Prof. Dr. Maria Daghofer

My group works on lowdimensional and strongly correlated materials where
quantum mechanical effects play an important role. It is mostly funded
by the DFG (Deutsche Forschungsgemeinschaft) as an EmmyNoether Junior
Research Group with the topic "Spinorbital entanglement and dynamic properties of spinorbital systems".
Some of our research is described below.
If you are interested in joining the group as a student or postdoc,
please write me an email.
Journal papers
2016
E.M. Plotnikova, M. Daghofer, J. van den Brink, K. Wohlfeld: JahnTeller Effect in Systems with Strong OnSite SpinOrbit Coupling, Physical Review Letters 116 (2016) Nr. 10, S. 106401/15 URLI. Rousochatzakis, U.K. Roessler, J. van den Brink, M. Daghofer: Kitaev anisotropy induces mesoscopic Z_{2} vortex crystals in frustrated hexagonal antiferromagnets, Physical Review B 93 (2016) Nr. 10, S. 104417/116 URL
2015
W. Brzezicki, M. Daghofer, A.M. Oles: Hole Propagation in the Orbital Compass Models, Acta Physica Polonica A 127 (2015) Nr. 2, S. 263265 URL2014
V. Bisogni, S. Kourtis, C. Monney, K. Zhou, R. Kraus, C. Sekar, V. Strocov, B. Buechner, J. van den Brink, L. Braicovich, T. Schmitt, M. Daghofer, J. Geck: Femtosecond dynamics of momentumdependent magnetic excitations from resonant inelastic XRay scattering in CaCu2O3, Physical Review Letters 112 (2014), S. 147401/15 URLW. Brzezicki, M. Daghofer, A.M. Ole: Mechanism of hole propagation in the orbital compass models, Physical Review B 89 (2014) Nr. 2, S. 24417/111 URL
M. Daghofer, M. Hohenadler: Phases of correlated spinless fermions on the honeycomb lattice, Physical Review B 89 (2014) Nr. 3, S. 35103/13 URL
J. Kim, M. Daghofer, A.H. Said, T. Gog, J. van den Brink, G. Khaliullin, B.J. Kim: Excitonic quasiparticles in a spinorbit Mott insulator, nature communications 5 (2014), S. 4453/16 URL
2013
M. Daghofer, M. Haque: Viewpoint: Toward fractional quantum hall physics with cold atoms, Physics 6 (2013), S. 49/13 URL2012
M. Daghofer, A. Fischer: Breaking of fourfold lattice symmetry in a model for pnictide superconductors, Superconductor Science and Technology 25 (2012) Nr. 8, S. 84003/15 URLM. Daghofer, A. Nicholson, A. Moreo: Spectral density in a nematic state of iron pnictides, Physical Review B 85 (2012) Nr. 18, S. 184515/17 URL
T. Haenke, S. Sykora, R. Schlegel, D. Baumann, L. Harnagea, S. Wurmehl, M. Daghofer, B. Buechner, J. van den Brink, C. Hess: Probing the unconventional superconducting state of LiFeAs by quasiparticle interference, Physical Review Letters 108 (2012) Nr. 12, S. 127001/15 URL
M. Hohenadler, S. Wessel, M. Daghofer, F.F. Assaad: Interactionrange effects for fermions in one dimension, Physical Review B 85 (2012) Nr. 19, S. 195115/110 URL
J. Kim, D. Casa, M.H. Upton, T. Gog, Y.J. Kim, J.F. Mitchell, M. van Veenendaal, M. Daghofer, J. van den Brink, G. Khaliullin, B.J. Kim: Magnetic excitation spectra of Sr2IrO4 probed by resonant inelastic XRay scattering: Establishing links to cuprate superconductors, Physical Review Letters 108 (2012) Nr. 17, S. 177003/15 URL
J.W. Kim, Y. Choi, J. Kim, J.F. Mitchell, G. Jackeli, M. Daghofer, J. van den Brink, G. Khaliullin, B.J. Kim: Dimensionality driven spinflop transition in layered iridates, Physical Review Letters 109 (2012) Nr. 3, S. 37204/15 URL
J. Kim, A.H. Said, D. Casa, M.H. Upton, T. Gog, M. Daghofer, G. Jackeli, J. van den Brink, Khaliullin, G., B.J. Kim: Large spinwave energy gap in the bilayer iridate Sr3Ir2O7: Evidence for enhanced dipolar interactions near the mott metalinsulator transition, Physical Review Letters 109 (2012), S. 157402/15 URL
