Recent discovery of superconductivity in CeRh$_2$As$_2$ clarified an unusual $H$-$T$ phase diagram with two superconducting phases [Khim et al. arXiv:2101.09522]. The experimental observation has been interpreted based on the even-odd parity transition characteristic of locally noncentrosymmetric superconductors. Indeed, the inversion symmetry is locally broken at the Ce site, and CeRh$_2$As$_2$ molds a new class of exotic superconductors. The low-temperature and high-field superconducting phase is a candidate for the odd-parity pair-density-wave state, suggesting a possibility of topological superconductivity as spin-triplet superconductors are. In this paper, we first derive the formula expressing the $\mathbb{Z}_2$ invariant of glide symmetric and time-reversal symmetry broken superconductors by the number of Fermi surfaces on a glide invariant line. Next, we conduct a first-principles calculation for the electronic structure of CeRh$_2$As$_2$. Combining the results, we show that the field-induced odd-parity superconducting phase of CeRh$_2$As$_2$ is a platform of topological crystalline superconductivity protected by the nonsymmorphic glide symmetry and accompanied by boundary Majorana fermions.
The discovery of the multiple $H$-$T$ phase diagram of CeRh$_2$As$_2$ offers a new route to designing topological superconductors. Although weak-coupling theories explain the experimental phase diagram qualitatively, a quantitative discrepancy between them has discouraged conclusive interpretation. In this Letter, we thoroughly study the effect of Coulomb interaction and the phase diagrams of locally noncentrosymmetric superconductors. We reveal even-odd parity transition and the enhancement of the parity transition field in strongly correlated superconductors, and an issue of CeRh$_2$As$_2$ i…
We study the pairing symmetry of the noncentrosymmetric heavy fermion superconductors CeRhSi$_3$ and CeIrSi$_3$ under pressures, which are both antiferromagnets at ambient pressure. We solve the Eliashberg equation by means of the random phase approximation and find that the mixed state of extended s-wave and p-wave rather than the $d+f$ wave state could be realized by enhanced antiferromagnetic spin fluctuations. It is elucidated that the gap function has line nodes on the Fermi surface and the resulting density of state in the superconducting state shows a similar character to that of usual …
Strong coupling effects on the upper critical fields $H_{c2}$ along the c-axis in the noncentrosymmetric heavy fermion superconductors near quantum criticality CeRhSi$_3$ and CeIrSi$_3$ are examined. For sufficiently large spin-orbit interactions due to the lack of inversion symmetry, $H_{c2}$ is mainly determined by the orbital depairing effects. From microscopic calculations taking into account the strong spin fluctuations, we show that $H_{c2}$ is extremely enhanced as the system approaches the quantum critical point, resulting in $H_{c2}\sim 30$T even in the case with the low transition te…
We performed $^{75}$As-NMR measurements to investigate the normal-state magnetic properties of CeRh$_2$As$_2$, a recently-discovered heavy-fermion superconductor. The magnitude and temperature dependence of the Knight shift at the As(2) site indicate easy-plane-type magnetic anisotropy in CeRh$_2$As$_2$. With regard to spin fluctuations, the temperature dependence of the nuclear spin-lattice relaxation rate $1/T_1$ arising from the 4$f$ electrons decreases from high-temperature constant behavior on cooling at $\sim$ 40~K, which is typical behavior of heavy-fermion systems. In addition, $1/T_1$…
Layered three-dimensional centrosymmetric crystals can exhibit characteristics of noncentrosymmetric materials. This happens when each individual layer alone lacks inversion, but, when combined, inversion symmetry is restored; hence the designation: locally noncentrosymmertic superconductors (LNCSs). In LNCSs, the effects of impurities and subdominant magnetic field induced pairing channels remain unexplored. Using a minimal model, we examine all pairing channels and show that there is always a subdominant superconducting instability that is favored at high magnetic fields, which can substanti…
We study the normal and the superconducting properties in noncentrosymmetric heavy fermion superconductors CeRhSi$_3$ and CeIrSi$_3$. For the normal state, we show that experimentally observed linear temperature dependence of the resistivity is understood through the antiferromagnetic spin fluctuations near the quantum critical point (QCP) in three dimensions. For the superconducting state, we derive a general formula to calculate the upper critical field $H_{c2}$, with which we can treat the Pauli and the orbital depairing effect on an equal footing. The strong coupling effect for general ele…
