Pauli-limited Superconductors Research Articles

Magnetotransport and Fermi surface segmentation in Pauli limited superconductors

We report the first theoretical investigation of the spectroscopic, electrical and optical transport signatures of d-wave Pauli limited superconductors, based on a non perturbative numerical approach. We demonstrate that the high magnetic field low temperature regime of these materials host a finite momentum paired superconducting phase. Multi-branched dispersion spectra with finite energy superconducting gaps, anisotropic segmentation of the Fermi surface and spatial modulations of the superconducting order characterizes this finite momentum paired phase and should be readily accessible through angle resolved photo emission spectroscopy, quasiparticle interference and differential conductance measurements. Based on the electrical and optical transport properties we capture the non Fermi liquid behavior of these systems at high temperatures, dominated by local superconducting correlations and characterized by resilient quasiparticles which survive the breakdown of the Fermi liquid description. We map out the generic thermal phase diagram of the d-wave Pauli limited superconductors and provide for the first time the accurate estimates of the thermal scales corresponding to the: (a) loss of (quasi) long range superconducting phase coherence (T c), (b) loss of local pair correlations (T pg), (c) breakdown of the Fermi liquid theory (T max) and cross-over from the non Fermi liquid to the bad metallic phase (T BR). Our thermal phase diagram mapped out on the basis of the spectroscopic and transport properties are found to be in qualitative agreement with the experimental observations on CeCoIn5 and κ-BEDT, in terms of the thermodynamic phases and the phase transitions. The results presented in this paper are expected to initiate important transport and spectroscopic experiments on the Pauli limited d-wave superconductors, providing sharp signatures of the finite momentum Cooper paired state in these materials.

Fulde–Ferrell–Larkin–Ovchinnikov State in Perpendicular Magnetic Fields in Strongly Pauli-Limited Quasi-Two-Dimensional Superconductors

We examine the Fermi-surface effect called the nesting effect for the FFLO state in strongly Pauli-limited Q2D superconductors, focusing on the effect of 3D factors, such as interlayer electron transfer, interlayer pairing, and off-plane magnetic fields including those perpendicular to the most conductive layers. We examine the systems with a large Maki parameter so that the orbital pair-breaking effect is negligible, except for the locking of the direction of the FFLO vector q in the field direction.It is known that the nesting effect for the FFLO state can be strong in QLD systems in which the orbital pair-breaking effect is suppressed by applying the mag. field parallel to the layers. Hence, it has sometimes been suggested that the nesting effect may hardly enhance the stability of the FFLO state for perpendicular fields. We illustrate that, contrary to this view, the nesting effect can strongly stabilize the FFLO state for perpendicular fields as well as for parallel fields when tz is small so that the Fermi surfaces are open in the kz-direction, where tz denotes the interlayer transfer energy. In particular, the nesting effect in perpendicular fields can be strong in interlayer states. For example, in systems with cylindrical Fermi surfaces warped by tz /= 0, interlayer states with Dlt_k prop sin k_z exhibit mu_e Hc=1.65 Dlt_a0 for perpendicular fields, which is much larger than typical values for parallel fields, such as mu_e Hc=Dlt_s0 of the s-wave state and mu_e Hc = 1.28 Delta_d0 of the d-wave state in cylindrical systems with tz=0. The present result could potentially provide a physical reason why the areas in the phase diagrams occupied by the high-field phases for the perpendicular and parallel fields are of the same order in CeCoIn5 and FeSe.

Pauli limited d-wave superconductors: quantum breached pair phase and thermal transitions

We report a quantum phase transition in Pauli limited d-wave superconductors and give the mean field estimates of the associated quantum critical point. For a population imbalanced d-wave superconductor a stable ground state phase viz quantum breached pair phase has been identified which comprises of spatial coexistence of gapless superconductivity and nonzero magnetization. Based on the thermodynamic and quasiparticle indicators we for the first time analyze this phase, discuss the thermal behavior of Pauli limited d-wave superconductor, give accurate estimates of the thermal scales associated with such systems and map out the pseudogap regime. Our work shows that while the Pauli limited superconductors are known to exhibit exotic modulated superconducting phase at large imbalance of fermion populations; in the regime of weak imbalance an intriguing phase of competing orders is realized. We have established that rather than the superconducting pairing field, it is the average magnetization of the system that quantifies this quantum phase transition. Given that the existing Pauli limited superconductors possess unconventional pairing state symmetry of the superconducting order, our work promises to open up new avenues in the experimental research of these materials. We have also demonstrated an alternate scenario wherein the quantum breached pair phase is a natural outcome for a d-wave superconductor with unequal effective masses of the fermion species.