S. Kourtis, J. van den Brink, M. Daghofer: Exact diagonalization results for resonant inelastic xray scattering spectra of onedimensional Mott insulators, Physical Review B 85 (2012) Nr. 6, S. 64423/17 URL
S. Kourtis, J.W.F. Venderbos, M. Daghofer: Fractional chern insulator on a triangular lattice of strongly correlated t2g electrons, Physical Review B 86 (2012), S. 235118/114 URL
A. Nicholson, W. Ge, J. Riera, M. Daghofer, A. Moreo, E. Dagotto: Pairing symmetries of a holedoped extended twoorbital model for the pnictides, Physical Review B 85 (2012) Nr. 2, S. 24532/18 URL
J.W.F. Venderbos, S. Kourtis, J. van den Brink, M. Daghofer: Fractional quantumhall liquid spontaneously generated by strongly correlated t2g electrons, Physical Review Letters 108 (2012) Nr. 12, S. 126405/15 URL
J.W.F. Venderbos, M. Daghofer, J. van den Brink, S. Kumar: Switchable quantum anomalous hall state in a strongly frustrated lattice magnet, Physical Review Letters 109 (2012), S. 166405/15 URL
K. Wohlfeld, M. Daghofer, G. Khaliullin, J. van den Brink: Dispersion of orbital excitations in 2D quantum antiferromagnets, Journal of Physics: Conference Series 391 (2012) Nr. 1, S. 12168/14 URL
2011
P.M.R. Brydon, M. Daghofer, C. Timm, J. van den Brink: Theory of magnetism and triplet superconductivity in LiFeAs, Physical Review B 83 (2011) Nr. 6, S. 60501(R)/14 URLP.M.R. Brydon, M. Daghofer, C. Timm: Magnetic order in orbital models of the iron pnictides, Journal of Physics / Condensed Matter 23 (2011) Nr. 24, S. 246001/118 URL
S. Liang, M. Daghofer, S. Dong, C. Sen, E. Dagotto: Emergent dimensional reduction of the spin sector in a model for narrowband manganites, Physical Review B 84 (2011) Nr. 2, S. 24408/18 URL
A. Nicholson, W. Ge, X. Zhang, J. Riera, M. Daghofer, A.M. Oles, G.B. Martins, A. Moreo, E. Dagotto: Competing pairing symmetries in a generalized twoorbital model for the pnictide superconductors, Physical Review Letters 106 (2011) Nr. 21, S. 217002/14 URL
A. Nicholson, Q. Luo, W. Ge, J. Riera, M. Daghofer, G.B. Martins, A. Moreo, E. Dagotto: Role of degeneracy, hybridization, and nesting in the properties of multiorbital systems, Physical Review B 84 (2011) Nr. 9, S. 94519/113 URL
J.W.F. Venderbos, M. Daghofer, J. van den Brink, S. Kumar: Macroscopic degeneracy and emergent frustration in a honeycomb lattice magnet, Physical Review Letters 107 (2011) Nr. 7, S. 76405/14 URL
J.W.F. Venderbos, M. Daghofer, J. van den Brink: Narrowing of topological bands due to electronic orbital degrees of freedom, Physical Review Letters 107 (2011) Nr. 11, S. 116401/15 URL
K. Wohlfeld, M. Daghofer, A.M. Oles: Spinorbital physics for p orbitals in alkali RO2 hyperoxides: Generalization of the GoodenoughKanamori rules, epl 93 (2011) Nr. 2, S. 27001/16 URL
K. Wohlfeld, M. Daghofer, S. Nishimoto, G. Khaliullin, J. van den Brink: Intrinsic coupling of orbital excitations to spin fluctuations in mott insulators, Physical Review Letters 107 (2011) Nr. 14, S. 147201/15 URL
2010
M. Daghofer, Q.L. Luo, R. Yu, D.X. Yao, A. Moreo, E. Dagotto: Orbitalweight redistribution triggered by spin order in the pnictides, Physical Review B 81 (2010) Nr. 18, S. 180514/14 URLM. Daghofer, N. Zheng, A. Moreo: Spinpolarized semiconductor induced by magnetic impurities in graphene, Physical Review B 82 (2010) Nr. 12, S. 121405/14 URL
