Paramagnetic Limit Research Articles

Upper critical field ofNaFe1−xCoxAs superconductors

The upper critical field of NaFe$_{1-x}$Co$_x$As was measured from $x=0$ to $x=0.08$, with the magnetic field applied parallel ($H_{\rm c2}^\parallel$) and normal ($H_{\rm c2}^\perp$) to the planes. The data were fitted using one-band and two-band models. The orbital and paramagnetic components of the upper critical field were extracted for $H_{\rm c2}^\parallel$, which we find to to be strongly dominated by paramagnetic pair-breaking. In the parent compound the paramagnetic limit is equal to the value expected by BCS theory. However, substitution of Fe by Co leads to an enhancement above the BCS limit by a factor of approximately 1.6. In the over-doped region, we observe a significant convex curvature in $H_{\rm c2}^\perp$ at low temperatures, which we attribute to the two-band nature of the superconductivity and the asymmetry between the two bands. Additionally, we discuss the behavior of critical field anisotropy, coherence length $\xi$, and the penetration depth $\lambda$.

Dimensional Crossover of the Fulde–Ferrell–Larkin–Ovchinnikov State in Strongly Pauli-Limited Quasi-One-Dimensional Superconductors

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is examined in quasi-one-dimensional s-wave and d-wave superconductors with particular attention paid to the effect of the Fermi-surface anisotropy. The upper critical field $H_{c2}(T)$ is found to exhibit a qualitatively different behavior depending on the ratio of the hopping energies $t_b/t_a$ and the direction of the FFLO modulation vector q, where $t_a$ and $t_b$ are the intra- and interchain hopping energies, respectively. In particular, when $t_b/t_a < 0.1$ and $\mathbf{q} \parallel \mathbf{a}$, we find a novel dimensional crossover of $H_{c2}(T)$ from one dimension to two dimensions, where a is the lattice vector of the most conductive chain. Just below the tricritical temperature $T^*$, the upper critical field $H_{c2}(T)$ increases steeply as in one-dimensional systems, but when the temperature decreases, the rate of increase in $H_{c2}(T)$ diminishes and a shoulder appears. Near $T = 0$, $H_{c2}(T)$ shows a behavior typical of the FFLO state in two-dimensional systems, i.e., an upturn with a finite field at $T = 0$. When the angle between $\mathbf{q}$ and $\mathbf{a}$ is large, the upper critical field curve is convex upward at low temperatures, as in three-dimensional systems, but the magnitude is much larger than that of a three-dimensional isotropic system. For $t_b/t_a > 0.15$, the upper critical fields exhibit a two-dimensional behavior, except for a slight shoulder in the range of $0.2 > t_b/t_a > 0.15$. The upper critical field is maximum for $\mathbf{q} \parallel \mathbf{a}$ both for s-wave and d-wave pairings, while it is only slightly larger than the Pauli paramagnetic limit for $\mathbf{q} \perp \mathbf{a}$. The relevance of the present results to the organic superconductor ${\rm (TMTSF)_2ClO_4}$ is discussed.

Effect of selenium doping on the superconductivity of Nb2Pd(S1−xSex)5

We study the isovalent substitution effect by partially introducing Se on S site in the newly discovered superconductor Nb$_2$PdS$_5$ ($T_c\sim$6 K) whose upper critical field is found to be far above its Pauli paramagnetic limit. In this Nb$_2$Pd(S$_{1-x}$Se$_x$)$_5$ (0$\leq$$x$$\leq$0.8) system, superconductivity is systematically suppressed by the Se concentration and ultimately disappears when $x\geq$ 0.5, after which a semiconducting-like ground state emerges. In spite of the considerably reduced $T_c$ with Se doping, the ratio of the upper critical field $H_{c2}$ to $T_c$, remains unaffected. Moreover, the size of the heat capacity jump at $T_c$ is smaller than that expected for a BCS superconductor, implying that a strong-coupling theory cannot be the origin of this large upper critical field. In addition, the low-lying quasiparticle excitations are consistent with a nodeless gap opening over the Fermi surface. These results combined impose severe constraints on any theory of exotic superconductivity in this system.

Magnetic-field-independent superconductivity of ultrathin Pb films on cleaved GaAs surface

We performed magnetotransport measurements on ultathin Pb films deposited onto cleaved GaAs surface and observed two-dimensional superconductivity for an amorphous 2.2-Å-thick film, which is below one monolayer. The superconducting transition is almost independent of parallel magnetic field as high as 14 T. This means that the superconducting state has much larger critical magnetic field than Pauli paramagnetic limit. We consider two different mechanism relating Rashba spin splitting.