Electrical and Magnetic Properties of Copper-Intercalated Topological Insulator Bi2Se3 Single Crystal

In this manuscript, the growth, structural characterization, electrical transport and magnetic properties of Cu-intercalated Bi2Se3 single crystals of excellent quality synthesized through an efficient two-step melt growth method are reported. The Cu0.1Bi2Se3 single crystals exhibit superconductivity due to Cu intercalation between two quintuple layers of Bi2Se3, which is also known as the van der Waals gap. The Hc2 versus Tc phase diagram obtained with the help of the electrical resistance measurements indicate that in the zero-temperature limit, the Hc2 can be as high as 27.1 kOe when the field is applied parallel to the c-axis, though the electrical transport is found to be highly anisotropic in nature. Estimation made on the basis of the present experimental results indicate that Cu0.1Bi2Se3 is a Pauli limited superconductor. In the superconducting state, the field dependence of magnetization seems to be consistent with a spin-triplet vortex state with odd parity. In the normal state, on the other hand, both the temperature dependence of magnetic susceptibility and the signature of the magnetoresistance indicate the presence of antiferromagnetic correlations in the sample.

Quantum FFLO State in Clean Layered Superconductors

We investigate the influence of Landau quantization on the superconducting instability for a pure layered superconductor in the magnetic field directed perpendicular to the layers. We demonstrate that the quantization corrections to the Cooper-pairing kernel with finite Zeeman spin splitting promote the formation of the nonuniform state in which the order parameter is periodically modulated along the magnetic field, i.e., between the layers (Fulde-Ferrell-Larkin-Ovchinnikov [FFLO] state). The conventional uniform state experiences such a quantization-induced FFLO instability at low temperatures even in a common case of predominantly orbital suppression of superconductivity when the Zeeman spin splitting is expected to have a relatively weak effect. The maximum relative FFLO temperature is given by the ratio of the superconducting transition temperature and the Fermi energy. This maximum is realized when the ratio of the spin-spitting energy and the Landau-level separation is half-integer. These results imply that the FFLO states may exist not only in the Pauli-limited superconductors but also in very clean materials with small Zeeman spin-splitting energy. We expect that the described quantization-promoted FFLO instability is a general phenomenon, which may be found in materials with different electronic spectra and order-parameter symmetries.

Multiple phase transitions in Pauli-limited iron-based superconductors

Specific heat measurements have been successfully used to probe unconventional superconducting phases in one-band heavy-fermion and organic superconductors. We extend the method to study successive phase transitions in multi-band materials such as iron-based superconductors. The signatures are multiple peaks in the specific heat, at low temperatures and high magnetic field, which can lead to the experimental verification of unconventional superconducting states with non-zero total momentum.

Enhancement of electronic spin susceptibility in Pauli-limited unconventional superconductors

We calculate the wave-vector dependent electronic spin susceptibility $\chi_{\alpha\beta}(\mathbf q, \mathbf H_0)$ of a d-wave superconductor in uniform magnetic field $\mathbf{H}_0$ with Pauli pair-breaking. We find that the transverse component of the susceptibility tensor can be greater than its normal state value; the longitudinal component also slightly increases but in a very limited range of $q$s. We identify several wave vectors $\{\mathbf q_\perp,\mathbf q_\parallel\}$, that correspond to the maxima of either $\chi_\perp$ or $\chi_\parallel$. We compare our results with available data on the high-field phase in heavy-fermion CeCoIn$_5$.

