural transition from tetragonal to orthorhombic symmetry Magnetic transition to an antiferromagnetic order with a wave vector of (p, 0) electron doping AFM/O: antiferromagnetism with orthorhombic distortion (anisotropy) SDW: spin density wave SC: superconductivity

Introduction to Iron Pnictides – Fermi Surfaces All d orbitals of Fe ions are active. Multiple Fermi surfaces due to the multiorbital structure.

Fermi Surface in dxz-dyz Model Fermi Surface in 2 D 1 st Brillouin Zone Hybridized New eigen basis has internal d-wave like form factor.

Effect of Orbital Order Breaking the degeneracy between dxz and dyz Orbital order = elongation of Fermi surface along one direction = nematic order anisotropy

Structural Phase Transition Interpreted as Orbital Order OR W. Lv, J. Wu, and P. Phillips, Phys. Rev. B 80, 224506

Quasiparticle Interferences in the Spectroscopic Imaging STM (SI-STM) FT, eiqr ry rx q qy qx

Unique Signatures of Quasiparticle interferences in Quasi-1 D Bands Fermi Surface QPI l Ideal quasi-1 D bands – Stripelike features l Hybridized quasi-1 D bands – Stripe-like feature remains because of symmetry!! Wei-Cheng Lee, Congjun Wu, Phys. Rev. Lett. 103, 176101 (2009)

SI-STM on Iron Pnictide Ca(Fe 1 -x. Cox)2 As 2 below Structural Phase Transition Chuang et. al. , Science 327, 181 (2010) W. -C. Lee and C. Wu, PRL 103, 176101 (2009)

Effect of fluctuations on single particle properties Review of quantum nematic fluid

Pomeranchuk Instabilities L. Landau I. Pomeranchuk Fermi Surface The phase with spontaneously elongation of the Fermi surface along one direction is the nematic order.

d-wave Landau interaction F 2 in dxz-dyz Model

Density Fluctuation Spectrum of the Quantum Nematic Liquid Quantum nematic fluid Fermi liquid Fermi surface Plasmon mode Overdamped z=3 collective mode at low momentum and frequency Non-Fermi Liquid (Hertz-Millis theory)

Emergence of Overdamped Collective Modes in Itinerant Systems Quantum nematicity (orbital order) rotational symmetry is broken but tranlational invariance remains instability at q=0 Particle-hole continuum J. A. Hertz, Phys. Rev. B 14, 1165 (1976); A. J. Millis, Phys. Rev. B 48, 7183 (1993)

Scattering Rate of the Fermi Liquid Phase space argument Fermi surface

Non-Fermi Liquid!!!

Multiorbital Hubbard Model

z=3 Overdamped Mode in Two-Orbital Model at Orbital Ordering QCP Patches for multidimensional bosonization Ka Wai Lo, Wei-Cheng Lee, and Philip W. Phillips, Europhys. Lett. 101, 50007 (2013).

RPA Study of a Five-band Model l Two-particle correlation function l Correction to electron self energy l Spectral function: Wei-Cheng Lee, and Philip W. Phillips, Phys. Rev. B 86, 245113

Self-Energy with One Loop Corrections Orbital fluctuation spectrum

Point Contact Spectroscopy For small voltage bias, For weakly interacting systems (e. g. , metal) Wei-Cheng Lee, et. al. , to be submitted.

Point Contact Specoscopy on Ba(Fe 1 -x. Cox)2 As 2 Novel enhancement conductance at zero bias below a temperature Tonset Zero bias enhancement exists in the shaded region. H. Z. Arham, et. al. , Phys. Rev. B 85, 214515 (2012)

Point Contact Specoscopy peaked at w=0!!! (Lawler, et al. , Phys. Rev. B 73, 085101 (2006))

Effect of orbital fluctuations on spin excitation spectra

Incommensurate-to-Commensurate Transformation in Fe 1 -x. Nix. Te 0. 5 Se 0. 5 Z. Xu, et. al. , Phys. Rev. Lett. 109, 227002 (2012)

Spin Excitation Spectra in Itinerant Model Fermi surfaces for doping=0. 125 Corresponding spin excitation in normal state Maier, et al. , Phys. Rev. B 79, 134520 (2009)

Our Theory True normal state Fluctuating orbital order (modeled by Gaussian fluctuation model) Orbital ordered state Wei-Cheng Lee, W. Lv, J. Tranquada, and P. Phillips, Phys. Rev. B 86, 094516 (2012)

Conclusion tetragonal symmetry (a=b≠c) Orbital order (structural phase transition) Non-Fermi liquid behavior Orbital fluctuations Change of the nature of the spin excitation Orbital-dependent Fermi surface

Ongoing Work l Can we detect the orbital/nematic fluctuations directly? ¡Neutron Scattering Measurement (with John Tranquada) ¡Raman Scattering (with L. Cooper) ¡Electron Energy Loss Spectroscopy (EELS, with Peter Abbamonte)

Collaborators Theorists Philip W. Phillips Weicheng Lv Ka Wai Lo Experimentalists Laura H. Greene Hamood Z. Arham John M. Tranquada Wan Kyu Park