Two-Dimensional Superconducting State of Monolayer Pb Films Grown on GaAs(110) in a Strong Parallel Magnetic Field

Two-dimensional (2D) superconductivity was studied by magnetotransport measurements on single-atomic-layer Pb films on a cleaved GaAs(110) surface. The superconducting transition temperature shows only a weak dependence on the parallel magnetic field up to 14T, which is higher than the Pauli paramagnetic limit. Furthermore, the perpendicular-magnetic-field dependence of the sheet resistance is almost independent of the presence of the parallel field component. These results are explained in terms of an inhomogeneous superconducting state predicted for 2D metals with a large Rashba spin splitting.

Temperature dependence of the upper critical field of FeSe single crystals

We present a careful study of the resistive superconducting transition in FeSe single crystals down to $T=40$ mK in continuous magnetic fields up to 30 T applied perpendicular and parallel to the $ab$ plane. In the $\mathbf{H}\ensuremath{\parallel}\mathbf{c}$ geometry the temperature dependence of the resistive upper critical field ${H}_{c2}^{*}$, determined as the field at which the in-plane resistivity in the transition region is 90$%$ of the normal state resistivity is down to temperatures $T/{T}_{c}&lt;0.006$, is in close agreement with the Werthamer-Helfand-Hohenberg (WHH) theoretical curve which describes the behavior of the upper critical field in conventional type-II superconductors. In contrast, for the $\mathbf{H}\ensuremath{\parallel}\mathbf{ab}$ geometry, the data depart from the WHH model with increasing applied magnetic field according to the paramagnetic limitation of superconductivity. An anisotropy parameter $\ensuremath{\gamma}$ in our FeSe crystals decreases with decreasing temperature and FeSe becomes nearly isotropic when the temperature $T\ensuremath{\rightarrow}0$.

Large room temperature magnetoresistance of transparent Fe and Ni doped ZnO thin films

The electrical, optical, and magnetic properties of pure, 1%Fe, and 1%Ni doped ZnO thin films grown by spray pyrolysis technique were studied. All samples are transparent (T ≈ 85%) in VIS and near infrared region of wavelength. Ni and Fe doped ZnO layers are paramagnetic. Resistivity versus temperature has semiconducting behavior. Large value of magnetoresistance at 300 K at 1.3 T: MR = 56%/T for 1%Fe doped ZnO and MR = 28%/T for 1%Ni doped samples have been observed. These exceptional values of MR at room temperature originate probably from hopping conductivity in polycrystalline diluted magnetic semiconductor in paramagnetic high dilution limit.

Unconventional Pairing State in Weakly Correlated Non-centrosymmetric Superconductors

We briefly review the recent progress on the study of weakly correlated non-centrosymmetric (NCS) superconductors, with an emphasis on their novel pairing symmetry and the upper critical field arising from the absence of inversion symmetry. Measurements of penetration depth, specific heat, NMR, etc., have shown that non-BCS-like superconductivity with a nodal gap structure may appear in simple metallic NCS superconductors, which allows the admixture of spin-singlet and spin-triplet pairing states attributed to the antisymmetric spin-orbital coupling (ASOC). Furthermore, large upper critical field with a value exceeding the Pauli paramagnetic limit was also experimentally observed in NCS superconductors.

On the origin of the anomalous upper critical field in quasi–one-dimensional superconductors

The upper critical field, Hc2, in quasi-1D superconductors is investigated by the weak coupling renormalization group technique. It is shown that Hc2 greatly exceeds not only the Pauli limit, but also the conventional paramagnetic limit of the Flude-Ferrell-Larkin-Ovchinnikov (FFLO) state. This increase is mainly due to the quasi-1D fluctuations effect as triggered by interference between unconventional superconductivity and density-wave instabilities. Our results give a novel viewpoint on the large Hc2 observed in TMTSF-salts in terms of a d-wave FFLO state that is predicted to be verified by Hc2 measurements under pressure.

Quantum-Fluctuation Effects in the Transport Properties of Ultrathin Films of Disordered Superconductors above the Paramagnetic Limit

We study the transport in ultrathin disordered film near the quantum critical point induced by the Zeeman field. We calculate corrections to the normal state conductivity due to quantum pairing fluctuations. The fluctuation-induced transport is mediated by virtual rather than real quasiparticle excitations. We find that at zero temperature, where the corrections come from purely quantum fluctuations, the Aslamazov-Larkin paraconductivity term, the Maki-Thompson interference contribution, and the density of states effects are all of the same order. The total correction leads to the negative magnetoresistance. This result is in qualitative agreement with the recent transport observations in the parallel magnetic field of the homogeneously disordered amorphous films and superconducting two-dimensional electron gas realized at the oxide interfaces.

