NMR investigation of the quasi-one-dimensional superconductor K(2)Cr(3)As(3)

Spin-triplet superconductivity in K2Cr3As3

A spin-triplet superconductor can harbor Majorana bound states that can be used in topological quantum computing. Recently, K₂Cr₃As₃ and its variants with critical temperature T_c as high as 8 kelvin have emerged as a new class of superconductors with ferromagnetic spin fluctuations. Here, we report a discovery in K₂Cr₃As₃ single crystal that the spin susceptibility measured by ⁷⁵As Knight shift below T_c is unchanged with the magnetic field H₀ applied in the ab plane but vanishes toward zero temperature when H₀ is along the c axis, which unambiguously establishes this compound as a spin-triplet superconductor described by a vector order parameter d→ parallel to the c axis. Combining with point nodal gap, we show that K₂Cr₃As₃ is a new platform for the study of topological superconductivity and its possible technical application.

Robust Superconductivity in Quasi-one-dimensional Multiband Materials

Recently it has been demonstrated that the pair-exchange coupling of quasi-one-dimensional (Q1D) bands with conventional higher-dimensional bands in one multiband superconducting material can result in the formation of a robust aggregate pair condensate. In particular, it has been found that the Q1D thermal pair fluctuations are suppressed in the presence of deep conventional band(s), for which the Fermi level is much larger than the characteristic cutoff energy. Here we report that the impact of the Q1D fluctuations is significantly weakened even in the presence of nearly shallow higher-dimensional band(s), which shed new light on the robust superconducting state observed in emerging chain-like-structured superconducting materials A₂Cr₃As₃ (A = K, Rb, Cs).

Microstructure of quasi-one-dimensional superconductor KCr3As3prepared by K-ion deintercalation

The microstructure of quasi-one-dimensional KCr₃As₃(133) superconductors, which were prepared by chemical cation deintercalation from their counterpart K₂Cr₃As₃(233) compounds, are investigated using scanning transmission electron microscopy. The nominal KCr₃As₃crystals generally exhibit irregular nanoscale 133-phase domains accompanied by an amorphous As-deficient phase and cracks as a result of alkali cation deintercalation processes. Analysis of local defective structures reveals the existence of an intermediate state in the transformation from 233 to 133 phase and a possible K-deficient 233-type structure as a nanoscale cluster. Our microscopic investigations offer insight into the microstructure of KCr₃As₃and the alkali metal cation deintercalation processes.

Multiband Material with a Quasi-1D Band as a Robust High-Temperature Superconductor

It is well known that superconductivity in quasi-one-dimensional (Q1D) materials is hindered by large fluctuations of the order parameter. They reduce the critical temperature and can even destroy the superconductivity altogether. Here it is demonstrated that the situation changes dramatically when a Q1D pair condensate is coupled to a higher-dimensional stable one, as in recently discovered multiband Q1D superconductors. The fluctuations are suppressed even by vanishingly small pair-exchange coupling between different band condensates and the superconductor is well described by the mean field theory. In this case the low dimensionality effects enhance the coherence of the system instead of suppressing it. As a result, the critical temperature of the multiband Q1D superconductor can increase by orders of magnitude when the system is tuned to the Lifshitz transition with the Fermi level close to the edge of the Q1D band.

Normal-state properties of the quasi-one-dimensional superconductor Ta4Pd3Te16

We examined the physical properties of the quasi-one-dimensional superconductor Ta₄Pd₃Te₁₆ in the normal state by detailed measurements of susceptibility, in-plane anisotropic resistivity, magnetoresistance, Hall resistivity, and Seebeck coefficient. The large Wilson ratio, as inferred from normal-state susceptibility, indicates strong electron-electron interaction. The Hall and Seebeck coefficients show not only significant temperature-dependent behavior, indicating the multiband effect, but also an obvious anomaly around T ₁  =  40 K. Analyses of both the Hall resistivity and thermopower using a two-band model indicate that the electrons dominate the electrical transport at low temperatures. Our results imply that it is the quantum fluctuations of the charge order taking place in the temperature range 30-50 K that may result in the abnormal normal-state properties of Ta₄Pd₃Te₁₆.