Field-induced collective spin-exciton condensation in a quasi-2D dx2–y2-wave heavy electron superconductor

The origin of the spin resonance observed in CeCoIn5 with Inelastic Neutron Scattering is subject to debate. It has been shown recently that in this heavy electron compound at low temperature an instability to a ground state with coexisting dx2-y2-wave superconductivity and Spin Density Wave (SDW) order in a magnetic field is a corollary of the consideration of a collective spin excitation mode in a quasi-2D dx2-y2-wave Pauli-limited superconductor. This provides a natural scenario for the occurence of the puzzling high-field-low-temperature phase highlighted in CeCoIn5. We present perspectives on this ground state transition and propose directions for future experiment.

Structure of magnetic order in Pauli limited unconventional superconductors

We analyze the magnetic structure of the antiferromagnetic order induced in Pauli limited $d$-wave superconductors by Zeeman coupling to magnetic field. We determine the phase diagram in the $H$-$T$ plane and find that the magnetic phase, which is stabilized at low temperatures and just below the upper critical field, can have two realizations depending primarily on the shape of the underlying Fermi surface. The double-$\mathbit{Q}$ magnetic ordering may persist over the entire coexistence range. Alternatively, there may exist a weak first order transition from a double-$\mathbit{Q}$ structure at lower fields to a single-$\mathbit{Q}$ modulation at higher fields. Together with the calculations of the NMR line shape these results suggest the second scenario as a serious candidate for describing the superconducting state of CeCoIn${}_{5}$.

Muon spin rotation in heavy-electron pauli-limit superconductors

The formalism for analyzing the magnetic field distribution in the vortex lattice of Pauli limited heavy electron superconductors is applied to the evaluation of the vortex lattice static linewidth relevant to Muon Spin Rotation ($\mu$SR) experiment. On the basis of the Ginzburg-Landau expansion for the superconductor free energy we study the evolution with respect to external field of the static linewidth both in the limit of independent vortices (low magnetic field) and in the near $H_\mathrm{c2}^\mathrm{p}(T)$ regime by using an extension of the Abrikosov analysis to Pauli limited superconductors. We conclude that in the Ginzburg-Landau regime with Pauli limit, the electrodynamics of the vortex lattice predicts anomalous variations with applied field of the static linewidth which is a result of the spin response contribution to screening supercurrents that dominates the usual charge response. The model is proposed as a benchmark for comparison with possible other effects including vortex core localized states or interplay with magnetism.

Complex mixed state of the Pauli-limited superconductor CeCoIn5

Magnetization measurements were performed on ${\mathrm{CeCoIn}}_{5}$ at temperatures down to 20 mK and magnetic fields up to 17 T applied along different crystallographic orientations. For field configurations nearly parallel to the $ab$ plane ($\ensuremath{\theta}\ensuremath{\lesssim}{40}^{\ensuremath{\circ}}$ and $T\ensuremath{\le}50\phantom{\rule{0.16em}{0ex}}\mathrm{mK}$), we have found an intriguing vortex dynamics regime revealed by a hysteretic and metastable anomalous peak effect (APE), which gives evidence of surface barrier effects enhanced by antiferromagnetic fluctuations in the mixed state of ${\mathrm{CeCoIn}}_{5}$. Furthermore, we have observed crossover features in the torque and magnetization traces at fields below ${H}_{c2}$, which are consistent with vortices lattice phase transitions and with the anomalies speculated to be the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) superconducting state in ${\mathrm{CeCoIn}}_{5}$. All of the above features were found to be dramatically perturbed in ${\mathrm{Ce}}_{0.98}{\mathrm{Gd}}_{0.02}{\mathrm{CoIn}}_{5}$.

Antiferromagnetic Order in Pauli-Limited Unconventional Superconductors

We develop a theory of the coexistence of superconductivity (SC) and antiferromagnetism (AFM) in CeCoIn(5). We show that in Pauli-limited nodal superconductors the nesting of the quasiparticle pockets induced by Zeeman pair breaking leads to incommensurate AFM with the magnetic moment normal to the field. We compute the phase diagram and find a first order transition to the normal state at low temperatures, the absence of normal state AFM, and the coexistence of SC and AFM at high fields, in agreement with experiments. We also predict the existence of a new double-Q magnetic phase.

