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Register a new userNernst effect of iron pnictide and cuprate superconductors: signatures of spin density wave and stripe order
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Christian Hess
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The Nernst effect has recently proven a sensitive probe for detecting unusual normal state properties of unconventional superconductors. In particular, it may sensitively detect Fermi surface reconstructions which are connected to a charge or spin density wave (SDW) ordered state, and even fluctuating forms of such a state. Here we summarize recent results for the Nernst effect of the iron pnictide superconductor $rm LaO_{1-x}F_xFeAs$, whose ground state evolves upon doping from an itinerant SDW to a superconducting state, and the cuprate superconductor $rm La_{1.8-x}Eu_{0.2}Sr_xCuO_4$ which exhibits static stripe order as a ground state competing with the superconductivity. In $rm LaO_{1-x}F_xFeAs$, the SDW order leads to a huge Nernst response, which allows to detect even fluctuating SDW precursors at superconducting doping levels where long range SDW order is suppressed. This is in contrast to the impact of stripe order on the normal state Nernst effect in $rm La_{1.8-x}Eu_{0.2}Sr_xCuO_4$. Here, though signatures of the stripe order are detectable in the temperature dependence of the Nernst coefficient, its overall temperature dependence is very similar to that of $rm La_{2-x}Sr_xCuO_4$, where stripe order is absent. The anomalies which are induced by the stripe order are very subtle and the enhancement of the Nernst response due to static stripe order in $rm La_{1.8-x}Eu_{0.2}Sr_xCuO_4$ as compared to that of the pseudogap phase in $rm La_{2-x}Sr_xCuO_4$, if any, is very small.
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When the Mott insulating state is suppressed by charge carrier doping, the pseudogap phenomenon emerges, where at the low-temperature limit, superconductivity coexists with some ordered electronic states. Within the framework of the kinetic-energy-driven superconductivity, the nature of the pair-density-wave order in cuprate superconductors is studied by taking into account the pseudogap effect. It is shown that the onset of the pair-density-wave order does not produce an ordered gap, but rather a novel hidden order as a result of the interplay of the charge-density-wave order with superconductivity. As a consequence, this novel hidden pair-density-wave order as a subsidiary order parameter coexists with the charge-density-wave order in the superconducting-state, and is absent from the normal-state.
Charge-density-wave (CDW) correlations within the quintessential CuO$_2$ planes have been argued to either cause [1] or compete with [2] the superconductivity in the cuprates, and they might furthermore drive the Fermi-surface reconstruction in high magnetic fields implied by quantum oscillation (QO) experiments for YBa$_2$Cu$_3$O$_{6+{delta}}$ (YBCO) [3] and HgBa$_2$CuO$_{4+{delta}}$ (Hg1201) [4]. Consequently, the observation of bulk CDW order in YBCO was a significant development [5,6,7]. Hg1201 features particularly high structural symmetry and recently has been demonstrated to exhibit Fermi-liquid charge transport in the relevant temperature-doping range of the phase diagram, whereas for YBCO and other cuprates this underlying property of the CuO$_2$ planes is partially or fully masked [8-10]. It therefore is imperative to establish if the pristine transport behavior of Hg1201 is compatible with CDW order. Here we investigate Hg1201 ($T_c$ = 72 K) via bulk Cu L-edge resonant X-ray scattering. We indeed observe CDW correlations in the absence of a magnetic field, although the correlations and competition with superconductivity are weaker than in YBCO. Interestingly, at the measured hole-doping level, both the short-range CDW and Fermi-liquid transport appear below the same temperature of about 200 K. Our result points to a unifying picture in which the CDW formation is preceded at the higher pseudogap temperature by $q$ = 0 magnetic order [11,12] and the build-up of significant dynamic antiferromagnetic correlations [13]. Furthermore, the smaller CDW modulation wave vector observed for Hg1201 is consistent with the larger electron pocket implied by both QO [4] and Hall-effect [14] measurements, which suggests that CDW correlations are indeed responsible for the low-temperature QO phenomenon.
