The nature of the superconducting pairing symmetry in the kagome metal CsV_3Sb_5 and its relationship with the charge density wave (CDW) order are central unresolved issues. Here, we investigate the evolution of superconductivity in CsV_3Sb_5 under in-situ uniaxial pressure using ^121Sb nuclear quadrupole resonance (NQR). We find that tensile strain significantly enhances the superconducting transition temperature, T_ c, while the CDW remains unchanged, demonstrating that superconductivity can be tuned independently of the bulk charge order. At a tensile strain of ε = +0.90

Spin-triplet topological superconductors are rare but of fundamental interest as they can host Majorana bound states that can be used in fault-tolerant quantum computing. Recent efforts have been devoted to searching for spin-triplet states in U-based compounds, but these materials have a low transition temperature (T_{c}) and coexisting competing orders, which creates significant experimental challenges and often leads to contradictory conclusions. The Cr-based candidate K_{2}Cr_{3}As_{3} offers a promising alternative: it has a much higher T_{c}≥6.2  K and no magnetic order. Here we report a hallmark signature of spin-triplet superconductivity arising from the internal spin degrees of freedom via nuclear magnetic resonance measurements, and demonstrate the high tunability of the topological phases. We discovered three distinct superconducting phases and revealed the evolution of the paired-spins direction [d(k)-vector]. At low magnetic fields, K_{2}Cr_{3}As_{3} evolves from a helical (Phase A) to a chiral state (Phase B) with a rotation of the d(k)-vector from in-plane to out-of-plane direction upon cooling, although both phases have point nodes in the gap. A line-nodal gap is realized in the high-field Phase C, where the d(k)-vector lies in the basal plane. These findings establish K_{2}Cr_{3}As_{3} as a model spin-triplet superconductor and a promising platform for manipulating topological phases.

Spin-triplet topological superconductors are rare but of fundamental interest as they can host Majorana bound states that can be used in fault-tolerant quantum computing. Recent efforts have been devoted to searching for spin-triplet states in U-based compounds, but these materials have a low transition temperature (Tc) and coexisting competing orders, which creates significant experimental challenges and often leads to contradictory conclusions. The Cr-based candidate K2Cr3As3 offers a promising alternative: it has a much higher Tc of 6.2 K and no magnetic order. Here we report a hallmark signature of spin-triplet superconductivity arising from the internal spin degrees of freedom via nuclear magnetic resonance measurements, and demonstrate the high tunability of the topological phases. We discovered three distinct superconducting phases and revealed the evolution of the paired-spins direction (d(k)-vector). At low magnetic fields, K2Cr3As3 evolves from a helical (Phase A) to a chiral state (Phase B) with a rotation of the d(k)-vector from in-plane to out-of-plane direction upon cooling, although both phases have point nodes in the gap. A linenodal gap is realized in the high-field Phase C, where the d(k)-vector lies in the basal plane. These findings establish K2Cr3As3 as a model spin-triplet superconductor and a promising platform for manipulating topological phases.

Loop-current (LC) order and the associated time-reversal symmetry breaking (TRSB) are pivotal for understanding hidden magnetism and unconventional superconductivity in strongly correlated quantum materials. The recently discovered kagome metal CsV_3Sb_5 provides a unique platform for exploring these intertwined phenomena. In this study, we utilize ^121Sb nuclear quadrupole resonance (NQR) and ^51V nuclear magnetic resonance (NMR) measurements to investigate the possible existence of the LC order in CsV_3Sb_5. Below T^∗≈ 45 K, we observe a field-independent NMR linewidth broadening at the V site in a high-quality single crystal, which indicates an internal magnetic field of 3.6 Oe at the V position. We show that this internal field arises from a static LC state that produces orbital magnetic moments μ_ orb ranging from 0.002 to 0.01 μ_B. Detailed analysis suggests that the observed LC state breaks C_6 rotational symmetry to possess a low symmetry of C_2. Our results provide microscopic evidence for LC order in the charge density wave (CDW) phase of CsV_3Sb_5 and show that TRSB is intertwined with electronic nematicity, imposing stringent constraints on microscopic descriptions of the kagome CDW and its relation to superconductivity.

