Session R10: Fe-based Superconductors -- Nematicity I

ARPES of iron-based superconductors: how nematic order sets the stage for magnetic and superconducting ground states in NaFeAs and FeSe

Angle-resolved photoemission spectroscopy (ARPES) gives a unique insight into the evolution of the electronic structure of iron-based superconductors. By varying the temperature and doping of the sample, one can investigate all regions of their phase diagrams, including the high-temperature normal state, the magnetic ground state, the so-called nematic state where four-fold symmetry is broken without magnetic order, and the superconducting state.
For example, ARPES measurements of FeSe give an exclusive opportunity to investigate the electronic structure in nematic phase without magnetic order. In our measurements, we found substantial shifts of both the electron and hole bands associated with the onset of the nematic order, however the interpretation of these data has caused some controversy due to the formation of twin orthorhombic domains in samples. Our high-resolution ARPES results obtained on FeSe crystals detwinned by application of mechanical strain, reveal remarkable anisotropies hidden in the measurements of twinned samples. We observe that in the nematic phase the Fermi surface consists of one elliptical hole-like pocket and only one orthogonally oriented electron-like pocket.
Moreover, we find the same effect in detwinned NaFeAs samples where the spectral weight from only one elliptical electron pocket is detected in the nematic phase.
Finally, we use synchrotron-based high-resolution ARPES to map the 3D momentum dependence of the superconducting gap in FeSe. We find that on both the hole and electron Fermi surfaces, the gap is highly anisotropic, with its magnitude following the distribution of d_yz orbital weight on each pocket. We show that this anisotropic gap structure can be naturally reproduced from theoretical calculations only when the one-electron pocket state, observed in the nematic phase, is taken into account. These results support the spin fluctuation mediated mechanism of superconductivity in FeSe.   

Characterizing the nematic phase in Ba122 iron arsenides with a SQCRAMscope

Microscopic imaging of local magnetic fields provides a window into the organizing principles of complex and technologically relevant condensed matter materials. However, a wide variety of strongly correlated and topologically nontrivial materials exhibit poorly understood phenomena outside the detection capability of state-of-the-art high-sensitivity, high-resolution scanning probe magnetometers. We have recently introduced the Scanning Quantum Cryogenic Atom Microscope (SQCRAMscope), a quantum-noise-limited scanning probe magnetometer that can operate from room-to-cryogenic temperatures. By employing a magnetically levitated atomic Bose-Einstein condensate (BEC) that can be scanned near the surface of a cryogenically cooled material, the microscope achieves unprecedented DC-field sensitivity at micron-scale resolution. Combining this unique probe with optical polarimetry, we present recent work on characterizing the nematic phase transition in unstrained Ba122 iron-based superconductors. Domain structure is visualized through spatial mapping of the current density, from which resistivity anisotropy is extracted as a proxy for the nematic order parameter. The temperature dependence of nematicity is studied and compared to optical polarimetry results from the same sample.   

Observation of orbital ordering and origin of nematic order in FeSe

Nematic order has being found to widely exist in the cuprates and in the Fe-based superconductors in most recent years. It is directly linked to the superconductivity because nematic instability is a characteristic feature of the normal state upon which at lower temperatures the superconductivity emerges. FeSe has been regarded as a model system for the study of the Fe-based superconductors. But it is highly controversial as to whether the nematic order is driven by spin order, AFM spin fluctuations, and/or orbital order. Here we report the experimental result of field-dependent ⁷⁷Se-NMR. Our results shows for the first time that the difference of the static internal field in the ab-plane in the orthorhombic phase at the Se-nucleus is predominantly from the Fe-ion 3d electron orbitals (essentially all orbital), not from the electron spins, and gaint AFM spin fluctuations are gradually developed below T ~ 40 K in the orthorhombic phase, which is far below the nematic order/structure phase transition temperature T_nem = T_s = 89 K, while AFM spin order is absent at all temperatures and at all fields. Therefore, for the first time we provide direct evidence that orbital ordering is unequivocally the origin of the nematic order in FeSe.   

Single Crystal Diffuse Scattering Investigation of Nematic Fluctuations in (Ba,Na)Fe2As2

The phase competition between nematic order and superconductivity has been intensively investigated in iron-based superconductors. Recent neutron pair-distribution-function (PDF) measurements on polycrystaline samples provide evidence of dynamic orthorhombic distortions, even within the C₄ tetragonal magnetic phase of hole-doped compounds [1]. We present synchrotron x-ray measurements of diffuse scattering from single crystals of (Ba,Na)Fe₂As₂, which show that these nematic fluctuations are predominantly two-dimensional. The measurements cover a sufficiently large volume of reciprocal space that they can be transformed into real space, generating 3D PDFs, from which both in-plane and out-of-plane correlation lengths are determined as a function of temperature and dopant concentration. These results will be compared to other measurements of the nematic susceptibility.