M. Daghofer, A. Moreo: Comment on “Nonmagnetic impurity resonances as a signature of signreversal pairing in FeAsbased superconductors, Physical Review Letters 104 (2010) Nr. 8, S. 89701/11 URL
Q. Luo, G. Martins, D.X. Yao, M. Daghofer, R. Yu, A. Moreo, E. Dagotto: Neutron and ARPES constraints on the couplings of the multiorbital Hubbard model for the iron pnictides, Physical Review B 82 (2010) Nr. 10, S. 104508/116 URL
X. Wang, M. Daghofer, A. Nicholson, A. Moreo, M. Guidry, E. Dagotto: Constraints imposed by symmetry on pairing operators for the iron pnictides, Physical Review B 81 (2010) Nr. 14, S. 144509/111 URL
Invited talks
2014
M. Daghofer: Fractional chern insulators in strongly correlated multiorbital systems, DPG Fruehjahrstagung Kondensierte Materie, Dresden, 3.4.14 (2014)M. Daghofer: Itinerant multiorbital models for Pnictide superconductors, Sommerschule "MultiCondensates Superconductivity", Erice/ Italy, 19.25.7.14 (2014)
M. Daghofer: The spinorbit coupled $ J=1/2 $ antiferromagnet in iridates, Workshop "Quantum Phenomena in Strongly Correlated Electrons", Krakow/ Poland, 15.18.6.14 (2014)
M. Daghofer: Correlations and topology in multiorbital models, TheorieKolloquium, Universitaet Erlangen, 7.1.14 (2014)
2013
M. Daghofer: Spontaneous fractional quantumHall state in strongly correlated multiorbital systems, Workshop "Flat Bands: Design, Topology, and Correlations", Dresden, 4.8.3.13 (2013)M. Daghofer: The spinorbit coupled j =1=2 antiferromagnet in iridates, Workshop "Electronic Properties of SpinOrbit Driven Oxides", Dresden, 4.7.9.13 (2013)
M. Daghofer: Topologically nontrivial and nearly at bands in multiorbital models, Seminar, Salerno/ Italy, 20.01.13 (2013)
M. Daghofer: Spinorbit coupling and correlations in iridates, Seminar, Univ. Tenn., Knoxville/ USA, 1.4.13 (2013)
M. Daghofer: Correlations and topology in multiorbital models, Seminar, Stanford Institute for Materials and Energy Sciences, Stanford/ USA, 25.3.13 (2013)
M. Daghofer: Z2vortex phase in the triangularlattice KitaevHeisenberg model, MPIFKF Stuttgart, 17.4.13 (2013)
M. Daghofer: Multiorbital models for Pnictide superconductors, Workshop "Tuning Superconductivity in Doped Semiconductors", JacobUniversity Bremen, 11.12.9.13 (2013)
2012
M. Daghofer: Topologically nontrivial and nearly flat bands in multiorbital models, Seminar, Universitaet Salerno/ Italien, 4.4.12 (2012)M. Daghofer: Topologically nontrivial states in strongly correlated multiorbital systems, Workshop, Alcudia/ Spanien, 2.5.10.12 (2012)
M. Daghofer: Correlations and topology in multiorbital models, Theoriekolloquium, Universitaet Kaiserslautern, 6.12.12 (2012)
M. Daghofer: Spontaneous fractional quantum Hall states in multiorbital models, Seminar, Max Planck Institut fuer Festkoerperforschung, Stuttgart, 10.10.12 (2012)
2011
M. Daghofer: Multiorbital models for Pnictide superconductors, EMRS Fall Meeting 2011, Warschau/ Poland, 19.21.9.2011 (2011)M. Daghofer: Spinpolarized semiconductor induced by magnetic impurities in graphene, APS March Meeting, Dallas/ USA, 25.3.11 (2011)
M. Daghofer: Multiorbital models for Pnictide superconductors, Seminar, Universitaet Augsburg, 3.5.11 (2011)
M. Daghofer: Spontaneous fractional quantumhall state in strongly correlated multiorbital systems , Seminar, Universitaet Wuerzburg, 17.11.11 (2011)
M. Daghofer: Multiorbital models for pnictide superconductors, Seminar, Jagiellonen Universitaet Krakau/ Poland, 1.7.11 (2011)
