A brief review on μSR studies of unconventional Fe-and Cr-based superconductors

Muon spin relaxation/rotation(μSR) is a vital technique for probing the superconducting gap structure, pairing symmetry and time reversal symmetry breaking, enabling an understanding of the mechanisms behind the unconventional superconductivity of cuprates and Fe-based high-temperature superconductors, which remain a puzzle. Very recently double layered Fe-based superconductors having quasi-2 D crystal structures and Cr-based superconductors with a quasi-1D structure have drawn considerable attention. Here we present a brief review of the characteristics of a few selected Fe-and Cr-based superconducting materials and highlight some of the major outstanding problems, with an emphasis on the superconducting pairing symmetries of these materials. We focus on μSR studies of the newly discovered superconductors ACa_2Fe_4As_4F_2(A = K, Rb, and Cs), ThFeAsN, and A_2Cr_3As_3(A = K, Cs), which were used to determine the superconducting gap structures, the presence of spin fluctuations, and to search for time reversal symmetry breaking in the superconducting states. We also briefly discuss the results of μSR investigations of the superconductivity in hole and electron doped BaFe_2As_2.     

Observation of a Ubiquitous(π,π)-Type Nematic Superconducting Order in the Whole Superconducting Dome of Ultra-Thin BaFe_(2-x)Ni_xAs_2 Single Crystals

In iron-based superconductors,the(0,π) or(π,0) nematicity,which describes an electronic anisotropy with a fourfold symmetry breaking,is well established and believed to be important for understanding the superconducting mechanism.However,how exactly such a nematic order observed in the normal state can be related to the superconducting pairing is still elusive.Here,by performing angular-dependent in-plane magnetoresistivity using ultra-thin flakes in the steep superconducting transition region,we unveil a nematic superconducting order along the(π,π) direction in electron-doped BaFe_(2-x)Ni_xAs_2 from under-doped to heavily overdoped regimes with x=0.065-0.18.It shows superconducting gap maxima along the(π,π) direction rotated by 45° from the nematicity along(0,π) or(π,0) direction observed in the normal state.A similar(π,π)-type nematicity is also observed in the under-doped and optimally doped hole-type Ba_(1-y)K_yFe_2 As_2,with y=0.2-0.5.These results suggest that the(π,π) nematic superconducting order is a universal feature that needs to be taken into account in the superconducting pairing mechanism in iron-based superconductors.     

High-order time-reversal symmetry breaking normal state

Spontaneous time-reversal symmetry breaking plays an important role in studying strongly correlated unconventional superconductors.When two superconducting gap functions with different symmetries compete,the relative phase channel(θ_-≡θ₁-θ₂)exhibits an Ising-type Z₂ symmetry due to the second order Josephson coupling,where θ_1,2 are the phases of two gap functions.In contrast,the U(1) symmetry in the channel of θ₊≡(θ₁+θ     

Broken Time-Reversal Symmetry in Superconducting Partially Filled Skutterudite Pr_(1-δ)Pt_4Ge_(12)

Time reversal symmetry(TRS)is a key symmetry for classification of unconventional superconductors,and the violation of TRS often results in a wealth of novel properties.Here we report the synthesis and superconducting properties of the partially filled skutterudite Pr_(1-δ)Pt_4Ge_(12).The results from x-ray diffraction and magnetization measurements show that the[Pt_4 Ge_(12)]cage-forming structure survives and bulk superconductivity is preserved below the superconducting transition temperature T_c = 7.80 K.The temperature dependence of both the upper critical field and the electronic specific heat can be described in terms of a two-gap model,providing strong evidence of multi-band superconductivity.TRS breaking is observed using zero Held muon-spin relaxation experiments,and the magnitude of the spontaneous field is nearly half of that in PrPt_4Ge_(12).     

Unusual Band Splitting and Superconducting Gap Evolution with Sulfur Substitution in FeSe

High-resolution angle-resolved photoemission measurements were taken on FeSe_1-xS_x（x=0,0.04,and 0.08）superconductors.With an ultrahigh energy resolution of 0.4 meV,unusual two hole bands near the Brillouin-zone center,which was possibly a result of additional symmetry breaking,were identified in all the sulfur-substituted samples.In addition,in both of the hole bands highly anisotropic superconducting gaps with resolution limited nodes were evidenced.We find that the larger ...     