We theoretically propose a mechanism to understand the violation of the Pauli-Clogston limit for the upper critical field H$_{\rm c2}$ observed in the Ce bearing heavy Fermion material CeRh$_2$As$_2$ from the view point of spin singlet pairing. It is based on a duality concept, the dual simultaneous aspects of an electron: the itinerant part and localized part of quasi-particles (QPs) originated from the 4f electrons of the Ce atoms. While the itinerant QPs directly participate in forming the Cooper pairs, the localized QPs exert the internal field so as to oppose the applied field through the…
We report normal and superconducting properties of the Rashba-type noncentrosymmetric com- pound CaIrSi3, using single crystalline samples with nearly 100% superconducting volume fraction. The electronic density of states revealed by the hard x-ray photoemission spectroscopy can be well explained by the relativistic first-principle band calculation. This indicates that strong spin-orbit interaction indeed affects the electronic states of this compound. The obtained H - T phase diagram exhibits only approximately 10% anisotropy, indicating that the superconducting properties are almost three di…
Motivated by the recent discovery of noncentrosymmetric superconductors, such as $CePt_{3}Si$, $CeRhSi_{3}$ and $CeIrSi_{3}$, we investigate theoretically the impurity resonance states with coexisting $s$- and p-wave pairing symmetries. Due to the nodal structure of the gap function, we find single nonmagnetic impurity-induced resonances appearing in the local density of state (LDOS). In particular, we analyze the evolution of the local density of states for coexisting isotropic s-wave and p-wave superconducting states and compare with that of anisotropic s-wave and p-wave symmetries of the su…
Anisotropic, spatially textured electronic states often emerge when the symmetry of the underlying crystalline structure is lowered. However, the possibility recently has been raised that novel electronic quantum states with real-space texture could arise in strongly correlated systems even without changing the underlying crystalline structure. Here we report evidence for such texture in the superconducting quantum fluid that is induced by pressure in the heavy-fermion compound CeRhIn5. When long-range antiferromagnetic order coexists with unconventional superconductivity, there is a significa…
Superconductivity in a crystalline lattice without inversion is subject to complex spin-orbit-coupling effects, which can lead to mixed-parity pairing and an unusual magnetic response. In this study, the properties of a layered superconductor with alternating Rashba spin-orbit coupling in the stacking of layers, hence (globally) possessing a center of inversion, is analyzed in an applied magnetic field, using a generalized Ginzburg-Landau model. The superconducting order parameter consists of an even- and an odd-parity pairing component which exchange their roles as dominant pairing channel up…
We examine intrinsic interfaces separating crystalline twin domains of opposite spin-orbit coupling in a noncentrosymmetric superconductor such as CePt3Si. At these interfaces, low-energy Andreev bound states occur as a consequence of parity-mixed Cooper pairing, and a superconducting phase which violates time reversal symmetry can be realized. This provides an environment allowing flux lines with fractional flux quanta to be formed at the interface. Their presence could have strong implications on the flux creep behavior in such superconductors.
Twin boundaries are generic crystalline defects in noncentrosymmetric crystal structures. We study theoretically twin boundaries in time-reversal symmetric noncentrosymmetric superconductors that admit parity-mixed Cooper pairing. Twin boundaries support spin currents as a consequence of this parity mixing. If the singlet and triplet components of the superconducting order parameter are of comparable magnitude, the superconducting state breaks spontaneously the bulk time-reversal symmetry locally near the twin boundary. By self-consistently evaluating the Bogoliubov-de-Gennes equations and the…
We show two-dimensional "strong" topological superconductivity in d-wave superconductors (SCs). Although the topological invariant of the bulk wave function cannot be defined in d_{x^2-y^2}-wave and d_{xy}-wave SCs because of nodal excitations, the bulk energy spectrum of d-wave SCs on a substrate is fully gapped in a magnetic field. Then the superconducting state is specified by a nontrivial Chern number, and hence topologically nontrivial properties are robust against disorders and interactions. We discuss high-temperature topological superconductivity in cuprate SCs recently fabricated on a…