S. Kourtis, J. Venderbos, J. van den Brink, M. Daghofer: Fractional quantumHall states in lattice models and their realization in multiorbital systems, Condensed Matter Theory Seminar, TU Dresden, 6.12.11 (2011)
2010
M. Daghofer: Numerical simulations for the interplay of spins and orbitals in multiorbital models for pnictides, Workshop, Lanzarote/ Spanien, 20.26.6.10 (2010)M. Daghofer: Multiorbital models for Pnictides: Pairing symmetries and numerical simulations, Workshop, MPIPKS, Dresden, 23.27.8.10 (2010)
M. Daghofer: Spinpolarized semiconductor induced by magnetic impurities in graphene, Seminar, University of Alberta/ USA, 7.5.10 (2010)
M. Daghofer: Correlated two and threeorbital models for ironpnictides, Seminar, MPIPKS, Dresden, 4.2.10 (2010)
M. Daghofer: Multiorbital models for pnictide superconductors, TheorieKolloquium, TU Dresden, 11.11.10 (2010)
M. Daghofer: Multiorbital models for Pnictide superconductors, Seminar, KIT Karlsruhe, 18.11.10 (2010)
Some of my current research interest in no particular order:
Dynamics of orbital and spinorbital excitations
If several orbitals contribute to lowenergy states of a transition metal oxide and if Coulomb repulsion is strong, charge fluctuations are suppressed and the Mott insulator resulting for one electron per site be described by a KugelKhomskiitype model [1], where spin spin and orbital degrees of freedom become formally almost equivalent. Excitations give information about the quantum dynamics, e.g., magnons in ferromagnetic manganites show that the main impact of alternating orbital order is a reduced magnon band width [2]. Apart from this reduced band width, the orbital background does not show up in the magnon dispersion, which implies that one can describe this situation by decoupling spins and orbitals in a meanfield approximation.
The analogous situation to a ferromagnet with alternating orbitals, but with reversed roles for spins and orbitals, is a ferroorbitally ordered antiferromagnet, see the first row of the figure to the left. Here, the orbital degree of freedom is "polarized" like the spin the ferromagnet and the spins alternate. The analogon to a spin flip is then an orbital excitation. The excitation can move (third and fourth rows) via virtual excitations with doubly occupied sites (second row). In the fourth row, "magnetic" and "orbital" parts of the original excitations have moved apart [3], in a similar manner to spincharge separation undergone by a hole in an antiferromagnetic (AF) chain.
Indeed, it turns out that the situation of the orbital excitation can be mapped onto the case of a hole moving in an AF background, at least for small Hund's rule coupling. As a consequence, this reversed situation leads to fundamentally different excitation spectra than the magnon case mentioned above, as can be seen in the figure to the right, where the spectrum obtained via the mapping is compared to the the line one would obtain in the meanfield decoupling. There are signature of spin"charge" separation in one dimension, the periodicity of the dispersion clearly reflects the doubled unit cell of the AF background and additional incoherent features arise [3,4]. The decisive impact of the lowered symmetries in the orbital sector is thus revealed in the differences between magnons and orbital excitations. Recently, spinorbit separation has been observed in resonant inelastic xray scattering (RIXS) for precisely this case, ferroorbital and antiferromagnetic onedimensional chains in Sr2CuO3 [5].