Tuning the Distance to a Possible Ferromagnetic Quantum Critical Point in A_{2}Cr_{3}As_{3}

Although superconductivity in the vicinity of an antiferromagnetic (AFM) instability has been extensively explored in the last three decades or so, superconductivity in compounds with a background of ferromagnetic (FM) spin fluctuations is still rare. We report ^{75}As nuclear quadrupole resonance measurements on the A_{2}Cr_{3}As_{3} family, which is the first group of Cr-based superconductors at ambient pressure, with A being alkali elements. From the temperature dependence of the spin-lattice relaxation rate (1/T_{1}), we find that by changing A in the order of A=Na, Na_{0.75}K_{0.25}, K, and Rb, the system is tuned to approach a possible FM quantum critical point (QCP). This may be ascribed to the Cr2-As2-Cr2 bond angle that decreases towards 90°, which enhances the FM interaction via the Cr2-As2-Cr2 path. Upon moving away from the QCP, the superconducting transition temperature T_{sc} increases progressively up to 8.0 K in Na_{2}Cr_{3}As_{3}, which is in sharp contrast to the AFM case where T_{sc} usually shows a maximum around a QCP. The 1/T_{1} decreases rapidly below T_{sc} with no Hebel-Slichter peak, and ubiquitously follows a T^{5} variation below a characteristic temperature T^{*}≈0.6 T_{sc}, which indicates the existence of point nodes in the superconducting gap function commonly in the family. These results suggest that the A_{2}Cr_{3}As_{3} family is a possible solid-state analog of superfluid ^{3}He.

Na-doping effects on structural evolution and superconductivity in (K1-x Na x )2Cr3As3 (x = 0-1)

In this report, we studied the effects of isovalent Na-doping on the recently discovered quasi-one-dimensional Cr-based unconventional superconductor K₂Cr₃As₃. A series of polycrystalline samples with nominal component (K_1-x Na _x )₂Cr₃As₃ (x  =  0-1) were synthesized by the solid state reaction method. From crystal structure and chemical phase characterizations, we found two distinct chemical phases with the same hexagonal structure but distinguished by different site occupancy of Na⁺ ions at the two kinds of K-site in the K₂Cr₃As₃ lattice structure. When x  ⩽  0.4, the doped samples form a continuous sosoloid phase of (K_1-x Na _x )₂Cr₃As₃ with the Na⁺ ions randomly doping at the K-sites (denoted as α-phase); when x  ⩾  0.5, a novel individual phase of (K_0.25Na_0.75)₂Cr₃As₃ emerges, in which the Na⁺ ions selectively occupy all the '3k' sites and the K⁺ ions occupy the '1c' sites (denoted as β-phase). No chemical phase of Na₂Cr₃As₃ was detected. Superconductivity in these samples was studied by electrical transport and magnetic susceptibility measurements, and it evolves in a much sophisticated manner. In the α-phase, the superconducting T _c decreases quickly upon Na-doping. All these α-phase samples have surprisingly low superconducting volume fraction and relatively low T _c compared with the undoped K₂Cr₃As₃. However, the β-phase has a clearly enhanced T _c up to 7.6 K which locates between the values of K₂Cr₃As₃ and Na₂Cr₃As₃, and exhibits a full superconducting shielding signal.

Triplet superconductivity in coupled odd-gon rings

Shedding light on the nature of spin-triplet superconductivity has been a long-standing quest in condensed matter physics since the discovery of superfluidity in liquid ³He. Nevertheless, the mechanism of spin-triplet pairing is much less understood than that of spin-singlet pairing explained by the Bardeen-Cooper-Schrieffer theory or even observed in high-temperature superconductors. Here we propose a versatile mechanism for spin-triplet superconductivity which emerges through a melting of macroscopic spin polarization stabilized in weakly coupled odd-gon (e.g., triangle, pentagon, etc) systems. We demonstrate the feasibility of sustaining spin-triplet superconductivity with this mechanism by considering a new class of quasi-one-dimensional superconductors A₂Cr₃As₃ (A = K, Rb, and Cs). Furthermore, we suggest a simple effective model to easily illustrate the adaptability of the mechanism to general systems consisting of odd-gon units. This mechanism provides a rare example of superconductivity from on-site Coulomb repulsion.