The doped topological insulator Cu_{x}Bi_{2}Se_{3} has attracted considerable attention as a new platform for studying novel properties of spin-triplet and topological superconductivity. In this work, we performed synchrotron x-ray diffraction measurements on Cu_{x}Bi_{2}Se_{3} (0.24≤x≤0.46) to investigate the coupling between the superconducting order parameter and crystal lattice. In the crystals in which the vector order parameter (d vector) is tilted from the crystal high-symmetry directions as evidenced by nematic diamagnetic susceptibility, we find a sizable lattice distortion (∼100  ppm) associated with the onset of superconductivity. In contrast, in crystals with the d vector aligned along the high-symmetry directions, we find no appreciable change in lattice constant. Together with a pronounced vestigial behavior of the distortion, the results are clear evidence for an odd-parity E_{u} order parameter that couples with trigonal lattice. Furthermore, in the crystal with x=0.46 where diamagnetic susceptibility is isotropic in the plane, no lattice distortion accompanying the superconducting transition is found, which is in line with a chiral superconducting state in the highly doped region. Our work shows that lattice distortion can be a powerful diagnosing quantity for nematic superconductivity with two-component order parameter.

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is a superconducting phase characterized by broken translational symmetry, where Cooper pairs form with nonzero momentum between Zeeman-split Fermi surfaces. This state is highly sensitive to band structure and pairing symmetry. In multiband superconductors, the FFLO state can significantly deviate from its standard form, but experimental verification has remained challenging. Here, we present 75As nuclear magnetic resonance (NMR) measurements on the multiband superconductor KFe2As2. In the low-temperature, high-magnetic-field region above the upper critical field Bc2, we observe a clear increase in the second moment of the NMR spectrum, along with a strong enhancement in the spin-lattice relaxation rate divided by temperature 1/T1T. These results indicate an emergence of superconducting spin smecticity and Andreev bound states from the spatial modulation of the superconducting gap, providing microscopic evidence for the FFLO state. The obtained phase diagram reveals a distinct boundary line between the FFLO and homogenous superconducting states with a low critical temperature of the FFLO state T & lowast; approximate to 0.2Tc, which can be attributed to the multiband effects in KFe2As2. Our results show that the iron-based superconductors are a good material platform for studying the FFLO state and highlight the importance of the multiband effects on this exotic phase.

The discovery of the kagome metal CsV 3 Sb 5 has generated significant interest in its complex physical properties, particularly its superconducting behavior under different pressures, though its nature remains debated. Here, we performed low-temperature, high-pressure 121/123 Sb nuclear quadrupole resonance (NQR) measurements to explore the superconducting pairing symmetry in CsV 3 Sb 5 . At ambient pressure, we found that the spin-lattice relaxation rate 1/ T 1 exhibits a kink at T ~ 0.4 T c within the superconducting state and follows a T 3 variation as temperature further decreases. This suggests the presence of two superconducting gaps with line nodes in the smaller one. As pressure increases beyond P c ~ 1.85 GPa, where the charge-density wave phase is completely suppressed, 1/ T 1 shows no Hebel-Slichter peak just below T c , and decreases rapidly, even faster than T 5 , indicating that the gap is fully opened for pressures above P c . In this high pressure region, the angular dependence of the in-plane upper critical magnetic field H c2 breaks the C 6 rotational symmetry. We propose the s + i d pairing at P > P c which explains both the 1/ T 1 and H c2 behaviors. Our findings indicate that CsV 3 Sb 5 is an unconventional superconductor and its superconducting state is even more exotic at high pressures.