[1] B. A. Frandsen, et al., Phys Rev Lett 119, 187001 (2017).   

Quantum critical nematic fluctuations and spin excitation anisotropy in the iron pnictides*

Quantum criticality in the iron pnictides involves the nematic and antiferromagnetic channels in a concurrent way [1,2]. To elucidate the nematic correlations, we study the spin excitation anisotropy defined by the difference between the dynamical spin susceptibilities at (pi,0) and (0,pi) [3]. We consider an effective Ginzburg-Landau theory involving spin and Ising-nematic degrees of freedom [1,2] in the presence of a small external C4-symmetry-breaking potential. Our analysis is carried out in a large N limit [2]. We establish a relation among the spin excitation anisotropy, the dynamical spin susceptibility and the nematic susceptibility, and then show how it can be used to extract the information of the nature of the quantum critical point. The relation we establish provides a means to understand the singular energy dependences observed for the spin excitation anisotropy in the avoided quantum critical regime of the optimally Ni-doped BaFe₂As₂ under a uniaxial strain. We also propose a mechanism accounting for these singular energy dependences.




References:
[1] J. Dai, Q. Si, J. X. Zhu, and E. Abrahams, PNAS 106, 4118, (2009).
[2] J. Wu, Q. Si and E. Abrahams, Phys. Rev. B 93, 104515 (2016).
[3] Y. Song et al., Phys. Rev. B 92, 180504 (2015).
*DOE BES Award # DE-SC0018197.   

Origin of diverse nematic orders in Fe-based superconductors: 45 degree rotated nematicity in AFe2As2 (A=Cs, Rb)

The origin of nematicity and their order parameters in strongly correlated superconductors have been attracting increasing attention. Both the orbital order without magnetization in FeSe and d-wave bond order in cuprate superconductors are satisfactorily explained based on the spin-fluctuation-driven mechanism [1-3]. Recently, new type nematic order has been discovered in heavily hole-doped (n_d = 5.5) compound AFe₂As₂ (A = Cs, Rb). The discovered nematicity has B_2g symmetry, rotated by 45 degrees from the B_1g nematicity in usual Fe-based superconductors. To reveal the origin of B_2g nematicity, we analyze the spontaneous symmetry-breaking in the self-energy [2] based on the multiorbital Hubbard model. We predict that the ``nematic bond order'', given by the symmetry-breaking in the d_xy orbital correlated hopping, is responsible for the B_2g nematic order in AFe₂As₂. It is concluded that not only conventional B_1g orbital order (n_xz ≠ n_xz), but also B_2g bond order with respect to d_xy orbital in AFe₂As₂ are caused by the same mechanism, that is, the charge-spin mode-coupling due to the Aslamazov-Larkin vertex correction. [1] S. Onari et al., PRL 116, 227001 (2016). [2] Y. Yamakawa et al., PRX 6, 021032 (2016). [3] M. Tsuchiizu et al., PRB 97, 165131 (2018).   

Orbital-selective superconductivity in the nematic phase of FeSe

The considerations of the orbital-selective Mott physics in the normal state [1,2] motivated the theoretical proposal for orbital-selective pairing [3]. The experimental evidence for the latter has come from both the iron pnictides [4] and iron selenides [5]. We study the superconductivity in the presence of nematic order in a multi-orbital model with frustrated spin-exchange interactions [6]. We found that the electron correlation effects amplified by the nematic order [7] give rise to an enhanced orbital-selective pairing. The latter produces a large gap anisotropy on the Fermi surface which naturally explains the experimental observations.

[1] R. Yu and Q. Si, PRL 110, 146402 (2013); PRB 84, 235115 (2011).
[2] M. Yi et al., PRL 110, 067003 (2013).
[3] R. Yu, J.-X. Zhu and Q. Si, PRB 89, 024509 (2014).
[4] C. Zhang et al., PRL 111, 207002 (2013).
[5] P. O. Sprau et al., Science 357, 75 (2017).
[6] H. Hu, R. Yu, E. M. Nica, J.-X. Zhu, and Q. Si, arXiv:1805.05915.
[7] R. Yu, J.-X. Zhu, and Q. Si, PRL in press, arXiv:1803.01733.   