Progress in Cr- and Mn-based superconductors: a key issues review

The presence of magnetic ions was first believed to be detrimental to superconductivity. However, unconventional superconductivity has been widely induced by doping or applying external pressure in magnetic systems such as heavy fermion, cuprate and iron-based superconductors in which magnetic fluctuations are suggested to serve as the pairing glue for Cooper pairs. The discovery of superconductivity in the magnetic compounds CrAs and MnP under high pressures has further expanded this family of superconductors and provided new platforms for investigating the interplay between magnetism and superconductivity. CrAs and MnP represent the first superconductors among the transition metal Cr- and Mn-based compounds in which the electronic states near the Fermi level are dominated by Cr/Mn 3d electrons. Shortly after their discovery, new types of Cr-based quasi-one-dimensional superconductors A₂Cr₃As₃ and ACr₃As₃ (A [Formula: see text] K, Rb, Cs or Na) were discovered at ambient pressure. The close proximity of superconductivity to magnetic instability in these systems suggests that spin fluctuations may play crucial roles in mediating the Cooper pairing. In this article we review the basic physical properties of these novel superconductors and the progress achieved in recent studies.

Frustrated Structural Instability in Superconducting Quasi-One-Dimensional K_{2}Cr_{3}As_{3}

We present density functional theory and neutron total scattering studies on quasi-one-dimensional superconducting K_{2}Cr_{3}As_{3} revealing a frustrated structural instability. Our first principles calculations find a significant phonon instability, which, under energy minimization, corresponds to a frustrated orthorhombic distortion. In neutron diffraction studies we find large atomic displacement parameters with anomalous temperature dependencies, which result from highly localized orthorhombic distortions of the CrAs sublattice and coupled K displacements. These results suggest a more complex phase diagram than previously assumed for K_{2}Cr_{3}As_{3} with subtle interplays of structure, electron-phonon, and magnetic interactions.

Superconductivity at 10.4 K in a novel quasi-one-dimensional ternary molybdenum pnictide K2Mo3As3

Here we report the discovery of the first ternary molybdenum pnictide based superconductor K₂Mo₃As₃. Polycrystalline samples were synthesized by the conventional solid state reaction method. X-ray diffraction analysis reveals a quasi-one-dimensional hexagonal crystal structure with (Mo₃As₃)^2- linear chains separated by K⁺ ions, similar as previously reported K₂Cr₃As₃, with the space group of P-6m2 (No. 187) and the refined lattice parameters a = 10.145(5) Å and c = 4.453(8) Å. Electrical resistivity, magnetic susceptibility, and heat capacity measurements exhibit bulk superconductivity with the onset T_c at 10.4 K in K₂Mo₃As₃ which is higher than the isostructural Cr-based superconductors. Being the same group VIB transition elements and with similar structural motifs, these Cr and Mo based superconductors may share some common underlying origins for the occurrence of superconductivity and need more investigations to uncover the electron pairing within a quasi-one-dimensional chain structure.

Effect of hydrostatic pressure on the superconducting properties of quasi-1D superconductor K2Cr3As3

