WeiCheng Lee Department of Physics University of Illinois at UrbanaChampaign More is Different Statistics Degrees of freedom to specify a single electron Spin Orbital Magnetism Superconductivity ID: 778697
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Slide1
Orbital Aspect of Iron-Based Superconductors
Wei-Cheng LeeDepartment of PhysicsUniversity of Illinois at Urbana-Champaign
Slide2Slide3More is Different
Statistics !!!
Degrees of freedom to specify a single electron
Spin
Orbital?
Magnetism
Superconductivity
Topological
Insulator
Momentum
k
Brillouin zone
Fermi surface
Slide4Slide5d Orbitals
Slide6Crystal Field Effect
atom
d
orbitals
cubic symmetry (a=b=c)
tetragonal symmetry (a=b
≠c)
Slide7Copper age (1986)
Iron age (2008)
Chronicle of Superconductor
Slide8Iron Age of Superhero (2008)
Slide9Introduction to Iron Pnictides – Crystal Structure
Fe-As layer is responsible for the most electronic properties.
Co, Ni, Rh, Pd,
Ir
,
Pt
,
Ru
P
K,
Sr
, Ca
Ba(FeAs)
2
Slide10Introduction to Iron Pnictides – Phase Diagram
Doping-induced superconductivity
electron doping
SDW: spin density wave
SC: superconductivity
AFM/O: antiferromagnetism with orthorhombic distortion (anisotropy)
Structural transition
from tetragonal to orthorhombic symmetry
Magnetic transition
to an antiferromagnetic order with a wave vector of (
p
,0)
Slide11Introduction to Iron Pnictides – Fermi Surfaces
All
d
orbitals of Fe ions are active.
Multiple Fermi surfaces due to the multiorbital structure.
Slide12Fermi Surface in dxz
-dyz Model
New eigen basis has internal
d
-wave like form factor.
Fermi Surface in 2D 1
st
Brillouin Zone
Hybridized
Slide13Effect of Orbital Order
Breaking the degeneracy between
d
xz
and
d
yz
Orbital order = elongation of Fermi surface along one direction = nematic order
anisotropy
Slide14Structural Phase Transition Interpreted as Orbital Order
OR
W. Lv, J. Wu, and P. Phillips, Phys. Rev. B
80
, 224506 (2009)
Slide15Quasiparticle Interferences in the Spectroscopic Imaging STM (SI-STM)
r
x
r
y
FT,
e
iqr
q
x
q
y
q
Slide16Unique Signatures of Quasiparticle interferences in Quasi-1D Bands
Ideal quasi-1D bands – Stripe-like features
Hybridized quasi-1D bands – Stripe-like feature remains because of symmetry!!
Wei-Cheng Lee, Congjun Wu, Phys. Rev. Lett.
103
, 176101 (2009)
Fermi Surface
QPI
Slide17SI-STM on Iron Pnictide Ca(Fe1-x
Cox)2As2 below Structural Phase Transition
Chuang et. al., Science
327
, 181 (2010)
W.-C. Lee and C. Wu,
PRL
103
, 176101 (2009)
Slide18Review of quantum nematic fluid
Effect of fluctuations on single particle properties
Slide19Pomeranchuk Instabilities
L. Landau
I. Pomeranchuk
Fermi Surface
The phase with spontaneously elongation of the Fermi surface along one direction is the
nematic order
.
Slide20d-wave Landau interaction
F2 in
dxz-dyz
Model
Slide21Density Fluctuation Spectrum of the Quantum Nematic Liquid
Fermi liquid
Quantum nematic fluid
Fermi surface
Plasmon mode
Overdamped z=3 collective mode at low momentum and frequency
Non-Fermi Liquid (Hertz-Millis theory)
Slide22Particle-hole continuum
Emergence of Overdamped Collective Modes in Itinerant Systems
J. A. Hertz, Phys. Rev. B
14
, 1165 (1976); A. J. Millis, Phys. Rev. B
48
, 7183 (1993)
Quantum nematicity (orbital order)
rotational symmetry is broken but tranlational invariance remainsinstability at
q=0
Slide23Scattering Rate of the Fermi Liquid
Phase space argument
Fermi surface
Slide24Non-Fermi Liquid!!!
Slide25Multiorbital Hubbard Model
Slide26z=3 Overdamped Mode in Two-Orbital Model at Orbital Ordering QCP
Ka Wai Lo, Wei-Cheng Lee, and Philip W. Phillips, Europhys. Lett.
101
, 50007 (2013).
Patches for multidimensional bosonization
Slide27RPA Study of a Five-band Model
Two-particle correlation functionCorrection to electron self energy
Spectral function:
Wei-Cheng Lee, and Philip W. Phillips,
Phys. Rev. B
86
, 245113 (2012)
Slide28Self-Energy with One Loop Corrections
Orbital fluctuation spectrum
Slide29Point Contact Spectroscopy
For weakly interacting systems (e.g., metal)
For small voltage bias,
Wei-Cheng Lee,
et. al.,
to be submitted.
Slide30Point Contact Specoscopy on Ba(Fe1-x
Cox)2As2
H.Z.
Arham
, et. al., Phys. Rev. B
85
, 214515 (2012)
Novel enhancement conductance at zero bias below a temperature T
onset
Zero bias enhancement exists in the shaded region.
Slide31Point Contact Specoscopy
(Lawler, et al., Phys. Rev. B
73
, 085101 (2006))
peaked at
w
=0!!!
Slide32Effect of orbital fluctuations on spin excitation spectra
Slide33Incommensurate-to-Commensurate Transformation in Fe1-x
NixTe0.5Se0.5
Z. Xu,
et. al.
,
Phys. Rev.
Lett
.
109
, 227002
(
2012)
Slide34Spin Excitation Spectra in Itinerant Model
Maier, et al., Phys. Rev. B
79
, 134520 (2009)
Fermi surfaces for doping=0.125
Corresponding spin excitation in normal state
Slide35Our Theory
Wei-Cheng Lee, W. Lv, J. Tranquada, and P. Phillips, Phys. Rev. B
86
, 094516 (2012)
True normal state
Orbital ordered state
Fluctuating orbital order (modeled by Gaussian fluctuation model)
Slide36Conclusion
tetragonal symmetry (a=b
≠c)
Orbital fluctuations
Orbital order (structural phase transition)
Non-Fermi liquid behavior
Change of the nature of the spin excitation
Orbital-dependent Fermi surface
Slide37Ongoing Work
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)
Slide38Collaborators
Theorists
Experimentalists
Philip W. Phillips
Laura H. Greene
Weicheng Lv
Ka Wai Lo
Hamood Z. Arham
Wan Kyu Park
John M. Tranquada