Spin or Orbital-based Physics in the Fe-based Superconductors? W. Lv, W. Lee, F. Kruger, Z. Leong, J. Tranquada. Thanks to: DOE (EFRC)+BNL

Spin or Orbital-based Physics in the Fe-based Superconductors? W. Lv, W. Lee, F. Kruger, Z. Leong, J. Tranquada Thanks to: DOE (EFRC)+BNL

Spin or Orbital-based Physics in the Fe-based Superconductors? W. Lv, W. Lee, F. Kruger, Z. Leong, J. Tranquada Thanks to: DOE (EFRC)+BNL ` =2

What is new with Fe-based superconductors?

What is new with Fe-based superconductors? d 6 not d 9

What is new with Fe-based superconductors? multi-orbital physics d 6 not d 9

What is new with Fe-based superconductors? multi-orbital physics d 6 not d 9 d orbitals atom cubic symmetry (a=b=c) tetragonal symmetry (a=b c)

Who is in the Driver s Seat?

Who is in the Driver s Seat? orbital order F. Krüger, et al. PRB (2009) R.R.P. Singh, arxiv:0903.4408 W. Lv, et al. PRB (2009) A.M. Turner, et al. PRB (2009) C.-C. Lee, et al. PRL (2009)

Who is in the Driver s Seat? orbital order spin order F. Krüger, et al. PRB (2009) R.R.P. Singh, arxiv:0903.4408 W. Lv, et al. PRB (2009) A.M. Turner, et al. PRB (2009) C.-C. Lee, et al. PRL (2009) C. Fang, et al. PRB (2008) C. Xu, et al. PRB (2008) P. Chandra, et al. PRL (1990) Nematic order in iron superconductors - who is in the driver's seat? R. M. Fernandes, A. V. Chubukov, J. Schmalian

Why Do I care?

Why Do I care? cuprates d 9 no orbital degree of freedom

Why Do I care? cuprates d 9 no orbital pnictides d 6 orbital degeneracy degree of freedom

Why Do I care? cuprates d 9 no orbital pnictides d 6 orbital degeneracy degree of freedom is the orbital degree of freedom important?

subtle problem O(3) Z 2

subtle problem O(3) Z 2 (, 0), (0, )

subtle problem O(3) Z 2 (, 0), (0, ) h h 2 yi = h 2 yi 6= h xi} 2 magnetic 2 fluctuations

subtle problem O(3) Z 2 (, 0), (0, ) h h 2 yi = h 2 yi 6= h xi} 2 magnetic 2 fluctuations h yi = h xi structural transition hn xz i6= hn yz i }nematic magnetism h yi 6= h xi

subtle problem O(3) Z 2 orbitals d xz,d yz (, 0), (0, ) h h 2 yi = h 2 yi 6= h xi} 2 magnetic 2 fluctuations h yi = h xi structural transition hn xz i6= hn yz i }nematic magnetism h yi 6= h xi

subtle problem O(3) Z 2 orbitals d xz,d yz hn 2 xzi = hn 2 yzi hn 2 xzi 6= hn 2 yzi hn xz i6= hn yz i (, 0), (0, ) h h 2 yi = h 2 yi 6= h xi} 2 magnetic 2 fluctuations h yi = h xi structural transition structural transition hn xz i6= hn yz i }nematic magnetism magnetism h yi 6= h xi

can this debate be settled? orbitals d xz,d yz spins (, 0), (0, )

Inelastic neutron scattering Experimental Puzzle 1? J. Zhao, et al. Nature Physics (2009) Why is the magnetism frustrated?

Experimental puzzle 2: What is the origin of the gap-like feature above the structural transition? H. Ahram, L. Greene,... (UIUC)

Nature 486, 382-385 (2012) origin? Matsuda, et al. Greene, et al.

Experimental puzzle 4: What is the origin of the incommensurate-commensurate transition incommensurate? commensurate something besides spin degree of freedom 11

Orbital Ordering t 2g only d_yz and d_xz break rotational symmetry in xy plane. e g 12

Orbital Ordering unequal occupancy of d xz and d yz drive the structural transition, magnetism,... t 2g only d_yz and d_xz break rotational symmetry in xy plane. e g 12

a) structural transition b) c) Lv, Wu, PP, 2009 13

a) structural transition Coulomb Repulsion: b) Energy Difference: c) Lv, Wu, PP, 2009 13

a) structural transition Coulomb Repulsion: b) Energy Difference: orbital ordering c) Lv, Wu, PP, 2009 13

SPT in Ising Universality Class H SPT = J SPT i,j M i M j M i = ±1, i = d yz, d xz 14

is the structural transition=nematic? 15

electron nematic is the structural transition=nematic? continuous symmetry breaking goldstone boson 15

electron nematic is the structural transition=nematic? pnictides C 4 T S continuous symmetry breaking goldstone boson C 2 no goldstone boson 15

no!

no! not really but this is not stopping anyone

SPT-induced Collinear AF

SPT-induced Collinear AF a) spin disordered

SPT-induced Collinear AF a) b) spin disordered

SPT-induced magnetism H SO = J SPT i,j M i M j + i,j J 2 (M i, M j ) S i S j + + i i J 1x (M i, M i+ˆx ) S i S i+ˆx J 1y (M i, M i+ŷ ) S i S i+ŷ J 1x (M i, M j ) = Mi,M j (J 1b Mi,1 + J 1a Mi, 1) J 1y (M i, M j ) = Mi,M j (J 1a Mi,1 + J 1b Mi, 1) J 2 (M i, M j ) = Mi,M j J 2 M i = ±1, i = d yz, d xz 122 Fe-Fe is shorter: J_{1b} is enhanced 18