The same mapping and analysis have also been applied to an orbital excitation in the twodimensional iridate Sr_{2}IrO_{4}. In this system, spinorbit coupling is very strong, so that the halffilled orbital consists of eigenstates of the total angular momentum with j=1/2 rather than of spins in an orbital. Nevertheless, the orbital excitation into the higher levels with j=3/2 can again be mapped onto a hole moving in an AF background, here with an additional orbital flavor. The mapping and the evaluation of the spectral density using the selfconsistent Born approximation give excellent agreement with RIXS data [6].
We also investigate the impact of corehole properties on the spectra, using numerical techniques [7]. Open questions in this context are the impact of stronger Hund's rule which couples the spin of the excited electron to the background.
[1] K.I. Kugel and D.I. Khomskii, Sov. Phys. Usp. 25, 231 (1982).
[2] F. Moussa, M. Hennion, J. RodriguezCarvajal, H. Moudden, L. Pinsard, and A. Revcolevschi, Phys. Rev. B 54, 15149 (1996).
[3] K. Wohlfeld, M. Daghofer, G. Khaliullin, J. van den Brink, Phys. Rev. Lett. 107, 147201 (2011).
[4] K. Wohlfeld, M. Daghofer, G. Khaliullin, and Jeroen van den Brink,arXiv:1111.5522.
[5] J. Schlappa et al., Nature 485, 82 (2012).
[6] Jungho Kim, D. Casa, M. H. Upton, T. Gog, YoungJune Kim, J. F. Mitchell, M. van Veenendaal, M. Daghofer, J. van den Brink, G. Khaliullin, B. J. Kim, Phys. Rev. Lett. 108, 177003 (2012).
[7] S. Kourtis, J. van den Brink, M. Daghofer, Phys. Rev. B 85, 064423 (2012).
Localized spins in strongly correlated materials, e.g. transition metal oxides, can lead to particularly fascinating properties when they form a frustrated lattice, where not all interactions can be optimized. Examples include magnetic monopoles in spin ice or large thermopower due to the presence of many nearly degenerate states.
In our work <a href="research.html#klm_hexa">[1]</a>, we find that on the unfrustrated honeycomb lattice, geometric frustration can spontaneously emerge as a consequence of the frustration between antiferromagnetic (AF) magnetic interactions and ferromagnetism driven by itinerant electrons. For relatively weak AF exchange, hexagons of almost ferromagnetic (FM) spins form (there is a small canting between them). Interactions between hexagons are AF and since the hexagons form a triangular lattice, their spins order in the manner expected for individual spins on a frustrated triangular lattice<a href="research.html#YK"> [2]</a>, namely with a 120degree angle between NN hexagons. The resulting state is shown to the left.
For somewhat stronger AF interactions, smaller FM building blocks arise, namely dimers. Order between the dimers is AF, however, spins only order along one direction and remain perfectly uncorrelated along the other direction. This can be seen by noticing that the two states shown to the right are both valid dimer coverings and yet have different spinspin correlation along the xaxis. Such a nematic order implies a groundstate degeneracy that is proportional to the number of columns, i.e., to the square root of the system size. It is thus intermediate between 0 and macroscopic and is related to a symmetry intermediate between global and local (gaugelike). Such symmetries are realized in Hamiltonians like the compass model. In the present case, in contrast, the peculiar symmetry is here not a property of the Hamiltonian, but emerges spontaneously as a property of the groundstate manifold.
A spontaneous decoupling into almost independent stripes was also found in a more complex twoorbital double exchange model including phonons [3]. The model is motivated by narrowband manganites, at hole doping 1/n, stripes of collinear spins and width n can be found. Spins in adjacent stripes are at right angles, but switching the relative orientation of stripes at larger distances only changes the total energy by a negligible amount. The spins thus form nematic order again and decompose into 1D stripes, so it is somewhat surprising that the kinetic energy of the electrons is fully twodimensional and also depends on the longrange spin order. The reason for the nematic decoupling of the spin stripes is found in the directionality of the e_{g} orbitals: at the border of the stripes, dispersionless states emerge that suppress electronic hoppings that would hybridize occupied and unoccupied states.