Nodeless superconductivity in a vanadium kagome metal

正The pairing symmetry of the superconducting order parameter contains key information about the pairing mechanism of the superconductor. For conventional superconductors, whose pairing is usually induced by the electron-phonon interaction, the pairing symmetry is s-wave, and the superconducting gap is fully open everywhere on the Fermi surface. For unconventional superconductors such as the cuprate and heavy fermion superconductors, other pairing symmetries may occur, leading to symmetry-mandated nodes in the superconducting order parameter.     

Structural classification and a binary structure model for superconductors

Based on structural and bonding features, a new classification scheme of superconductors is proposed to classify them into three classes: three-dimensional, two-dimensional and molecule-assembled superconductors. The sandwich model' for the high-T_c cuprates is extended to a `binary structure model': i.e., the crystal structure of most superconductors can be partitioned into two parts, a superconducting active component and a supplementary component. Partially metallic covalent bonding is found to be a common feature in all superconducting active components, and the electron states of the atoms in the active components usually make a dominant contribution to the energy band near the Fermi surface. Possible directions to explore new superconductors are discussed based on the structural classification and the binary structure model.     

Physical properties and phase diagram of NaFe1-xVxAs

We grew a series of NaFe_1-xV_x As(0 ≤ x ≤ 0.03) single crystals and performed the measurements of resistance,magnetic susceptibility, and specific heat to study the superconducting phase diagram by doping V into Na Fe As. Both the structural and the spin-density-wave(SDW) transitions are slightly suppressed by V-doping. While superconducting transition temperature is enhanced to the maximum value of 15 K when the optimal doping level x = 0.007 and then is suppressed rapidly with further V-doping, displaying a small superconducting dome. Our results suggest that V-impurities should act as strong magnetic scattering centers which cause the sharp suppression of superconductivity in NaFe_1-xV_x As.     

Pressure-Dependent Point-Contact Spectroscopy of Superconducting PbTaSe_2 Single Crystals

We develop an experimental tool to investigate the order parameter of superconductors by combining pointcontact spectroscopy measurement with high-pressure technique.It is demonstrated for the first time that planar point-contact spectroscopy measurement on noncentrosymmetric superconducting PbTaSe_2 single crystals is systematically subjected to hydrostatic pressures up to 12.1 kbar.Under such a high pressure,the normal-state contact resistance is sensitive to the applied pressure,reflecting the underlying variation of contact transparency upon pressures.In a superconducting state,the pressure dependence of the energy gap △_0 and the critical temperature T_c for gap opening/closing are extracted based on a generalized Blond-Tinkham-Klapwijk model.The gap ratio 2△_0/k_B T_c indicates a crossover from weak coupling to strong coupling in electron pairing strength upon pressure for PbTaSe_2.Our experimental results show the accessibility and validity of high-pressure pointcontact spectroscopy,offering rich information about high-pressure superconductivity.     

Dynamical Evolution of an Effective Two-Level System with PT Symmetry

We investigate the dynamics of parity-and time-reversal(PT) symmetric two-energy-level atoms in the presence of two optical and one radio-frequency fields. The strength and relative phase of fields can drive the system from the unbroken to the broken PT symmetric regions. Compared with the Hermitian model, Rabi-type oscillation is still observed, and the oscillation characteristics are also adjusted by the strength and relative phase in the region of the unbroken symmetry. At the exception point, the oscillation breaks down. To better understand the underlying properties we study the effective Bloch dynamics and find that the emergence of the PT components of the fixed points is the feature of the PT symmetry breaking and the projections in the x–y plane can be controlled with high flexibility compared with the standard two-level system with the PT symmetry. It helps to study the dynamic behavior of the complex PT symmetric model.     

Dynamical Breaking of Generalized Yang-Mills Theory

The dynamical breaking of a generalized Yang-Mills theory is discussed. It is shown, in terms of the Nambu Jona-Lasinio mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills theory. The combination of the generalized Yang-Mills theory and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.     

