We discuss superconductivity in a model on a cubic lattice for a $Γ_3$ non-Kramers system. In previous studies, it is revealed that $d$-wave superconductivity with $E_g$ symmetry occurs in a wide parameter range in a $Γ_3$ system. Such anisotropic superconductivity can break the cubic symmetry of the lattice. In a $Γ_3$ system, the quadrupole degrees of freedom are active and the effect of the cubic symmetry breaking should be important. Here, we investigate the coexisting states of the $d$-wave superconductivity and quadrupole order by a mean-field theory. In particular, we discuss possible competition and cooperation between the superconductivity and quadrupole order depending on types of them. We find nematic superconductivity breaking the cubic symmetry and coexisting with quadrupole order. In the present model, we also find $d+id$ superconductivity, which breaks time-reversal symmetry but retains the cubic symmetry. We also discuss the effects of uniaxial stress on these superconducting states.
To seek high-$T_c$ pairing mechanism, many scientists have focused on the mysterious spontaneous rotational symmetry breaking above Tc, such as nematic order at $q=0$ and smectic order at $q\ne0$. Such exotic correlation-driven symmetry breaking in metals has become a central issue in condensed matter physics. We demonstrate the emergence of the nematic and smectic orders due to orbital polarization ($n_{xz}\ne n_{yz}$) and the symmetry breaking in the correlated intersite hopping (= bond order $δt_{i,j}$) in Fe-based and cuprate superconductors. In addition, we discuss exotic spontaneous loop…
The quarter-filling extended Hubbard model on the triangular lattice is studied to explore pairing instability in the three-fold charge-ordered (CO) metal. We derive a second-order strong-coupling effective Hamiltonian of doped carriers into the three-fold CO insulator at electron density of $n=2/3$, and then study the $f$- and $d_{xy}$-wave superconductivities down to $n=1/2$ by using the BCS mean-field approximation. It is found that the triplet $f$-wave pairing is more stable than the $d_{xy}$-wave one. We also point out that this coexisting state of the charge ordering and superconductivit…
In recent years, there have been increasing experimental evidence suggesting the existence of an electronic nematic state in a number of unconventional $d$-wave superconductors. Interestingly, it is expected that the long-range nematic order can coexist with $d$-wave superconductivity. We analyze the in-plane upper critical field $H_{c2}$ after taking the influence of nematic state into account, and find that the four-fold oscillation of angle-dependent $H_{c2}$ in a pure $d$-wave superconducting state is turned into a novel two-fold oscillation pattern by a weak nematic order. Moreover, such …
We study the thermal transport in a two-dimensional system with coexisting superconducting (SC) and nematic orders. We analyze the nature of the coexistence phase in a tight-binding square lattice where the nematic state is modelled as a $d$-wave Pomeranchuk type instability and the feedback of the symmetry breaking nematic state on the SC order is accounted for by mixing of the $s$, $d$ paring interaction. The electronic thermal conductivity is computed within the framework of Boltzmann kinetic theory where the impurity scattering collision is treated in the both the Born and Unitary limits. …
The importance of antiferromagnetic fluctuations are widely acknowledged in most unconventional superconductors. In addition, cuprates and iron pnictides often exhibit unidirectional (nematic) electronic correlations, including stripe and orbital orders, whose fluctuations may also play a key role for electron pairing. However, these nematic correlations are intertwined with antiferromagnetic or charge orders, preventing us to identify the essential role of nematic fluctuations. This calls for new materials having only nematicity without competing or coexisting orders. Here we report systemati…
Recent observations of broken symmetries have partly demystified the pseudogap phase. Here we review evidence for long-range intra-unit-cell(IUC) nematic order and its unexpectedly strong coupling to the phase of the fluctuating stripes in the pseudogap states of underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. In particular, we focus on the analysis techniques that reveal this evidence in scanning tunneling spectroscopy data, the definition of the extracted IUC nematic order parameter, and a phenomenological theory of the coupling between the IUC nematic order and the previously reported coexisting …
The nature of superconductivity in newly discovered Kagome materials, $\text{AV}_3\text{Sb}_5$ (A=K, Rb, Cs), has been a subject of intense debate. Recent experiments suggest the presence of orbital current order on top of the charge density wave (CDW) and superconductivity. Since the orbital current order breaks time-reversal symmetry, it may fundamentally affect possible superconducting states. In this work, we investigate the mutual influence between the orbital current order and superconductivity in Kagome metal with characteristic van Hove singularity (vHS). By explicitly deriving the Lan…
The in-plane London penetration depth, $Δλ(T)$, was measured using a tunnel diode resonator technique in single crystals of Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ with doping levels $x$ ranging from heavily underdoped, $x$=0.16 ($T_{c}$=7~K) to nearly optimally doped, $x$= 0.34 ($T_{c}=$39 K). Exponential saturation of $Δλ(T)$ in the $T\to0$ limit is found in optimally doped samples, with the superfluid density $ρ_{s}(T)\equiv(λ(0)/λ(T))^{2}$ quantitatively described by a self-consistent $γ$-model with two nodeless isotropic superconducting gaps. As the doping level is decreased towards the extreme…
Due to the presence of a nontrivial three-dimensional spin-orbital entanglement, Sr$_2$RuO$_4$ may be a time-reversal invariant nematic $p$-wave superconductor with coexisting in-plane and out-of-plane pairings. Here we discuss various signatures of such a state if the out-of-plane pairing component is dominant. First, the enhancement of the superconducting $T_c$ under in-plane uniaxial strains is nearly a quadratic function of the strain, because the out-of-plane pairing lacks a linear-order coupling to the strain. Second, when the strain applies along a certain in-plane direction, the nemati…
The coexistence of multiple quasi-degenerate orders is the hallmark of the strongly correlated materials. Experiments often reveal several spatially modulated orders in the underdoped cuprates. This has come to the forefront with the possible detection of the pair density wave states. However, microscopic calculations often struggle to stabilize such spatially modulating orders as the ground state in the strong correlation limit. This work uses the $t-t^\prime-J$-model with an additional nearest-neighbor repulsion to stabilize spatially oscillating charge, bond, and pairing orders in the under…
We survey the use of spectroscopic imaging STM to probe the electronic structure of underdoped cuprates. Two distinct classes of electronic states are observed in both the d-wave superconducting (dSC) and the pseudogap (PG) phases. The first class consists of the dispersive Bogoliubov quasiparticle excitations of a homogeneous d-wave superconductor, existing below a lower energy scale E=Delta0. We find that the Bogoliubov quasiparticle interference signatures of delocalized Cooper pairing are restricted to a k-space arc which terminates near the lines connecting k=\pm(pi/a0,0) to k=\pm(pi/a0).…
Iron-Based Superconductors: A Decade of Materials, Magnetism, and Mechanisms
Beijing Normal University（北京师范大学）；Renmin University of China（中国人民大学）；Fudan University（复旦大学）；Institute of Science Tokyo（东京科学大学）；Korea University（高丽大学）；Rice University（莱斯大学）
Evolution of charge density waves from three-dimensional to quasi-two-dimensional in Kagome superconductors Cs(V$_{1-x}M_{x}$)$_3$Sb$_5$ ($M$ = Nb, Ta)
