Chiral carbon nanostructures have been found to display unexpected magnetic behaviors. Several theoretical calculations performed in the macroscopic limit q=0 have addressed or predicted some of these findings. To gain more insight into the magnetism of these systems at finite q, here we use linear response theory to calculate the wave-vector-dependent spin susceptibility χ(q,0) in a half-filling tight-binding model of a helix of carbon atoms with intrinsic spin-orbit coupling (SOC). We find that at the nesting wave number q=2kF the paramagnetic state of the system is unstable with respect to the formation of a spin-density-wave type state. Chirality has a small effect on the paramagnetic phase but has no impact on the spin-density-wave type state. Published by the American Physical Society 2024

Some theoretical studies using perturbation and tight-binding methods have tried to shed light on the magnetic behaviors of carbon-based nanostructures in the limit of wave vector 𝐪=0 . In a recent work, we studied a half-filled model of helical carbon chains to gain new insights for 𝐪 0 . Although in carbon the energy bands are usually derived from partially filled atomic p-shells, here we explore the hole contribution to these magnetic responses. We calculate the longitudinal spin susceptibility of an almost-filled tight-binding model of a helical chain for 𝐪 0 . We find that when the Fermi level lies at the band edges, the system shows for positive chirality a divergent paramagnetic susceptibility. This result is in agreement with that previously reported for the macroscopic limit 𝐪=0 .

By determining the superconducting lower and upper critical fields H-c1(T) and H-c2(T), respectively, in a high-purity spherical Sr2RuO4 sample via ac-susceptibility measurements, we obtain the temperature dependence of the coherence length xi and the penetration depth lambda down to 0.04T(c). Given the high sample quality, the observed T-2 dependence of lambda at low temperatures cannot be explained in terms of impurity effects. Instead, we argue that the weak type-II superconductor Sr2RuO4 has to be treated in the nonlocal limit. By comparing our data with existing theory in that limit, the penetration depth in Sr2RuO4 agrees with a gap structure having vertical line nodes, while horizontal line nodes cannot account for the observation. The work highlights the potential benefits of purifying other unconventional superconductors in order to access the fascinating nonlocal regime in more materials and to determine their Cooper pair wave functions.

We report a $\mu$SR investigation of a non-centrosymmetric superconductor (LaNiC$_2$) in single crystal form. Compared to previous $\mu$SR studies of non-centrosymmetric superconducting polycrystalline and powder samples, the unambiguous orientation of single crystals enables a simultaneous determination of the absolute value of the magnetic penetration depth and the vortex core size from measurements that probe the magnetic field distribution in the vortex state. The magnetic field dependence of these quantities unambiguously demonstrates the presence of two nodeless superconducting energy gaps. In addition, we detect weak internal magnetic fields in the superconducting phase, confirming earlier $\mu$SR evidence for a time-reversal symmetry breaking superconducting state. Our results suggest that Cooper pairing in LaNiC$_2$ is characterized by the same interorbital equal-spin pairing model introduced to describe the pairing state in the centrosymmetric superconductor LaNiGa$_2$.

We report measurements of the temperature dependence of the magnetic penetration depth in different quality polycrystalline samples of noncentrosymmetric LaNiC2 down to 0.05 K. This compound has no magnetic phases and breaks timereversal symmetry. In our highest quality sample we observe a T 2 dependence below 0.4Tc indicative of nodes in the energy gap. We argue that previous results suggesting conventional s-wave behavior may have been affected by magnetic impurities. PACS numbers: 74.20.Rp, 74.25.Nf, 74.70.Dd E-mail: ijbonalde@gmail.com ‡ Present address: Laboratoire National des Champs Magnétiques Intenses, INSA UPS UJF CNRS, UPR 3228, Université de Toulouse, 143 av. de Rangueil, 31400 Toulouse, France.

In most strongly correlated electron systems superconductivity appears nearby a magnetic quantum critical point (QCP) which is believed to cause unconventional behaviors. In order to explore this physics, we present here a study of the heavy-fermion superconductors CeIrSi3 and CeRhSi3 carried out using a newly developed system for high-resolution magnetic penetration-depth measurements under pressure. Superconductivity in CeIrSi3 shows a change from an excitation spectrum with a line-nodal gap to one which is entirely gapful when pressure is close but not yet at the QCP. In contrast, CeRhSi3 does not possess a T = 0 quantum phase transition and the superconducting phase remains for all accessible pressures with a nodal gap. Combining both results suggests that in these compounds unconventional superconducting behaviors are rather connected with the coexisting antiferromagnetic order. This study provides another viewpoint on the interplay of superconductivity, magnetism, and quantum criticality in CeIrSi3 and CeRhSi3 and maybe in other heavy fermions.