Nodal superconducting gap in LiFeP revealed by NMR:Contrast with LiFeAs

Identifying the uniqueness of FeP-based superconductors may shed new lights on the mechanism of superconductivity in iron-pnictides.Here,we report nuclear magnetic resonance(NMR) studies on LiFeP and LiFeAs which have the same crystal structure but different pnictogen atoms.The NMR spectrum is sensitive to inhomogeneous magnetic fields in the vortex state and can provide the information on the superconducting pairing symmetry through the temperature dependence of London penetration depth λ_L.We find that λ_L saturates below T～0.2 T_C in LiFeAs,where T_C is the superconducting transition temperature,indicating nodeless superconducting gaps.Furthermore,by using a two-gaps model,we simulate the temperature dependence of λ_L and obtain the superconducting gaps of LiFeAs,as Δ_1=1.2 k_B T_C and Δ_2=2.8 k_BT_C,in agreement with previous result from spin-lattice relaxation.For LiFeP,in contrast,λ_L does not show any saturation down to T～0.03 T_C,indicating nodes in the superconducting gap function.Finally,we demonstrate that strong spin fluctuations with diffusive characteristics exist in LiFeP,as in some cuprate high temperature superconductors.     

Visualizing the charge order and topological defects in an overdoped （Bi,Pb）2Sr2CuO6+x superconductor

Electronic charge order is a symmetry breaking state in high-Tc cuprate superconductors. In scanning tunneling microscopy, the detected charge-order-induced modulation is an electronic response of the charge order. For an overdoped(Bi,Pb)2Sr2CuO6+x sample, we apply scanning tunneling microscopy to explore local properties of the charge order. The ordering wavevector is nondispersive with energy, which can be confirmed and determined. By extracting its order-parameter field, we identify dislocations in the stripe structure of the electronic modulation, which correspond to topological defects with an integer winding number of ±1. Through differential conductance maps over a series of reduced energies, the development of different response of the charge order is observed and a spatial evolution of topological defects is detected. The intensity of charge-order-induced modulation increases with energy and reaches its maximum when approaching the pseudogap energy. In this evolution, the topological defects decrease in density and migrate in space. Furthermore, we observe appearance and disappearance of closely spaced pairs of defects as energy changes. Our experimental results could inspire further studies of the charge order in both high-Tccuprate superconductors and other charge density wave materials.     

Effect of transparency on Josephson junction between s+g-wave superconductors

In this paper, a dc Josephson junction between borocarbide superconductors has been studied theoretically. The s+g-wave pairing symmetry which is observed in rare earth complex of borocarbides has a huge anisotropy and is an interesting form of unconventional superconductivity. We calculate the Josephson current in a superconductor--insulator--superconductor (SIS) Josephson junction with s+g-wave superconducting pairing symmetry. In our planar junction c-axis is parallel to an interface with finite transparency but ab-planes of two tetragonal superconductors are misorientated by angle α. We obtain that the Josephson current is strongly dependent on mis-orientation between the left and the right ab-planes. An insulator sandwiched between two superconductors which acts as a potential barrier is demonstrated by a transparency coefficient. The effects of the potential barrier and the mis-orientation on the current are studied analytically and numerically. Occurrence of 0--π transition in this s+g-wave junction is investigated in this paper. A comparison between d-wave Josephson junction and s+g-wave one is also made in the present paper.     

Neutron Powder Diffraction Study on the Non-Superconducting Phases of ThFeAsN_(1-x)O_x(x=0.15,0.6)Iron Pnictide

We use neutron powder diffraction to study the non-superconducting phases of ThFeAsN_(1-x)O_x with x = 0.15,0.6.In our previous results of the superconducting phase ThFeAsN with T_c = 30 K,no magnetic transition is observed by cooling down to 6 K,and possible oxygen occupancy at the nitrogen site is shown in the refinement[Europhys.Lett.117(2017)57005].Here in the oxygen doped system ThFeAsN_(1-x)O_x,two superconducting regions(0≤x≤0.1 and 0.25≤x≤0.55)are identified by transport experiments[J.Phys.:Condens.Matter30(2018)255602].However,within the resolution of our neutron powder diffraction experiment,neither the intermediate doping x= 0.15 nor the heavily overdoped compound x = 0.6 shows any magnetic order from 300 K to 4 K.Therefore,while it shares the common phenomenon of two superconducting domes as most 1111-type iron-based superconductors,the magneticall.y ordered parent compound may not exist in this nitride family.     