We thus find that frustration between competing charge, spin, and orbital degrees of freedom can lead to exotic magnetic phases reminiscent of geometrically frustrated lattices.
[1] J. W. F. Venderbos, M. Daghofer, J. van den Brink, and S. Kumar, Phys. Rev. Lett. 107, 076405 (2011).
[2] Y. Yafet and C. Kittel, Phys. Rev. 87, 290 (1952).
[3] S. Liang, M. Daghofer, S. Dong, C. Sen, E. Dagotto, Phys. Rev. B 83, 024408 (2011).
Fractional Chern insulators in strongly correlated multiorbital systems
The oldest known "topologically nontrivial" phase are integer quantum Hall states, which are characterized by a quantized invariant and thus robust against distortions of the system. As a consequence, the quantization of the Hall conductance is extremely precise and the vonKlitzing constant is thus used as a standard for electrical resistance. Analogous states can also arise by breaking of timereversal symmetry by other means that by a magnetic field [1], e.g. via spinorbit coupling, as in topological insulators [2].
Recently, it was proposed that nearly flat and topologically nontrivial bands in lattice models might allow an analogous generalization of fractional quantumHall (FQH) states [3]. If the Coulomb repulsion is both large compared to the band width and small compared to the gap separating the band from its neighbors, it can stabilize FQHlike states.
We were able to show that an orbital degree of freedom can substantially flatten bands, which have a topological character due to an "effective magnetic flux" induced by noncoplanar "chiral" magnetic order [4]. In the figure to the right, the spin pattern of the chiral phase on the triangular lattice is schematically shown: The four spin of the unit cell, in (a), point to the corners of a tetrahedron, see (b); the chirality S_{i}(S_{j}xS_{k}) enclosed by three spins around a triangular plaquette is nonzero.
We showed this effect for a chiral state on both the triangular and the kagome lattices, and find that is work for either e_{g} or t_{2g} orbitals. The e_{g} orbitals are also shown in panel (d), where we illustrate how octahedra in perovskites build a triangular lattice.
In our first study, we had built on the fact that frustrated lattices are known to be able to support chiral magnetic phases. We were then able to show that a chiral phase with topologically nontrivial and very flat bands arises selfconsistently in a strongly correlated threeorbital model for t_{2g} orbitals on a triangular lattice [5]. The figure to the right shows an example for the oneparticle bands obtained in mean field. Here, periodic boundary conditions were used along one directions, and open along the other, i.e., we use a tube. Momentum is thus only conserved along the first direction and gives the xaxis of the plot. For each k_{x}, one finds several bands, their width is determined by the dispersion along the ydirection. One clearly sees some very flat bands of mostly a_{1g} character, especially the one directly above the chemical potential. The red and blue dashes and dots decorate edge states living on the top and bottom edges of the tube, which are absent for fully periodic boundary conditions. They connect the bands above and below the chemical potential and are an indication of the topologically nontrivial character of the bands.
The bandflattening effect is very robust in this model, both the chiral phase and the nearly flat bands arise for large parameter regions. As the flat band is well separated from other bands, one can map it onto an effective oneband model with a twosite unit cell. The twosite unit cell is given by the chiral magnetic order and allows the nontrivial topological character. The flatness of the band is caused by effective longerrange hopping due to virtual excitations.
The much simpler oneband model can be treated on finite clusters with exact diagonalization and we were indeed able to establish signatures of FQHlike states for a large number of filling fractions [5,6]. These Fractional Chern insulators reveal themselves through a variety of signatures, both in the energy levels and in a fractional value of the Hall conductance. Of course, FCI states compete with other phases; as they rely on longrange Coulomb repulsion, chargedensity waves are obvious competitors. We study the stability of both phases and find that the chargedensity wave wins if it is favored by Fermisurface nesting. If the Fermi surface is not well nested, even quite dispersive bands can host a fractional Chern insulator [6].
[1] F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).