In this work we aim to analyze the effect of a strong antisymmetric spin–orbit coupling (ASOC) on the superconductivity of noncentrosymmetric LaPtSi. We study the energy gap structure of polycrystalline LaPtSi by using magnetic penetration depth measurements down to 0.02Tc. We observed a dirty s-wave behavior, which provides compelling evidence that the spin-singlet component of the mixed pairing state is highly dominant. This is consistent with previous results in the sense that the mere presence of a strong ASOC does not lead to unconventional behaviors. Our result also downplays LaPtSi as a good candidate for realizing time-reversal invariant topological superconductivity.

Superconductivity in noncentrosymmetric LaNiC2 is expected to be induced by electron-phonon interactions due to its lack of magnetic instabilities. The non-Bardeen-Cooper-Schrieffer (BCS) behaviors found in this material call into question the long-standing idea that relates unconventional superconductivity with magnetic interactions. Here we report magnetic penetration-depth measurements in a high-purity single crystal of LaNiC2 at pressures up to 2.5 GPa and temperatures down to 0.04 K. At ambient pressure and below 0.5T(c) the penetration depth goes as T-4 for the in-plane and T-2 for the out-of-plane component, firmly implying the existence of point nodes in the energy gap and the unconventional character of this superconductor. The present study also provides evidence of magnetism in LaNiC2 by unraveling a pressure-induced antiferromagnetic phase inside the superconducting state at temperatures below 0.5 K, with a quantum critical point around ambient pressure. The results presented here maintain a solid base for the notion that unconventional superconductivity only arises near magnetic order or fluctuations.

This work extends the calculations performed by G. Litak, T. Ord, K. Rage, and A. Vargunin, Physica C 483, 30 (2012), by including second nearest neighbors in an attractive two-orbital Hubbard model. We assumed that both the intra-orbital (U-i,U-j with i = 1, 2) and the inter-orbital Hubbard correlations (U-i,U- j with i not equal j) are negative; namely, U-i,U-j <= 0, for all(i, j). We calculated the T - n phase diagram in the mean-field approximation. For a finite chemical potential xi(0)(1) and a certain second nearest-neighbor parameter t(2) superconductivity develops in two dome-like regions, each of which has its own energy gap. Notoriously, for t(2)/vertical bar t1 vertical bar = 0.70 and xi 0(1)/vertical bar t1 vertical bar = 3 where t(1) is the nearest-neighbor parameter, T-c becomes zero around n = 2.5. (C) 2017 Elsevier B.V. All rights reserved.

Superconductivity and magnetism are mutually exclusive in most alloys and elements, so it is striking that superconductivity emerges around a magnetic quantum critical point (QCP) in many strongly correlated electron systems (SCES). In the latter case superconductivity is believed to be unconventional and directly influenced by the QCP. However, experimentally unconventional superconductivity has neither been established nor directly been linked to any mechanism of the QCP. Here we report measurements in the heavy-fermion superconductors CeIrSi$_3$ and CeRhSi$_3$. The measurements were performed with a newly developed system, first of its kind, that allows high-resolution studies of the superconducting gap structure under pressure. Superconductivity in CeIrSi$_3$ shows a change from an excitation spectrum with a line-nodal gap to one which is entirely gapful when pressure is close but not yet at the QCP. In contrast, CeRhSi$_3$ does not possess an obvious pressure-tuned QCP and the superconducting phase remains for all accessible pressures with a nodal gap. Combining both results suggests that unconventional behaviours may be connected with the coexisting antiferromagnetic order. This study provides a new viewpoint on the interplay of superconductivity and magnetism in SCES.

We present a magnetic-penetration-depth study on polycrystalline and granular samples of SrPtAs, a pnictide superconductor with a hexagonal structure containing PtAs layers that individually break inversion symmetry (local noncentrosymmetry). Compact samples show a clear-cut $s$-wave-type BCS behavior, which we consider to be the intrinsic penetration depth of SrPtAs. Granular samples display a sample-dependent second diamagnetic drop, attributed to the intergrain coupling. Our experimental results point to a nodeless isotropic superconducting energy gap in SrPtAs, which puts strong constraints on the driven mechanism for superconductivity and the order parameter symmetry of this compound.

We study the two-component Ginzburg–Landau (GL) theory, in the presence of a self-consistent vortex line, to obtain the penetration depth (λ) and the effective healing length (ξ), in the asymptotic limit r → ∞. All these parameters versus T/Tc are analyzed for the materials MgB 2, V 3 Si and LiFeAs in the interval 0.88 ≤ T/Tc ≤ 1.0, where the GL theory is assumed to be valid. We find that κ ≡ λ/ξ, which is another parameter not related to the GL parameter, is T-independent for V 3 Si and LiFeAs , while is T-dependent for the compound MgB 2. This result suggests that even though all these three materials display two-gap superconductivity overall, near Tc superconductivity in V 3 Si and LiFeAs seems to be different from the one in MgB 2. The use of this parameter, κ, as a new way to "study" the superconducting materials, under the presence of a single vortex, is valid for 0.88Tc≲ T ≤ Tc, namely, in the GL formalism.