K₂Cr₃As₃ is a newly discovered quasi-1D superconductor with a T _c  =  6.1 K and an upper critical field µ ₀ H _c2(0)  ≈  40 T three times larger than the Pauli paramagnetic limit µ ₀ H _p that is suggestive of a spin-triplet Cooper pairing. In this paper, we have investigated the effects of hydrostatic pressure on its T _c and µ ₀ H _c2 by measuring the ac magnetic susceptibility χ'(T) under magnetic fields at various hydrostatic pressures up to 7.5 GPa. The major findings include: (1) T _c is suppressed gradually to below 2 K at 7.5 GPa; (2) the estimated µ ₀ H _c2(0) decreases dramatically to below µ ₀ H _p above ~2 GPa and becomes slight lower than the orbital limiting field [Formula: see text] estimated from the initial slope of upper critical field via [Formula: see text]  =  -0.73T _cdH _c2/[Formula: see text] in the clean limit; (3) the estimated Maki parameter α  =  √2[Formula: see text]/H _p drops from 4 at ambient pressure to well below 1 at P  >  2 GPa, suggesting the crossover from Pauli paramagnetic limiting to orbital limiting in the pair breaking process upon increasing pressure. These observations suggested that the application of hydrostatic pressure could drive K₂Cr₃As₃ away from the ferromagnetic instability and lead to a breakdown of the spin-triplet pairing channel. We have also made a side-by-side comparison and discussed the distinct effects of chemical and physical pressures on the superconducting properties of K₂Cr₃As₃.

Anisotropic upper critical magnetic fields in Rb2Cr3As3 superconductor

Rb₂Cr₃As₃ is a structurally one-dimensional superconductor containing Cr₃As₃ chains with a superconducting transition temperature of [Formula: see text] K. Here we report the electrical resistance measurements for Rb₂Cr₃As₃ single crystals, under magnetic fields up to 29.5 T and at temperatures down to 0.36 K, from which the upper critical fields, [Formula: see text], can be obtained in a broad temperature range. For field parallel to the Cr₃As₃ chains, [Formula: see text] is paramagnetically limited with an initial slope of [Formula: see text]d[Formula: see text]/d[Formula: see text] T [Formula: see text] and a zero-temperature upper critical field of [Formula: see text] T. For field perpendicular to the Cr₃As₃ chains, however, [Formula: see text] is only limited by orbital pair-breaking effect with [Formula: see text]d[Formula: see text]/d[Formula: see text] T [Formula: see text]. As a consequence, the anisotropy [Formula: see text] decreases sharply near T _c and reverses below 2 K. Remarkably, the low-temperature [Formula: see text] down to 0.075 [Formula: see text] remains to increase linearly up to over three times the Pauli paramagnetic limit, which strongly suggests dominant spin-triplet superconductivity in Rb₂Cr₃As₃.

Multiband One-Dimensional Electronic Structure and Spectroscopic Signature of Tomonaga-Luttinger Liquid Behavior in K_{2}Cr_{3}As_{3}

We present angle-resolved photoemission spectroscopy measurements of the quasi-one-dimensional superconductor K_{2}Cr_{3}As_{3}. We find that the Fermi surface contains two Fermi surface sheets, with linearly dispersing bands not displaying any significant band renormalizations. The one-dimensional band dispersions display a suppression of spectral intensity approaching the Fermi level according to a linear power law, over an energy range of ∼200  meV. This is interpreted as a signature of Tomonoga-Luttinger liquid physics, which provides a new perspective on the possibly unconventional superconductivity in this family of compounds.

Superconductivity and spin-orbit coupling in non-centrosymmetric materials: a review

In non-centrosymmetric superconductors, where the crystal structure lacks a centre of inversion, parity is no longer a good quantum number and an electronic antisymmetric spin-orbit coupling (ASOC) is allowed to exist by symmetry. If this ASOC is sufficiently large, it has profound consequences on the superconducting state. For example, it generally leads to a superconducting pairing state which is a mixture of spin-singlet and spin-triplet components. The possibility of such novel pairing states, as well as the potential for observing a variety of unusual behaviors, led to intensive theoretical and experimental investigations. Here we review the experimental and theoretical results for superconducting systems lacking inversion symmetry. Firstly we give a conceptual overview of the key theoretical results. We then review the experimental properties of both strongly and weakly correlated bulk materials, as well as two dimensional systems. Here the focus is on evaluating the effects of ASOC on the superconducting properties and the extent to which there is evidence for singlet-triplet mixing. This is followed by a more detailed overview of theoretical aspects of non-centrosymmetric superconductivity. This includes the effects of the ASOC on the pairing symmetry and the superconducting magnetic response, magneto-electric effects, superconducting finite momentum pairing states, and the potential for non-centrosymmetric superconductors to display topological superconductivity.

