Point-like Disorder Research Articles

Response of the Verwey transition in magnetite to controlled point-like disorder induced by 2.5 MeV electron irradiation

Controlled point-like disorder induced by low temperature 2.5 MeV electron irradiation was used to probe the nature of the Verwey transition in magnetite, Fe3O4. Two large single crystals, one with optimal transition temperature, TV≈121 K, and another with TV≈109 K, as well as magnetite magnetosome nanocrystals harvested from the lysed cells of the marine magnetotactic vibrio Magnetovibrio blakemorei strain MV-1, TV≈110 K, were examined. Temperature-dependent resistivity is consistent with the semiconductor-to-semiconductor (insulator) sharp, step-like Verwey transition from a state with a small bandgap of around 60 meV to a state with a large bandgap of about 300 meV. The irradiation causes an up-shift of the resistivity curves above the transition without transition smearing or broadening. It also causes an apparent down-shift of the resistivity maximum at high temperatures. In the lower TV crystal, the electron irradiation drives the transition temperature into a “forbidden” interval of TV , believed to separate the first order from the second order phase transition. Contrary to this belief, the transition itself remains sharp and hysteretic without a significant change in the hysteresis width indicating the strong 1st order character of the Verwey transition for all TV values. The separate 2nd order - looking transition is likely due to sample inhomogeneities. We conclude that the sudden change of the bandgap accompanied (or driven) by the monoclinic distortion and the change of magnetic anisotropy is the reason for the Verwey transition in magnetite and the effect of additional disorder is mostly in the smearing of the sharp gap edges near the Fermi level.

Ion-Selective Scattering Studied Using the Variable-Energy Electron Irradiation in the Ba0.2K0.8Fe2As2 Superconductor.

Low-temperature variable-energy electron irradiation was used to induce non-magnetic disorder in a single crystal of a hole-doped iron-based superconductor, Ba1-xKxFe2As2, x = 0.80. To avoid systematic errors, the beam energy was adjusted non-consequently for five values between 1.0 and 2.5 MeV when sample resistance was measured in situ at 22 K. For all energies, the resistivity raises linearly with the irradiation fluence suggesting the creation of uncorrelated dilute point-like disorder (confirmed by simulations). The rate of the resistivity increase peaks at energies below 1.5 MeV. Comparison with calculated partial cross-sections points to the predominant creation of defects in the iron sublattice. Simultaneously, superconducting Tc, measured separately between the irradiation runs, is monotonically suppressed as expected, since it depends on the total scattering rate, hence on the total cross-section, which is a monotonically increasing function of the energy. Our work experimentally confirms an often-made assumption of the dominant role of the iron sub-lattice in iron-based superconductors.

Crossing the ballistic-ohmic transition via high energy electron irradiation

The delafossite metal ${\mathrm{PtCoO}}_{2}$ is among the highest-purity materials known, with low-temperature mean free path up to 5 $\ensuremath{\mu}\mathrm{m}$ in the best as-grown single crystals. It exhibits a strongly faceted, nearly hexagonal Fermi surface. This property has profound consequences for nonlocal transport within this material, such as in the classic ballistic-regime measurement of bend resistance in mesoscopic squares. Here, we report the results of experiments in which high-energy electron irradiation was used to introduce pointlike disorder into such squares, reducing the mean free path and therefore the strength of the ballistic-regime transport phenomena. We demonstrate that high-energy electron irradiation is a well-controlled technique to cross from nonlocal to local transport behavior and therefore determine the nature and extent of unconventional transport regimes. Using this technique, we confirm the origins of the directional ballistic effects observed in delafossite metals and demonstrate how the strongly faceted Fermi surface both leads to unconventional transport behavior and enhances the length scale over which such effects are important.

Possible unconventional pairing in (Ca,Sr)3(Ir,Rh)4Sn13 superconductors revealed by controlling disorder