[2] For review articles, see M. Hasan and C. Kane, Rev. Mod. Phys. 82, 3045 (2010); X.L. Qi and S.C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
[3] E. Tang, J.W. Mei, and X.G. Wen, Phys. Rev. Lett. 106, 236802 (2011); K. Sun, Z. Gu, H. Katsura, and S. D. Sarma, Phys. Rev. Lett. 106, 236803 (2011); T. Neupert, L. Santos, C. Chamon, and C. Mudry, Phys. Rev. Lett. 106, 236804 (2011).
[4] J. W.F. Venderbos, M. Daghofer, J. van den Brink, Phys. Rev. Lett. 107, 116401 (2011).
[5] J. W.F. Venderbos, S. Kourtis, J. van den Brink, M. Daghofer, Phys. Rev. Lett. 108, 126405 (2012).
[6] S. Kourtis, J. W.F. Venderbos, M. Daghofer, Phys. Rev. B 86, 235118 (2012).
As several (at the very least two) orbitals contribute weight to states near the Fermi level of ironbased superconductors, the question of orbital physics naturally arises [1]. Recently, we looked at one particular issue, namely the rotational symmetry breaking associated with a structural phase transition, which occurs at temperatures slightly above the onset of a spindensity wave in several compounds [2]. It could be due to the lattice distortion, but the differences in bond lengths seem too small to explain a spectral density A(k, ω) whose broad features look closer to the spindensity wave than to the symmetric hightemperature state. Spontaneous orbital order could explain this [3], however, tendencies to orbital polarization in the spindensity wave itself are very weak [4]. Another possible explanation is based on breaking the rotational symmetry through spin fluctuations, which select ordering vector (π,0) over the equivalent (0,π) without establishing longrange magnetic order right way [5]. A(k, ω) can readily be calculated in the first case, at least on a meanfiled level, but the same straightforward approach does not work in the spinnematic scenario: we need shortrange spin correlations to break rotational symmetry, but meanfield would then immediately stabilize longrange order. We worked around this issue by coupling small realspace clusters (where shortrange correlations break rotational symmetry) in momentum space (without longrange magnetic order) in clusterperturbation theory. This allows us to establish that a spinnematic state agrees better with experiment than bruteforce orbital order [6]. Results become a bit more complicated once onsite Coulomb correlations are included, as orbital and nematic order then lead to more similar predictions for A(k, ω). However, we found that correlations do not make it easier to induce orbital order, making spontaneous orbital order a less likely scenario [7]. Moreover, total orbital polarization is not a good predictor of features near the Fermi surface, as states with and without orbital order may differ mostly in spectral weight at higher excitation energies [6]. Orbital character of lowenergy states and total orbital occupation numbers, orbital polatization as in the orbitalorder scenario, can thus be quite different. Finally, we also found that pure lattice distortions cannot give the experimentally observed A(k, ω), with or without onsite Coulomb correlations [7].
[1] F. Krueger, S. Kumar, J. Zaanen, J. van den Brink, Phys. Rev. B 79, 054504 (2009).
[2] M Yi et al., PNAS 108, 12238 (2011); M Yi et al., New J. Phys. 14, 073019 (2012); C. He et al., Phys. Rev. Lett. 105, 11702 (2010); Y Zhang et al., Phys. Rev. B 85, 085121 (2012).
[3] W. Lv and P. Phillips, Phys. Rev. B 84, 174512 (2011).
[4] M. Daghofer, A. Nicholson, A. Moreo, E. Dagotto, Phys. Rev. B 81, 014511 (2010); M. Daghofer et al., Phys. Rev. B 81, 180514 (2010); B. Valenzuela, E. Bascones, and M. Calderon, Phys. Rev. Lett. 105, 207202 (2010).
[5] R. M. Fernandes, A. V. Chubukov, J. Knolle, I. Eremin, J. Schmalian, Phys. Rev. B 85, 024534 (2012).
[6] M. Daghofer, A. Nicholson, A. Moreo, Phys. Rev. B 85, 184515 (2012).
[7] M. Daghofer and A. Fischer, Supercond. Sci. Technol. 25, 084003 (2012).