Correlation between superconductivity and bond angle of CrAs chain in non-centrosymmetric compounds A2Cr3As3 (A = K, Rb)

Non-centrosymmetric superconductors, whose crystal structure is absent of inversion symmetry, have recently received special attentions due to the expectation of unconventional pairings and exotic physics associated with such pairings. The newly discovered superconductors A2Cr3As3 (A = K, Rb), featured by the quasi-one dimensional structure with conducting CrAs chains, belongs to such kind of superconductor. In this study, we are the first to report the finding that superconductivity of A2Cr3As3 (A = K, Rb) has a positive correlation with the extent of non-centrosymmetry. Our in-situ high pressure ac susceptibility and synchrotron x-ray diffraction measurements reveal that the larger bond angle of As-Cr-As (defined as α) in the CrAs chains can be taken as a key factor controlling superconductivity. While the smaller bond angle (defined as β) and the distance between the CrAs chains also affect the superconductivity due to their structural connections with the α angle. We find that the larger value of α-β, which is associated with the extent of the non-centrosymmetry of the lattice structure, is in favor of superconductivity. These results are expected to shed a new light on the underlying mechanism of the superconductivity in these Q1D superconductors and also to provide new perspective in understanding other non-centrosymmetric superconductors.

Formation of Molecular-Orbital Bands in a Twisted Hubbard Tube: Implications for Unconventional Superconductivity in K_{2}Cr_{3}As_{3}

We study a twisted Hubbard tube modeling the [CrAs]_{∞} structure of quasi-one-dimensional superconductors A_{2}Cr_{3}As_{3} (A=K, Rb, Cs). The molecular-orbital bands emerging from the quasi-degenerate atomic orbitals are exactly solved. An effective Hamiltonian is derived for a region where three partially filled bands intersect the Fermi energy. The deduced local interactions among these active bands show a significant reduction compared to the original atomic interactions. The resulting three-channel Luttinger liquid shows various interaction-induced instabilities including two kinds of spin-triplet superconducting instabilities due to gapless spin excitations, with one of them being superseded by the spin-density-wave phase in the intermediate Hund's coupling regime. The implications of these results for the alkali chromium arsenides are discussed.

Ferromagnetic Spin Fluctuation and Unconventional Superconductivity in Rb2Cr3As3 Revealed by 75As NMR and NQR

We report (75)As nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) studies on the superconductor Rb(2)Cr(3)As(3) with a quasi-one-dimensional crystal structure. Below T∼100  K, the spin-lattice relaxation rate (1/T(1)) divided by temperature, 1/T(1)T, increases upon cooling down to T(c)=4.8  K, showing a Curie-Weiss-like temperature dependence. The Knight shift also increases with decreasing temperature. These results suggest ferromagnetic spin fluctuation. In the superconducting state, 1/T(1) decreases rapidly below T(c) without a Hebel-Slichter peak, and follows a T(5) variation below T∼3  K, which points to unconventional superconductivity with point nodes in the gap function.

Links between the Crystal and Electronic Structure in the New Family of Unconventional Superconductors A2Cr3As3 (A = K, Rb, Cs)

The electronic structure of a new family of superconductors is examined through density functional theory calculations. In contrast with other quasi-1D superconductors, these phases exhibit a relatively complex electronic structure and the Fermi surface contains both 1D and 3D components. It is shown that cations have an almost nil influence on the electronic structure. The absence of a structural Peierls modulation is discussed, and the differences with the structurally related M2Mo6Se6 (M = Tl, In, ...) superconductors are stressed. The large electron mass renormalization and the lack of clear correlation between N(EF) and Tc suggest the existence of strong electron correlations and an unconventional origin of the superconductivity.