Basic principles of disorder-induced electronic nematicity

Resolving the phenomenon of nematicity, i.e., the breaking of fourfold-rotational (C4) symmetry, remains an outstanding problem in the field of iron-based superconductors. A wide range of techniques have provided experimental evidence for electronic nematic behavior, while more recently, the nucleation of local nematicity around impurities has been also detected. While some of these results may be attributable to residual sample strain, the possible induction of local nematicity due to disorder appears as a prominent and, at the moment, a poorly-explored phenomenon. To shed light on this physics, we perform a detailed theoretical study of the role of disorder in systems exhibiting an electronic nematic instability, with an emphasis on temperatures above the critical temperature at which the spontaneous C4-symmetry breaking sets in. We employ both a phenomenological Ginzburg-Landau theory, as well as a microscopic model, and identify the spatial profile generated by a disorder configuration which either respects or explicitly breaks the fourfold rotational symmetry. In the former case, we find that while such a potential cannot induce net nematicity, it still modifies the Stoner criterion for the nematic instability, thus, generally enhancing the nematic critical temperature.   

Emergent XY-nematic fluctuations in heavily-hole doped iron-based superconductors

Electronic nematicity, rotational symmetry broken state originating from electronic mechanism, has been identified in several strong correlated systems. However, in contrast to its liquid crystal counterparts, the director of electronic nematic domains cannot point in an arbitrary direction (XY- nematic), but is confined to specific directions via non-negligible coupling to the lattice (Ising-nematic). Here we report the elastoresistance measurements in Ba_1-xRb_xFe₂As₂ and CsFe₂As₂, which can evaluate the nematic fluctuations from the change in the resistance induced by uniaxial strain. In RbFe₂As₂ and CsFe₂As₂, we found that B_1g nematic fluctuations is more significant than B_2g nematic fluctuations, providing the evidence for the nematicity along Fe-As direction in these compounds, 45 degree rotated from the unusual nematicity along Fe-Fe direction in the underdoped region. Furthermore, for the intermediate doping between these two distinct Ising-nematic phase, B_1g and B_2g nematic fluctuations exhibit identical Curie-Weiss behaviors, revealing that nearly XY-nematic fluctuation regime. This observation opens up a new route to realizing the novel electronic liquid crystal state in iron-based superconductors.   

Nematic fluctuations close to quantum criticality: a new method for comparing simulations and experiments

The comparison of numerical simulations and spectroscopic results is notoriously difficult because of the analytic continuation in the complex energy plane. In addition to the analytic continuation, life times and mass enhancement factors must be extracted from the experimental spectra using, e.g., Kramers-Kronig transformation with the well-known problems resulting from the extrapolations to low and high energies.
One way out of this dilemma is a transformation of the experimental results from real to imaginary frequencies which provides us with an imaginary-time-ordered correlation function Λ(τ). For determining Λ(τ), the cutoff is much faster. From this transformation, one can extract the quantity βΛ(β/2) with β=1/k_BT. We show in this contribution how this quantity can be derived from the electronic Raman spectra of the iron pnictide Ba(Fe_1-xCo_x)₂As₂ and varies with doping and temperature. We compare the results with those obtained via the Kramers-Kronig formalism at zero frequency. Additionally, we highlight the perspectives of this method with view on quantum criticality and the comparison of experiment and theory.   

The anomalous high magnetic field electronic state of the nematic iron-based superconductor FeSe1-xSx

Superconductivity is closely linked to the electronic states from which it emerges. Here we investigate the normal electronic state of the nematic superconductor FeSe_1-xS_x using magneto-transport and Hall Effect studies in magnetic fields up to 35 T (Nijmegen) and 70 T (Toulouse) over a large temperature range. Inside the nematic phase we find anomalous magneto-resistivity behaviour in very high magnetic fields, well above the upper critical field. The behaviour changes outside the nematic phase, where we show that at low temperatures Fermi-liquid behaviour is recovered. We account for the multiband structure and trace the carrier densities and motilities across the nematic phase transition. We also investigate the regime of superconducting fluctuations, which is expected to varying significantly in this isoelectronic series. We will discuss our results in relation to both Fermi liquid and non-Fermi liquid behaviour, and superconducting fluctuations.   

Charge order and structural evolution in nematic superconductor Ba(0.33)Sr(0.67)Ni2As2

Recent discoveries of charge order in the cuprates and electron nematic order in the iron-based superconductors has pointed towards the possibilities of both orderings being tied to mechanisms of high Tc superconductivity. The (Ba,Sr)Ni2As2 superconducting system has very recently been shown to exhibit both types of ordering without the presence of any magnetic order. Through single crystal x-ray diffraction reports, the Ba parent compound shows the emergence of an incommensurate charge density wave (CDW) before transitioning from a tetragonal structure to a triclinic structure with the emergence of a new commensurate triclinic CDW. We report single crystal x-ray observations how the charge order and structure of the system has evolved up through a Sr concentration of x=.67, just before the complete extinction of the triclinic phase and maximal superconducting Tc.