Experimental and semiempirical method to determine the Pauli-limiting field in quasi-two-dimensional superconductors as applied toκ-(BEDT-TTF)2Cu(NCS)2: Strong evidence of a FFLO state

We present upper critical field data for $\ensuremath{\kappa}$-(BEDT-TTF)${}_{2}$Cu(NCS)${}_{2}$ with the magnetic field close to parallel and parallel to the conducting layers. We show that we can eliminate the effect of vortex dynamics in these layered materials if the layers are oriented within 0.3${}^{\ensuremath{\circ}}$ of parallel to the applied magnetic field. Eliminating vortex effects leaves one remaining feature in the data that corresponds to the Pauli paramagnetic limit (${H}_{p}$). We propose a semiempirical method to calculate the ${H}_{p}$ in quasi-2D superconductors. This method takes into account the energy gap of each of the quasi-2D superconductors, which is calculated from specific-heat data, and the influence of many-body effects. The calculated Pauli paramagnetic limits are then compared to critical field data for the title compound and other organic conductors. Many of the examined quasi-2D superconductors, including the above organic superconductors and CeCoIn${}_{5}$, exhibit upper critical fields that exceed their calculated ${H}_{p}$ suggesting unconventional superconductivity. We show that the high-field low-temperature state in $\ensuremath{\kappa}$-(BEDT-TTF)${}_{2}$Cu(NCS)${}_{2}$ is consistent with the Fulde-Ferrell-Larkin-Ovchinnikov state.

Two-dimensional superconductivity in the layered organic superconductorκH-(DMEDO-TSeF)2[Au(CN)4](THF) with thick dielectric insulating layers

We have systematically investigated the resistive superconducting transition in the layered organic superconductor ${\ensuremath{\kappa}}_{\mathrm{H}}$-(DMEDO-TSeF)${}_{2}$[Au(CN)${}_{4}$](THF) [where DMEDO-TSeF is dimethyl(ethylenedioxy)tetraselenafulvalene and THF is tetrahydrofuran], which consists of two crystallographically independent conducting layers and one independent thick dielectric insulating layer. Applying a slight pressure of up to 0.35 GPa suppresses the superconducting phase. The angular dependence of the upper critical field and the short interlayer coherence length indicate that the present compound is a highly two-dimensional superconductor. The upper critical field parallel to the conducting layers exceeds the Pauli paramagnetic limit. These superconducting properties are consistent with the crystal structure in which the superconducting layers are well separated by a thick anion insulating layer.

D-Wave-like nodal superconductivity in the organic conductor (TMTSF)2ClO4

We suggest theoretical explanation of the high upper critical magnetic field, perpendicular to conducting chains, Hc2b′, experimentally observed in the superconductor (TMTSF)2ClO4, in terms of singlet superconducting pairing. In particular, we compare the results of d-wave-like nodal, d-wave-like node-less, and s-wave scenarios of superconductivity. We show that, in d-wave-like nodal scenario, superconductivity can naturally exceed both the orbital upper critical magnetic field and Clogston–Shandrasekhar paramagnetic limit as well as reach experimental value, Hc2b′≃6T, in contrast to d-wave-like node-less and s-wave scenarios. In our opinion, the obtained results are strongly in favor of d-wave-like nodal superconductivity in (TMTSF)2ClO4, whereas, in a sister compound, (TMTSF)2PF6, we expect either the existence of triplet order parameter or the coexistence of triplet and singlet order parameters.

On the Sarma-Type Phase Transitions in Ferromagnet/Superconductor/Ferromagnet Tunneling Junctions with Highly Spin-Polarized Ferromagnets

In the ferromagnet/superconductor/ferromagnet double tunneling junctions, the spin-polarized tunneling current in the antiparallel alignment of the magnetization induces spin imbalance in the superconductor, which has a pair breaking effect depressing superconductivity in the same way that the Zeeman effect does in the paramagnetic limit. In particular, it is shown that when the ferromagnets are highly spin polarized, the strong spin imbalance may lead to a first-order phase transition from the superconducting phase to the normal phase at low temperature and low bias voltage. This phase transition accompanies a large discontinuous drop in superconducting gap parameter bring in distinctive features in low energy transport.

Hidden reentrant superconducting phase in a magnetic field in (TMTSF)2ClO4

We suggest explanation of the high upper critical magnetic field, perpendicular to conducting chains and parallel to conducting layers H c2 b′ ≃ 6 T, experimentally observed in the organic superconductor (TMTSF)2ClO4. In particular, we show that H c2 b′ can be higher than both the quasiclassical upper critical field and Clogston-Chandrasekhar paramagnetic limit in a singlet quasi-one-dimensional superconductor. We predict the coexistence of the hidden Reentrant and Larkin-Ovchinnikov-Fulde-Ferrell phases in a magnetic field. Our results are compared to the recent experimental data and shown to be in a good agreement with the experiments.