The recent discovery of superconductivity in La3Ni2O7-delta with a transition temperature Tc close to 80 K at high pressures has attracted significant attention, due particularly to a possible density wave (DW) transition occurring near the superconducting dome. Identifying the type of DW order is crucial for understanding the origin of superconductivity in this system. However, owing to the presence of La4Ni3O10 and other intergrowth phases in La3Ni2O7-delta samples, extracting the intrinsic information from the La3Ni2O7 phase is challenging. In this study, we employed 139La nuclear quadrupole resonance (NQR) measurements to eliminate the influence of other structural phases in the sample and obtain microscopic insights into the DW transition in La3Ni2O7-delta. Below the DW transition temperature TDW similar to 153 K, we observe a distinct splitting in the +/- 5/2 <-> +/- 7/2 transition of the NQR resonance peak at the La(2) site, while only a line broadening is seen in the +/- 3/2 <-> +/- 5/2 transition peak. Through further analysis of the spectra, we show that the line splitting is due to a unidirectional charge modulation. A magnetic line broadening is also observed below TDW, accompanied by a large enhancement of the spin-lattice relaxation rate, indicating the formation of magnetically ordered moments in the DW state. Our results suggest a simultaneous formation of charge- and spin-density wave orders in La3Ni2O7-delta, thereby offering critical insights into the electronic correlations in Ni-based superconductors.

AbstractThe mechanism of high-temperature superconductivity in copper oxides (cuprate) remains elusive, with the pseudogap phase considered a potential factor. Recent attention has focused on a long-range symmetry-broken charge-density wave (CDW) order in the underdoped regime, induced by strong magnetic fields. Here by 63,65Cu-nuclear magnetic resonance, we report the discovery of a long-range CDW order in the optimally doped Bi2Sr2−xLaxCuO6 superconductor, induced by in-plane strain exceeding ∣ε∣ = 0.15 %, which deliberately breaks the crystal symmetry of the CuO2 plane. We find that compressive/tensile strains reduce superconductivity but enhance CDW, leaving superconductivity to coexist with CDW. The findings show that a long-range CDW order is an underlying hidden order in the pseudogap state, not limited to the underdoped regime, becoming apparent under strain. Our result sheds light on the intertwining of various orders in the cuprates.

We measured the DC magnetic susceptibility of single crystals of the quasi-one-dimensional superconductor Cs2Cr3As3. Diamagnetism appears below 1.2 and 2 K for magnetic fields parallel and perpendicular to the c-axis, respectively, whereas the Meissner effect emerges at 1.2 K in both directions, suggesting that, between 1.2 and 2 K, superconductivity is filamentary along the c-axis.

Electronic nematicity, a consequence of rotational symmetry breaking, is an emergent phenomenon in various new materials. In order to fully utilize the functions of these materials, ability of tuning them through a knob, the nematic director, is desired. Here we report a successful manipulation of the nematic director, the vector order-parameter (d-vector), in the spin-triplet superconducting state of CuxBi2Se3 by magnetic fields. At H = 0.5 T, the ac susceptibility related to the upper critical field shows a two-fold symmetry in the basal plane. At H = 1.5 T, however, the susceptibility shows a six-fold symmetry, which has never been reported before in any superconductor. These results indicate that the d-vector initially pinned to a certain direction is unlocked by a threshold field to respect the trigonal crystal symmetry. We further reveal that the superconducting gap in different crystals converges to p_x symmetry at high fields, although it differs at low fields.

We report single crystal growth of strongly-correlated compound K$_2$Cr$_3$As$_3$ with superconducting temperature $T_{\textrm c}$=6.2 K, and the measurements of magnetic susceptibility $\chi$ above $T_{\textrm c}$. We determined the hyperfine coupling constants directly from the relation between the Knight shift ($K$) and susceptibility ($K$-$\chi$ plot) and obtained the orbital contribution $K_{\textrm{orb}}$. Our results of $K_{\textrm{orb}}$ is in fairly good agreement with the previous estimate using a novel method, and reinforce the conclusion that K$_2$Cr$_3$As$_3$ is a spin-triplet superconductor.

Spin-triplet superconductors are novel materials capable of harboring Majorana bound states that can be used in topological quantum computing. However, such bulk materials are still rare. Here we review the results that established K2Cr3As3 as a spin-triplet superconductor with transition temperature T_c as high as 6.5 K. We focus on the multiple-phases feature, and its exquisite distance to a ferromagnetic quantum critical point which is likely responsible for the high T_c. We touch on the topological aspect of the superconducting state, and suggest that it is a new route to the technical implementation using a topological spin-triplet superconductor at the highest temperature ever.

