The nature of the nematicity in iron pnictides is studied with a proposed magnetic fluctuation. The spin-driven order in the iron-based superconductor has been realized in two categories: stripe SDW state and nematic state. The stripe SDW order opens a gap in the band structure and causes a deformed Fermi surface. The nematic order does not make any gap in the band structure and still deforms the Fermi surface. The electronic mechanism of nematicity is discussed in an effective model by solving the self-consistent Bogoliubov-de Gennes equations. The nematic order can be visualized as crisscross horizontal and vertical stripes. Both stripes have the same period with different magnitudes. The appearance of the orthorhombic magnetic fluctuations generates two uneven pairs of peaks at ±π0 and 0±π in its Fourier transformation. In addition, the nematic order breaks the degeneracy of dxz and dyz orbitals and causes the elliptic Fermi surface near the Γ point. The spatial image of the local density of states reveals a dx2-y2-symmetry form factor density wave.

Emerging evidence for the presence of strongly anisotropic electronic states in the underdoped regime of both cuprate and iron-based high temperature superconductors suggests the possibility of an important role for electronic nematic order in these materials. The central theme of my thesis work has been the experimental study of electronic nematicity in iron-based superconductors via measurement of resistivity anisotropy. To do this, I have developed several new experimental techniques, on the one hand enabling detwinning of sub-mm size single crystals in the broken-symmetry orthorhombic state, and on the other hand revealing the nematic susceptibility in the high-symmetry tetragonal state. A major part of my thesis work has involved measurement of the elastoresistance; that is, the change in the resistance of a material as a consequence of the strains that it experiences. In this thesis, I will show how differential elastoresistance measurements can directly reveal the nematic susceptibility of a material in the tetragonal state. I will introduce the appropriate tensor formalism necessary to describe these measurements, and describe an experimental technique to determine these coefficients using piezoelectric stacks to provide anisotropic bi-axial strain. Results in the tetragonal state of various underdoped families based on the parent compound BaFe2As2 explicitly demonstrate that the tetragonal-to-orthorhombic structural transition in these materials is fundamentally driven by an electronic nematic instability. These results also suggest that the resistivity anisotropy in the paramagnetic orthorhombic state is dominated by the Fermi surface anisotropy, rather than an anisotropy in the scattering rate. Finally, similar measurements of a wide variety of optimally doped iron-pnictides and iron-chalcogenides reveal that a divergence of the nematic susceptibility in the B2g symmetry channel appears to be a generic feature of optimally-doped iron-based superconductors. In addition to the above, I also employ a mechanical detwinning technique to reveal the resistivity anisotropy in the orthorhombic state of the same Fe-based superconductors. For the isovalently-substituted material BaFe2(As1-xPx)2, these measurements reveal a strong coupling between external stress and both the Neel temperature and the superconducting critical temperature.

This book covers different aspects of the physics of iron-based superconductors ranging from the theoretical, the numerical and computational to the experimental ones. It starts from the basic theory modeling many-body physics in Fe-superconductors and other multi-orbital materials and reaches up to the magnetic and Cooper pair fluctuations and nematic order. Finally, it offers a comprehensive overview of the most recent advancements in the experimental investigations of iron based superconductors.

Since the discovery of superconductivity, a great number of theoretical and experimental efforts have been made to describe this new phase of matter that emerged in many body systems. In this regard, theoretical models have been presented; the most famous of which was the BCS theory that can only describe conventional superconductors. With the discovery of new class superconductors, the superconducting mechanism became a new challenge in the field of condensed matter physics. This unexpected discovery opened a new area in the history of superconductivity, and experimental researchers started trying to find new compounds in this class of superconductors. These superconductors are often characterized by the anisotropic character in the superconducting gap function with nodes along a certain direction in the momentum space. Since the pairing interaction has an important role in the superconducting gap structure, its determination is very important to explain the basic pairing mechanism.In this regard, this book includes valuable theoretical and experimental discussions about the properties of superconductors. Here you will find valuable research describing the properties of unconventional superconductors.

Strong electronic nematic fluctuations have been discovered near optimal doping for several families of Fe-based superconductors, raising the question of what role, if any, these fluctuations might play in the superconducting pairing interaction. Underdoped Fe-based superconductors undergo a second order tetragonal-to-orthorhombic structural transition driven by electronic nematic order that accompanies or precedes an antiferromagnetic transition and borders the superconducting dome. In the tetragonal phase Fe-based superconductors are highly sensitive to perturbations of the same symmetry as the nematic order, such as antisymmetric (in this case B2g) strain. Elastoresistivity is described by a high rank tensor (fourth-rank +) as it relates changes in resistivity (second-rank) to strain (second-rank) experienced by a material and is a sensitive probe of broken symmetries. Previously, elastoresistivity measurements of the linear resistivity response to antisymmetric strain have revealed a divergent electronic nematic susceptibility in underdoped materials and has been used to characterize the nematic fluctuations in the tetragonal phase above the zero-field superconducting dome. In this work, I develop two new extensions to elastoresistivity measurements in order to probe the effects of electronic nematic fluctuations in greater detail in a representative family of these materials, the prototypical electron-doped pnictide Ba(Fe(1-x)Cox)2As2. First, I go beyond the first order response via a measurement of the nonlinear elastoresistivity. I find that the strong nematic fluctuations play a large role in the isotropic electronic response of these materials--as evidenced by a diverging nonlinear symmetric elastoresistivity response to antisymmetric strain. Second, I performed elastoresistivity measurements in magnetic fields large enough to suppress superconductivity to investigate the potential that the nematic fluctuations are related to a quantum critical point. I do not observe a magnetic field dependence of the nematic fluctuations and find that they continue to grow with decreasing temperature beneath the zero-field superconducting dome. I performed high magnetic field measurements on samples with a fine distribution of dopings and find that close to the putative quantum critical point, the nematic susceptibility appears to obey power law behavior over almost a decade of variation in composition. This is consistent with basic notions of nematic quantum criticality which, for clean systems, is associated with power law scaling in both doping and temperature. Paradoxically, however, I also find that the temperature dependence of the nematic susceptibility for compositions close to the critical value cannot be described by a single power law.

In this book the author presents two important findings revealed by high-precision magnetic penetration depth measurements in iron-based superconductors which exhibit high-transition temperature superconductivity up to 55 K: one is the fact that the superconducting gap structure in iron-based superconductors depends on a detailed electronic structure of individual materials, and the other is the first strong evidence for the presence of a quantum critical point (QCP) beneath the superconducting dome of iron-based superconductors. The magnetic penetration depth is a powerful probe to elucidate the superconducting gap structure which is intimately related to the pairing mechanism of superconductivity. The author discusses the possible gap structure of individual iron-based superconductors by comparing the gap structure obtained from the penetration depth measurements with theoretical predictions, indicating that the non-universal superconducting gap structure in iron-pnictides can be interpreted in the framework of A1g symmetry. This result imposes a strong constraint on the pairing mechanism of iron-based superconductors. The author also shows clear evidence for the quantum criticality inside the superconducting dome from the absolute zero-temperature penetration depth measurements as a function of chemical composition. A sharp peak of the penetration depth at a certain composition demonstrates pronounced quantum fluctuations associated with the QCP, which separates two distinct superconducting phases. This gives the first convincing signature of a second-order quantum phase transition deep inside the superconducting dome, which may address a key question on the general phase diagram of unconventional superconductivity in the vicinity of a QCP.