Mixing of spin singlet and spin triplet superconducting pairing state is expected in noncentrosymmetric superconductors (NCS) due to the inherent presence of Rashba-type antisymmetric spin-orbit coupling. Unlike low symmetry (tetragonal or monoclinic) NCS, parity is isotropicaly broken in space for cubic NCS and can additionally lead to the coexistence of magnetic and superconducting state under certain conditions. Motivated with such enriched possibility of unconventional superconducting phases in cubic NCS we are reporting successful formation of single crystalline cubic noncentrosymmetric P…
Strength of Rashba type antisymmetric spin orbit coupling has the crucial effect on superconducting and normal state properties in noncentrosymmetric (NCS) superconductors. This can be seen on various anisotropic properties of the system. For a system with lowered crystalline symmetry as in noncentrosymmetric crystals, the superconducting pairing state can have correlation to the normal state properties. In our earlier work we have shown that alfa-BiPd which has a monoclinic (P_21) structure with the absence of the centre of inversion exhibits bulk superconductivity at 3.8 K. In order to under…
Dynamical behavior of vortices plays central roles in the quantum phenomena of two-dimensional (2D) superconductors. Quantum metallic state, for example, showing an anomalous temperature-independent resistive state down to low-temperatures, has been a common subject in recently developed 2D crystalline superconductors, whose microscopic origin is still under debate. Here, we unveil a new aspect of the vortex dynamics in a noncentrosymmetric 2D crystalline superconductor of MoS$_{2}$ through the nonreciprocal transport measurement. The second harmonic resistance $R^{2w}$ at low temperature with…
The superconducting gap structure of a topological crystalline insulator (TCI) candidate ZrRuAs ($T^{\rm on}_{\rm c}$ = 7.9(1) K) with a noncentrosymmetric crystal structure has been investigated using muon spin rotation/relaxation ($μ$SR) measurements in transverse-field (TF) and zero-field (ZF) geometries. We also present the results of magnetization, electrical resistivity and heat capacity measurements on ZrRuAs, which reveal bulk superconductivity below 7.9~K. The temperature dependence of the effective penetration depth obtained from the analysis of the TF-$μ$SR spectra below $T_{\rm c}$…
Based on the first-principles calculations and experimental measurements, we report that the hexagonal phase of ternary transition metal pnictides TT'X (T=Zr, Hf; T'=Ru; X=P, As), which are well-known noncentrosymmetric superconductors with relatively high transition temperatures, host nontrivial bulk topology. Before the superconducting phase transition, we find that HfRuP belongs to a Weyl semimetal phase with 12 pairs of type-II Weyl points, while ZrRuAs, ZrRuP and HfRuAs belong to a topological crystalline insulating phase with trivial Fu-Kane $\mathbb Z_2$ indices but $nontrivial$ mirror …
We study topological phase transitions in three-dimensional odd-parity or noncentrosymmetric superconductors with mirror symmetry when time-reversal symmetry is broken. We construct a generic phase diagram for Weyl superconductivity in the mirror-symmetric superconductors. It is shown that Weyl superconductivity generally emerges between the trivial and the topological crystalline superconductor phases. We demonstrate how a trajectory of the Weyl nodes determines the change in mirror Chern numbers in the topological phase transition. We also discuss a relationship between particle-hole symmetr…
Ising superconductivity and anomalous metallic states in a bulk crystal with artificial unidirectional stacking layers
ShanghaiTech University（上海科技大学）；East China Normal University（华东师范大学）；University of Science and Technology of China（中国科学技术大学）；Zhengzhou University of Aeronautics（郑州航空工业管理学院）；Fudan University（复旦大学）；Chinese Academy of Sciences（中国科学院）
We report the electronic properties of superconductivity in the topological nodal-line semimetal PbTaSe$_2$. Angle-resolved photoemission measurements accompanied by band calculations confirmed the nodal-line band structure in the normal state of single crystalline PbTaSe$_2$. Resistivity, magnetic-susceptibility and specific heat measurements have also been performed on high-quality single crystals. We observed upward features and large anisotropy in upper critical field ($H_{c2}$) measured in-plane (H//\textbf{ab}) and out-plane (H//\textbf{c}), respectively. Especially, $H_{c2}$ measured in…
Unconventional superconductors have Cooper pairs with lower symmetries than in conventional superconductors. In most unconventional superconductors, the additional symmetry breaking occurs in relation to typical ingredients such as strongly correlated Fermi liquid phases, magnetic fluctuations, or strong spin-orbit coupling in noncentrosymmetric structures. In this article, we show that the time-reversal symmetry breaking in the superconductor LaNiGa$_2$ is enabled by its previously unknown topological electronic band structure. Our single crystal diffraction experiments indicate a nonsymmorph…