Temperature and doping dependent flat-band superconductivity on the Lieb-lattice

We consider the superconducting properties of Lieb lattice, which produces a flat-band energy spectrum in the normal state under the strong electron–electron correlation. Firstly, we show the hole-doping dependent superconducting order amplitude with various electron–electron interaction strengths in the zero-temperature limit. Secondly, we obtain the superfluid weight and Berezinskii–Kosterlitz–Thouless(BKT) transition temperature with a lightly doping level. The large ratio between the gap-opening temperature and BKT transition temperature shows similar behavior to the pseudogap state in high-T_c superconductors. The BKT transition temperature versus doping level exhibits a dome-like shape in resemblance to the superconducting dome observed in the high-T_c superconductors. However, unlike the exponential dependence of T_c on the electron–electron interaction strength in the conventional high-T_c superconductors, the BKT transition temperature for a flat band system depends linearly on the electron–electron interaction strength. We also show the doping-dependent superconductivity on a lattice with the staggered hoping parameter in the end. Our predictions are amenable to verification in the ultracold atoms experiment and promote the understanding of the anomalous behavior of the superfluid weight in the high-T_c superconductors.     

Quantifying Spontaneously Symmetry Breaking of Quantum Many-Body Systems

Spontaneous symmetry breaking is related to the appearance of emergent phenomena, while a non-vanishing order parameter has been viewed as the sign of turning into such symmetry-breaking phase. We study the spontaneous symmetry breaking in the conventional superconductor and Bose–Einstein condensation with a continuous measure of symmetry by showing that both the many-body systems can be mapped into the many spin model. We also formulate the underlying relation between the spontaneous symmetry breaking and the order parameter quantitatively. The degree of symmetry stays unity in the absence of the two emergent phenomena, while decreases exponentially at the appearance of the order parameter which indicates the inextricable relation between the spontaneous symmetry and the order parameter.     

Crossover from a pseudogap state to a superconducting state

This paper deduces that the particular electronic structure of cuprate superconductors confines Cooper pairs to be first formed in the antinodal region which is far from the Fermi surface,and these pairs are incoherent and result in the pseudogap state.With the change of doping or temperature,some pairs are formed in the nodal region which locates the Fermi surface,and these pairs are coherent and lead to superconductivity.Thus the coexistence of the pseudogap and the superconducting gap is explained when the two kinds of gaps are not all on the Fermi surface.It also shows that the symmetry of the pseudogap and the superconducting gap are determined by the electronic structure,and non-s wave symmetry gap favours the high-temperature superconductivity.Why the high-temperature superconductivity occurs in the metal region near the Mott metal-insulator transition is also explained.     

Raman phonon anomalies in Sr(Fe1-xCox)2As2

Phonon anomalies have been reported in iron-pnictide superconductors indicating a diverse interplay between different orders in the materials.Here,we report Raman scattering measurements on Sr(Fe_1-xCo_x)₂As₂(x=0 and x=0.04)single crystals in the B;symmetry with respect to a 1 Fe unit cell.Upon cooling,we observe a larger split(13 cm;)of Eg Raman phonon modes pertaining to in-plane Fe and As displacements as the crystals undergo the tetragonal-toorthorhombic structural phase transition,although a considerable split(9 cm;)has been reported in BaFe_1-xCo_x)₂As₂.Furthermore,the splitting of E;phonon modes is strongly reduced upon doping.We perform an order-parameter analysis revealing a similar doping dependence of E;phonon splitting as reported in other compounds of the 122 family,indicating these phonon anomalies widely exist in 122 iron-based superconductors and might share the same mechanisms.