We measured the temperature dependence of the magnetic penetration depth of La3Pd4Si4 down to 0.02 T-c. We observe a temperature- independent behaviour below 0.25 T-c, which is firm evidence for a nodeless superconducting gap in this material. The data display a very small anomaly around 1 K which we attribute to the possible presence of a superconducting impurity phase. The superfluid density is well described by a two- phase model, considering La3Pd4Si4 and the impurity phase. The present analysis suggests that the superconducting energy gap of La3Pd4Si4 is isotropic, as expected for conventional BCS superconductors.

We report on measurements of the temperature dependence of the magnetic penetration depth of a high-quality sample of BaPtSi3 (Tc = 2.25 K). We observe a temperature-independent behaviour below T ≃ 0.2 Tc, which is firm evidence for the presence of an isotropic superconducting gap in this material. In the whole temperature range the superfluid density is described well by a strong-coupling Bardeen-Cooper-Schrieffer (BCS) model with an isotropic gap Δ0 ≈ 2kBTc. Our results provide further support for conventional BCS superconductivity in the nonmagnetic members of the noncentrosymmetric family of superconductors that crystallize with the BaNiSn3-type tetragonal structure.

We propose a thermodynamic version of the Axelrod model of social influence. In one-dimensional (1D) lattices, the thermodynamic model becomes a coupled Potts model with a bonding interaction that increases with the site matching traits. We analytically calculate thermodynamic and critical properties for a 1D system and show that an order–disorder phase transition only occurs at T=0 independent of the number of cultural traits q and features F. The 1D thermodynamic Axelrod model belongs to the same universality class of the Ising and Potts models, notwithstanding the increase of the internal dimension of the local degree of freedom and the state-dependent bonding interaction. We suggest a unifying proposal to compare exponents across different discrete 1D models. The comparison with our Hamiltonian description reveals that in the thermodynamic limit the original out-of-equilibrium 1D Axelrod model with noise behaves like an ordinary thermodynamic 1D interacting particle system.

In this chapter we discuss the physical properties of a particular family of non-centrosymmetric superconductors belonging to the class heavy-fermion compounds. This group includes the ferromagnet UIr and the antiferromagnets CeRhSi3, CeIrSi3, CeCoGe3, CeIrGe3 and CePt3Si, of which all but CePt3Si become superconducting only under pressure. Each of these superconductors has intriguing and interesting properties. We first analyze CePt3Si, then review CeRhSi3, CeIrSi3, CeCoGe3 and CeIrGe3, which are very similar to each other in their magnetic and electrical properties, and finally discuss UIr. For each material we discuss the crystal structure, magnetic order, occurrence of superconductivity, phase diagram, characteristic parameters, superconducting properties and pairing states. We present an overview of the similarities and differences between all these six compounds at the end.

We have carried out the electrical resistivity measurements under high pressures up to 24 GPa for CeTX3 (T: Co and Ir, X: Si and Ge), CePd5Al2 and YbIr2Zn20 in order to investigate quantum criticality and superconductivity. Antiferromagnets CeTX3 with the non-centrosymmetric tetragonal structure show superconductivity under high pressures and reveal a huge upper critical field for H‖ [001]. An antiferromagnet CePd5Al2, which is an isostructural family of a heavy fermion superconductor NpPd5Al2, also shows superconductivity under high pressures. In these compounds, superconductivity appears in the vicinity of quantum critical point. On the other hand, YbIr2Zn20 without magnetic ordering approaches to the quantum critical point with increasing pressure and exhibits a super-heavy fermion state exceeding 10 J/(K2· mol).

In this chapter we discuss the physical properties of a parti cular family of non-centrosymmetric superconductors belonging to the cla ss heavy-fermion compounds. This group includes the ferromagnet UIr and the anti ferromagnets CeRhSi 3, CeIrSi3, CeCoGe3, CeIrGe3 and CePt 3Si, of which all but CePt 3Si become superconducting only under pressure. Each of these supercond u tors has intriguing and interesting properties. We first analyze CePt 3Si, then review CeRhSi 3, CeIrSi3, CeCoGe3 and CeIrGe3, which are very similar to each other in their magnetic and electrical properties, and finally discuss UIr. For each mat eri l we discuss the crystal structure, magnetic order, occurrence of superconductivi ty, phase diagram, characteristic parameters, superconducting properties and pair ing states. We present an overview of the similarities and differences between all th ese six compounds at the end.