Bulk two-dimensional Pauli-limited superconductor

We present a nearly perfect Pauli-limited critical field phase diagram for the anisotropic organic superconductor \$\alpha$-(ET)$_2$NH$_4$(SCN)$_4$ when the applied magnetic field is oriented parallel to the conducting layers. The critical fields (${H_{c_2}$) were found by use of penetration depth measurements. Because ${H_{c_2}$ is Pauli-limited, the size of the superconducting energy gap can be calculated. The role of spin-orbit scattering and many-body effects play a role in explaining our measurements.

Field-Induced Coupled Superconductivity and Spin Density Wave Order in the Heavy Fermion CompoundCeCoIn5

The high-field superconducting state in CeCoIn(5) has been studied by transverse field muon spin rotation measurements with an applied field parallel to the crystallographic c axis close to the upper critical field mu(0)H(c2) = 4.97 T. At magnetic fields mu(0)H > or = 4.8 T the muon Knight shift is enhanced and the superconducting transition changes from second order towards first order as predicted for Pauli-limited superconductors. The field and temperature dependence of the transverse muon spin relaxation rate sigma reveal paramagnetic spin fluctuations in the field regime from 2 T < or = mu(0)H < 4.8 T. In the normal state close to H(c2) correlated spin fluctuations as described by the self-consistent renormalization theory are observed. The results support the formation of a mode-coupled superconducting and antiferromagnetically ordered phase in CeCoIn(5) for H directed parallel to the c axis.

Pauli-limited superconductors with fluctuating magnetic moments

We examine the phase diagram of a paramagnetically limited superconductor in the presence of fluctuating magnetic moments, under an applied magnetic field. We consider a Ginzburg–Landau functional for the superconducting order and include classical (Gaussian) fluctuations of the magnetization. We locate the tricritical point between the first and the second order transitions and analyze the properties of the modulated (Fulde–Ferrell–Larkin–Ovchinnikov, FFLO-like) superconducting phase in its vicinity.

Anisotropy of the heat capacity in Pauli limited unconventional superconductors

Diamagnetically coupled magnetic field can be used as a probe of nodal positions in unconventional superconductors. The heat capacity depends on the angle ϕ 0 between the magnetic field and the nodal directions. We show that the anisotropy C( ϕ 0) persists even in systems with strong paramagnetic coupling to the electrons’ spins.

Anisotropy of the upper critical field in URu 2Si 2 and FFLO state in antiferromagnetic superconductors

Experimental data of the upper critical field of the heavy-fermion superconductor URu 2Si 2 are analysed, in the clean limit, taking account of both orbital and Pauli limits. A discussion on the possible existence of a non-uniform superconducting state expected in clean Pauli-limited superconductors (FFLO state) follows. We also present calculations determining the influence of an AF ground state on the existence of such a non-uniform superconducting state.

Fulde-Ferrell state in quasi-two-dimensional superconductors.

Inhomogeneous superconductivity proposed by Fulde and Ferrell (FF state) is studied in a strongly Pauli-limited type-II superconductor with a cylindrical Fermi surface. The phase diagram of the FF state, BCS state, and normal state is obtained. It is found that the FF state is remarkably enhanced owing to the two-dimensional Fermi-surface structure in comparison to the spherical symmetric case. We discuss that the Fermi-surface nesting is also advantageous to the FF state as well as nesting instabilities. Our result obtained in the cylindrical symmetric case is applicable in general to quasi-low-dimensional superconductors in which the nesting is sufficiently incomplete so that the nesting instabilities are suppressed. Relation to the exotic superconductors discovered recently is briefly discussed.

Pauli Limiting and the Possibility of Spin Fluctuations in theA15Superconductors

From the critical-field data on the strongly Pauli limited superconductor ${\mathrm{V}}_{3}$Ga it is shown that large electron-electron interactions (and their associated spin fluctuations) may play an important role in the superconductivity of the $A15$ superconductors. This possibility is shown to be consistent with existing ${T}_{c}$, heat-capacity, and spin-susceptibility data on several $A15$ superconductors.