We report ^{195}Pt nuclear magnetic resonance (NMR) measurements on topological superconductor candidate YPtBi, which has broken inversion symmetry and topological nontrivial band structures due to the strong spin-orbit coupling. In the normal state, we find that Knight shift K is field- and temperature independent, suggesting that the contribution from the topological bands is very small at low temperatures. However, the spin-lattice relaxation rate 1/T_{1} divided by temperature (T), 1/T_{1}T, increases with decreasing T, implying the existence of antiferromagnetic spin fluctuations. In the superconducting state, no Hebel-Slichter coherence peak is seen below T_{c} and 1/T_{1} follows T^{3} variation, indicating the unconventional superconductivity. The finite spin susceptibility at zero-temperature limit and the anomalous increase of the NMR linewidth below T_{c} point to a mixed state of spin-singlet and spin-triplet (or spin-septet) pairing.

Clarifying the interplay between charge-density waves (CDWs) and superconductivity is important in the kagome metal CsV 3 Sb 5 , and pressure ( P ) can play a crucial role. Here, we present 121/123 Sb nuclear quadrupole resonance (NQR) measurements under hydrostatic pressures up to 2.43 GPa in CsV 3 Sb 5 single crystals. We demonstrate that the CDW gradually changes from a commensurate modulation with a star-of-David (SoD) pattern to an incommensurate one with a superimposed SoD and Tri-hexagonal (TrH) pattern stacking along the c -axis. Moreover, the linewidth δ ν of 121/123 Sb-NQR spectra increases with cooling down to T CDW , indicating the appearance of a short-range CDW order due to CDW fluctuations pinned by quenched disorders. The δ ν shows a Curie–Weiss temperature dependence and tends to diverge at P c ~ 1.9 GPa, suggesting that a CDW quantum critical point (QCP) exists at P c where T c shows the maximum. For P > P c , spin fluctuations are enhanced when the CDW is suppressed. Our results suggest that the maximal T c at P c ~ 1.9 GPa is related to the CDW QCP, and the presence of spin fluctuations prevents the T c from a rapid decrease otherwise, after the CDW is completely suppressed.

AV3Sb5 (A = K, Rb, Cs) is a novel kagome superconductor coexisting with the charge density wave (CDW) order. Identifying the structure of the CDW order is crucial for understanding the exotic normal state and superconductivity in this system. Here, we report 51V nuclear magnetic resonance (NMR) and 121/123Sb nuclear quadrupole resonance (NQR) studies on kagome-metal CsV3Sb5. Below the CDW transition temperature TCDW ~ 98 K, an abrupt change of spectra was observed, indicating that the transition is of the first order. By further analyzing the spectra, we find that the CDW order is commensurate. And most remarkably, the obtained experimental results suggest that the charge modulation of the CDW order is of star-of-David pattern and accompanied by an additional charge modulation in bulk below T* ~ 40 K. Our results revealing the unconventional CDW order provide new insights into AV3Sb5.

The discovery of a magnetic -field-induced charge-density-wave (CDW) order in the pseudogap state via nuclear magnetic resonance (NMR) studies has highlighted the importance of "charge" in the physics of high transition temperature (T-c) superconductivity in copper oxides (cuprates). Herein, after briefly reviewing the progress achieved in the last few years, we report new results of Cu-63,Cu-65-NMR measurements on the CDW order and its fluctuation in the single-layered cuprate Bi2Sr2-xLaxCuO6+delta. The NMR spectrum under both in-and out-of-plane magnetic fields above H = 10 T indicates that the CDW replaces the antiferromagnetic order before superconductivity appears, but disappears before superconductivity is optimized. We found that the CDW onset temperature TCDW scales with the pseudogap temperature T*. Comparison between Cu-63 and Cu-65 NMR indicates that the spin-lattice relaxation process is dominated by charge fluctuations in the doping regions where the CDW appears as well as at the pseudogap end point (T* = 0). These results suggest that charge orders and fluctuations exist in multiple doping regions and over a quite wide temperature range.

A spin-triplet superconductor with ferromagnetic spin fluctuation superconducts at a critical temperature of 6.5 K.

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 Tc 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 Tc 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.