We use the Nernst effect to delineate the boundary of the pseudogap phase in the temperature-doping phase diagram of cuprate superconductors. New data for the Nernst coefficient $ u(T)$ of YBa$_{2}$Cu$_{3}$O$_{y}$ (YBCO), La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ (Eu-LSCO) and La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ (Nd-LSCO) are presented and compared with previous data including La$_{2-x}$Sr$_x$CuO$_4$ (LSCO). The temperature $T_ u$ at which $ u/T$ deviates from its high-temperature behaviour is found to coincide with the temperature at which the resistivity deviates from its linear-$T$ dependence, which we take as the definition of the pseudogap temperature $T^star$- in agreement with gap opening detected in ARPES data. We track $T^star$ as a function of doping and find that it decreases linearly vs $p$ in all four materials, having the same value in the three LSCO-based cuprates, irrespective of their different crystal structures. At low $p$, $T^star$ is higher than the onset temperature of the various orders observed in underdoped cuprates, suggesting that these orders are secondary instabilities of the pseudogap phase. A linear extrapolation of $T^star(p)$ to $p=0$ yields $T^star(pto 0)simeq T_N(0)$, the Neel temperature for the onset of antiferromagnetic order at $p=0$, suggesting that there is a link between pseudogap and antiferromagnetism. With increasing $p$, $T^star(p)$ extrapolates linearly to zero at $psimeq p_{rm c2}$, the critical doping below which superconductivity emerges at high doping, suggesting that the conditions which favour pseudogap formation also favour pairing. We also use the Nernst effect to investigate how far superconducting fluctuations extend above $T_{rm c}$, as a function of doping, and find that a narrow fluctuation regime tracks $T_{rm c}$, and not $T^star$. This confirms that the pseudogap phase is not a form of precursor superconductivity.
When passing through a phase transition, electronic system saves energy by opening energy gaps at the Fermi level. Delineating the energy gap anisotropy provides insights into the origin of the interactions that drive the phase transition. Here, we report the angle-resolved photoemission spectroscopy (ARPES) study on the detailed gap anisotropies in both the tetragonal magnetic and superconducting phases in Sr$_{1-x}$Na$_x$Fe$_2$As$_2$. First, we found that the spin-density-wave (SDW) gap is strongly anisotropic in the tetragonal magnetic phase. The gap magnitude correlates with the orbital character of Fermi surface closely. Second, we found that the SDW gap anisotropy is isostructural to the superconducting gap anisotropy regarding to the angular dependence, gap minima locations, and relative gap magnitudes. Our results indicate that the superconducting pairing interaction and magnetic interaction share the same origin. The intra-orbital scattering plays an important role in constructing these interactions resulting in the orbital-selective magnetism and superconductivity in iron-based superconductors.
In iron-based superconductors, a spin-density-wave (SDW) magnetic order is suppressed with doping and unconventional superconductivity appears in close proximity to the SDW instability. The optical response of the SDW order shows clear gap features: substantial suppression in the low-frequency optical conductivity, alongside a spectral weight transfer from low to high frequencies. Here, we study the detailed temperature dependence of the optical response in three different series of the Ba122 system [Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$, Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ and BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$]. Intriguingly, we found that the suppression of the low-frequency optical conductivity and spectral weight transfer appear at a temperature $T^{ast}$ much higher than the SDW transition temperature $T_{SDW}$. Since this behavior has the same optical feature and energy scale as the SDW order, we attribute it to SDW fluctuations. Furthermore, $T^{ast}$ is suppressed with doping, closely following the doping dependence of the nematic fluctuations detected by other techniques. These results suggest that the magnetic and nematic orders have an intimate relationship, in favor of the magnetic-fluctuation-driven nematicity scenario in iron-based superconductors.
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