Hidden Reentrant and Larkin-Ovchinnikov-Fulde-Ferrell Superconducting Phases in a Magnetic Field in a(TMTSF)2ClO4

We solve a long-standing problem about a theoretical description of the upper critical magnetic field, parallel to conducting layers and perpendicular to conducting chains, in a (TMTSF)(2)ClO(4) superconductor. In particular, we explain why the experimental upper critical field, H(c2)(b')≃6 T, is higher than both the quasiclassical upper critical field and the Clogston paramagnetic limit. We show that this property is due to the coexistence of the hidden reentrant and Larkin-Ovchinnikov-Fulde-Ferrell phases in a magnetic field in the form of three plane waves with nonzero momenta of the Cooper pairs. Our results are in good qualitative and quantitative agreement with the recent experimental measurements of H(c2)(b') and support a singlet d-wave-like scenario of superconductivity in (TMTSF)(2)ClO(4).

Field-induced superconducting phase in superconductor–normal metal and superconductor-superconductor bilayers

We study the proximity effect in a superconductor (S)-normal metal (N) bilayer under in-plane magnetic field. A compensation between the Zeeman effect and the energy splitting between bonding and anti-bonding levels leads to a magnetic field induced superconducting phase in the (H,T) phase diagram of the S-N bilayer well above the standard paramagnetic limit. We demonstrate that the presence of the non-magnetic impurities shrink the region of field induced superconductivity existence in S-N and S-S bilayers.

Correlation energy of the spin-polarized uniform electron gas at high density

The correlation energy per electron in the high-density uniform electron gas can be written as $\Ec(r_s,\zeta) = \lam_0(\zeta) \ln r_s + \eps_0(\zeta) + \lam_1(\zeta) \,r_s \ln r_s + O(r_s)$, where $r_s$ is the Seitz radius and $\zeta$ is the relative spin polarization. We derive an expression for $\lam_1(\zeta)$ which is exact for any $\zeta$, including the paramagnetic and ferromagnetic limits, $\lam_1(0)$ and $\lam_1(1)$, and discover that the previously published $\lam_1(1)$ value is incorrect. We trace this error to an integration and limit that do not commute. The spin-resolution of $\lam_1(\zeta)$ into contributions of electron pairs is also derived.

Upper critical field of the molecular organic superconductor (DMET)2I3

We report the temperature dependence of the upper critical magnetic field in the quasi-one-dimensional molecular organic superconductor (DMET)${}_{2}$I${}_{3}$, for magnetic field applied along the intrachain, interchain, and interplane directions. The upper critical field tends to saturation at low temperature for field in all directions and does not exceed the Pauli paramagnetic limit. Superconductivity in (DMET)${}_{2}$I${}_{3}$ thus appears to be conventional spin singlet, in contrast to the status of the isostructural Bechgaard salts. We also discuss a magnetic field-induced dimensional crossover effect in the normal metallic state which had previously appeared to be associated with superconductivity.

Thermodynamic phase diagram ofFe(Se0.5Te0.5)single crystals in fields up to 28 tesla

We report on specific heat ($C_p$), transport, Hall probe and penetration depth measurements performed on Fe(Se$_{0.5}$Te$_{0.5}$) single crystals ($T_c \sim 14$ K). The thermodynamic upper critical field $H_{c2}$ lines has been deduced from $C_p$ measurements up to 28 T for both $H\|c$ and $H\|ab$, and compared to the lines deduced from transport measurements (up to 55 T in pulsed magnetic fields). We show that this {\it thermodynamic} $H_{c2}$ line presents a very strong downward curvature for $T \rightarrow T_c$ which is not visible in transport measurements. This temperature dependence associated to an upward curvature of the field dependence of the Sommerfeld coefficient confirm that $H_{c2}$ is limited by paramagnetic effects. Surprisingly this paramagnetic limit is visible here up to $T/T_c \sim 0.99$ (for $H\|ab$) which is the consequence of a very small value of the coherence length $\xi_c(0) \sim 4 \AA$ (and $\xi_{ab}(0) \sim 15 \AA$), confirming the strong renormalisation of the effective mass (as compared to DMFT calculations) previously observed in ARPES measurements [Phys. Rev. Lett. 104, 097002 (2010)]. $H_{c1}$ measurements lead to $\lambda_{ab}(0) = 430 \pm 50$ nm and $\lambda_c(0) = 1600 \pm 200$ nm and the corresponding anisotropy is approximatively temperature independent ($\sim 4$), being close to the anisotropy of $H_{c2}$ for $T\rightarrow T_c$. The temperature dependence of both $\lambda$ ($\propto T^2$) and the electronic contribution to the specific heat confirm the non conventional coupling mechanism in this system.