Orbital-polarized Fermi surface in antiferromagnetic state of BaFe 2 As 2 Shimojima, et al. arxiv:0904.1632 Polarized ARPES

Orbital-polarized Fermi surface in antiferromagnetic state of BaFe 2 As 2 Shimojima, et al. arxiv:0904.1632 Polarized ARPES d xz in domain A d xz in domain B

minority spins majority spins (a) PM state: 1. d xz, d yz degenerate 2. Fermi surface is composed by multiple orbitals (b) AF state: 1. Localized moment is formed by d xz 2. Fermi surface is orbital-polarized

50 mev as in Na111 and Ba122 21

Inelastic neutron scattering Experimental Puzzle 1? J. Zhao, et al. Nature Physics (2009) Why is the magnetism frustrated?

Double-Exchange Model unlike manganites J H 23

answer: emergent ferro-orbital order from Hund coupling WL, FK, PP, Phys. Rev. B, vol. 82, p. 045125 (2010)

answer: emergent ferro-orbital order from Hund coupling WL, FK, PP, Phys. Rev. B, vol. 82, p. 045125 (2010) Comparison with experiments:

localized/extended electrons+hund s coupling unfrustrated magnetism, SPT, RA orbital ordering 25

high T paramagnetic state low T ordered state 26

high T paramagnetic state low T ordered state prediction: Landau damping increases as T increases Z. Leong, et al, PRB, xxx,2014 26

Experimental puzzle 2: What is the origin of the excess conductance above the structural transition? H. Ahram, L. Greene,... (UIUC)

Fermi surface in Brillouin zone 28

Fermi surface in Brillouin zone d xz mainly d yz mainly 28

Fermi surface in Brillouin zone d xz mainly d yz mainly on-site interaction anisotropic in hybridized basis 28

Fermi surface in Brillouin zone d xz mainly d yz mainly on-site interaction anisotropic in hybridized basis orbital ordering in multi-orbital system = nematic order 28

Multiorbital Hubbard Model Theoretical approaches: Multidimensional Bosonization for two-orbital model Generalized RPA for realistic five orbital model

z=3 Overdamped Mode in Two-Orbital Model at Orbital Ordering QCP Patches for multidimensional bosonization

Self-Energy with One Loop Corrections (2-band model) Text Wei-Cheng Lee, and Philip W. Phillips, Phys. Rev. B 86, 245113 (2012)

Self-Energy with One Loop Corrections (2-band model) Text possible ARPES experiment Wei-Cheng Lee, and Philip W. Phillips, Phys. Rev. B 86, 245113 (2012)

Self-Energy with One Loop Corrections (2-band model) Text possible ARPES experiment Lawler, et al., Phys. Rev. B 73, 085101 (2006) zero-bias anomaly Wei-Cheng Lee, and Philip W. Phillips, Phys. Rev. B 86, 245113 (2012)

resistivity anisotropy and NFL are linked prediction: no ZBC in holedoped pnictides! (future work)

Point Contact Spectroscopy Wei-Cheng Lee, et. al., submitted, PNAS.

Point Contact Spectroscopy Using Keldysh formalism, for small voltage bias, Wei-Cheng Lee, et. al., submitted, PNAS.

Point Contact Spectroscopy Using Keldysh formalism, for small voltage bias, For metals Wei-Cheng Lee, et. al., submitted, PNAS.

Point Contact Spectroscopy Using Keldysh formalism, for small voltage bias, For metals For non-fermi liquid due to nematic QCP, Wei-Cheng Lee, et. al., submitted, PNAS.

Point Contact Spectroscopy Using Keldysh formalism, for small voltage bias, For metals For non-fermi liquid due to nematic QCP, Wei-Cheng Lee, et. al., submitted, PNAS. a peak at ev=0!!! M. J. Lawler, et. al., Phys. Rev. B 73, 085101 (2006).

Incommensurate-to-Commensurate Transformation in Fe 1-x Ni x Te 0.5 Se 0.5 Non-superconducting - Incommensurate magnetic excitation all the time Z. Xu, et. al., Phys. Rev. Lett. 109, 227002 (2012)

Our Theory RPA + Gaussian Fluctuations normal state without orbital fluctuations Fluctuating orbital order (modeled by Gaussian fluctuation model) Orbital ordered state

magnetic transition enhanced ZBC orbital ordering incommensurate commensurate structural transition

magnetic transition enhanced ZBC orbital ordering incommensurate commensurate structural transition thanks to DOE (EFRC)

Routes to High-T_c CuFeTe_2, Li_xNi_{1-x}O_2,?FeSe?

Routes to High-T_c cuprates: one Cu spin Mott Physics CuFeTe_2, Li_xNi_{1-x}O_2,?FeSe?

Routes to High-T_c pnictides: several unapired Fe spins cuprates: one Cu spin Mott Physics bad metals CuFeTe_2, Li_xNi_{1-x}O_2,?FeSe?

Routes to High-T_c pnictides: several unapired Fe spins cuprates: one Cu spin Mott Physics bad metals are multi-orbital Mott systems higher T_c materials? CuFeTe_2, Li_xNi_{1-x}O_2,?FeSe?

Possible systems (multi-orbital Mott systems)? Simple complex (oxychalchogenides hole-doping a system. Does it superconduct? A= La, Y M=Se, S, Te Co and Cu- based 38