We study the evolution of temperature-dependent resistivity with controlled point-like disorder induced by 2.5 MeV electron irradiation in stoichiometric compositions of the "3-4-13" stannides, $(\text{Ca,Sr})_{3}(\text{Ir,Rh})_{4}\text{Sn}_{13}$.Three of these cubic compounds exhibit a microscopic coexistence of charge-density wave (CDW) order and superconductivity (SC), while $\text{Ca}_{3}\text{Rh}_{4}\text{Sn}_{13}$ does not develop CDW order. As expected, the CDW transition temperature, $T_{\text{CDW}}$, is universally suppressed by irradiation in all three compositions. The superconducting transition temperature, $T_{c}$, behaves in a more complex manner. In $\text{Sr}_{3}\text{Rh}_{4}\text{Sn}_{13}$, it increases initially in a way consistent with a direct competition of CDW and SC, but quickly saturates at higher irradiation doses. In the other three compounds, $T_{c}$ is monotonically suppressed by irradiation. The strongest suppression is found in $\text{Ca}_{3}\text{Rh}_{4}\text{Sn}_{13}$, which does not have CDW order. We further examine this composition by measuring the London penetration depth, $\lambda(T)$, from which we derive the superfluid density. The result unambiguously points to a weak-coupling, full single gap, isotropic superconducting state. Therefore, we must explain two seemingly incompatible experimental observations: a single isotropic superconducting gap and a significant suppression of $T_{c}$ by non-magnetic disorder. We conduct a quantitative theoretical analysis based on a generalized Anderson theorem which points to an unconventional multiband $s^{+-}$-pairing state where the sign of the order parameter is different on one (or a small subset) of the smaller Fermi surface sheets, but remains overall fully-gapped.

Strong pinning at high growth rates in rare earth barium cuprate (REBCO) superconductor films grown with liquid-assisted processing (LAP) during pulsed laser deposition

We present a simple liquid-assisted processing (LAP) method, to be used in situ during pulsed laser deposition growth to give both rapid growth rates (50 Hz deposition leading to >250 nm min−1 with a single plume) and strong pinning (improved ×5–10 at 30 K and below, over plain standard YBCO films grown at similar rates). Achieving these two important features simultaneously has been a serious bottleneck to date and yet for applications, it is critical to overcome it. The new LAP method uses a non-stoichiometric target composition, giving rise to a small volume fraction of liquid phase during film growth. LAP enhances the kinetics of the film growth so that good crystalline perfection can be achieved at up to 60× faster growth rates than normal, while also enabling artificial pinning centres to be self-assembled into fine nanocolumns. In addition, LAP allows for RE mixing (80% of Y with 20% of Yb, Sm, or Yb + Sm), creating effective point-like disorder pinning centres within the rare earth barium cuprate lattice. Overall, LAP is a simple method for use in pulsed laser deposition, and it can also be adopted by other in situ physical or vapour deposition methods (i.e. MOCVD, evaporation, etc) to significantly enhance both growth rate and performance.

Effect of controlled pointlike disorder induced by 2.5-MeV electron irradiation on the nematic resistivity anisotropy of hole-doped (Ba,K)Fe2As2

In-plane anisotropy of electrical resistivity was studied in samples of the hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ in the composition range $0.21 \leq x \leq 0.26$ where anisotropy changes sign. Low-temperature ($\sim$20~K) irradiation with relativistic 2.5 MeV electrons was used to control the level of disorder and residual resistivity of the samples. Modification of the stress-detwinning technique enabled measurements of the same samples before and after irradiation, leading to conclusion of anisotropic character of predominantly inelastic scattering processes. Our main finding is that the resistivity anisotropy is of the same sign irrespective of residual resistivity, and remains the same in the orthorhombic $C_2$ phase above the re-entrant tetragonal transition. Unusual $T$-linear dependence of the anisotropy $\Delta \rho \equiv \rho_a(T)-\rho_b(T)$ is found in pristine samples with $x=$0.213 and $x=$0.219, without similar signatures in either $\rho_a(T)$ or $\rho_b(T)$. We show that this feature can be reproduced by a phenomenological model of R.~M.~Fernandes {\it et al.} Phys. Rev. Lett. {\bf 107},217002 (2011). We speculate that onset of fluctuations of nematic order on approaching the instability towards the re-entrant tetragonal phase contributes to this unusual dependence.

Observation of two-dimensional Anderson localisation of ultracold atoms

Anderson localisation —the inhibition of wave propagation in disordered media— is a surprising interference phenomenon which is particularly intriguing in two-dimensional (2D) systems. While an ideal, non-interacting 2D system of infinite size is always localised, the localisation length-scale may be too large to be unambiguously observed in an experiment. In this sense, 2D is a marginal dimension between one-dimension, where all states are strongly localised, and three-dimensions, where a well-defined phase transition between localisation and delocalisation exists as the energy is increased. Here, we report the results of an experiment measuring the 2D transport of ultracold atoms between two reservoirs, which are connected by a channel containing pointlike disorder. The design overcomes many of the technical challenges that have hampered observation of localisation in previous works. We experimentally observe exponential localisation in a 2D ultracold atom system.

Interplay between superconductivity and itinerant magnetism in underdoped Ba1\u2212xKxFe2As2 (x\u2009=\u20090.2) probed by the response to controlled point-like disorder

The response of superconductors to controlled introduction of point-like disorder is an important tool to probe their microscopic electronic collective behavior. In the case of iron-based superconductors, magnetic fluctuations presumably play an important role in inducing high-temperature superconductivity. In some cases, these two seemingly incompatible orders coexist microscopically. Therefore, understanding how this unique coexistence state is affected by disorder can provide important information about the microscopic mechanisms involved. In one of the most studied pnictide family, hole-doped Ba1−xKxFe2As2 (BaK122), this coexistence occurs over a wide range of doping levels, 0.16 ≲ x ≲ 0.25. We used relativistic 2.5 MeV electrons to induce vacancy-interstitial (Frenkel) pairs that act as efficient point-like scattering centers. Upon increasing dose of irradiation, the superconducting transition temperature Tc decreases dramatically. In the absence of nodes in the order parameter this provides a strong support for a sign-changing s± pairing. Simultaneously, in the normal state, there is a strong violation of the Matthiessen’s rule and a decrease (surprisingly, at the same rate as Tc) of the magnetic transition temperature Tsm, which indicates the itinerant nature of the long-range magnetic order. Comparison of the hole-doped BaK122 with electron-doped Ba(FexCo1−x)2As2 (FeCo122) with similar Tsm ~ 110 K, x = 0.02, reveals significant differences in the normal states, with no apparent Matthiessen’s rule violation above Tsm on the electron-doped side. We interpret these results in terms of the distinct impact of impurity scattering on the competing itinerant antiferromagnetic and s± superconducting orders.

Robust s± pairing in CaK(Fe1−xNix)4As4 ( x=0 and 0.05) from the response to electron irradiation

Controlled point-like disorder introduced by 2.5 MeV electron irradiation was used to probe the superconducting state of single crystals of \CaKx\ superconductor at $x = 0$ and 0.05 doping levels. Both compositions show an increase of the residual resistivity and a decrease of the superconducting transition temperature, $T_c$ at the rate of $dT_c/d\rho(T_c) \approx$ 0.19 K(\textmu$\Omega$cm)$^{-1}$ for $x=0$ and 0.38 K(\textmu$\Omega$cm)$^{-1}$ for $x=\:$0.05, respectively. In Ni - doped, $x = 0.05$, compound the coexisting spin-vortex crystal (SVC) magnetic phase is suppressed at the rate of $dT_N/d\rho(T_N)\approx$ 0.16 K(\textmu$\Omega$cm)$^{-1}$. Low - temperature variation of London penetration depth is well approximated by the power law, $\Delta \lambda (T) = AT^n$ with $n\approx\,$2.5 for $x=0$ and $n\approx\,$1.9 for $x=0.05$ in the pristine state. Electron irradiation leads to the exponent $n$ increase above 2 in $x=0.05$ suggesting superconducting gap with significant anisotropy that is smeared by the disorder scattering. Detailed analysis of $\lambda (T)$ and \(T_{c}\) evolution with disorder is consistent with two effective nodeless superconducting energy gaps due to robust s$_{\pm}$ pairing. Overall the behavior of \CaKx\ at $x = 0$ is similar to a slightly overdoped \BaK\ at $y \approx$ 0.5 and at $x= 0.05$ to an underdoped composition at $y \approx$ 0.2.

Enhancement of superconducting transition temperature by pointlike disorder and anisotropic energy gap in FeSe single crystals

A highly anisotropic superconducting gap is found in single crystals of FeSe by studying the London penetration depth, $\Delta \lambda$, measured down to 50 mK in samples before and after 2.5 MeV electron irradiation. The gap minimum increases with introduced point - like disorder, indicating the absence of symmetry - imposed nodes. Surprisingly, the superconducting transition temperature, $T_c$, \textit{increases} by 0.4 K from $T_{c0} \approx$ 8.8 K while the structural transition temperature, $T_s$, \textit{decreases} by 0.9 K from $T_{s0} \approx$91.2 K after electron irradiation. We discuss several explanations for the $T_c$ enhancement, and propose that local strengthening of the pair interaction by irradiation-induced Frenkel defects most likely explains the phenomenon.

Simulation of Anderson localization in two-dimensional ultracold gases for pointlike disorder

Anderson localization has been observed for a variety of media, including ultracold atomic gases with speckle disorder in one and three dimensions. However, observation of Anderson localization in a two-dimensional geometry for ultracold gases has been elusive. We show that a cause of this difficulty is the relatively high percolation threshold of a speckle potential in two dimensions, resulting in strong classical localization. We propose a realistic point-like disorder potential that circumvents this percolation limit with localization lengths that are experimentally observable. The percolation threshold is evaluated for experimentally realistic parameters, and a regime of negligible classical trapping is identified. Localization lengths are determined via scaling theory, using both exact scattering cross sections and the Born approximation, and by direct simulation of the time-dependent Schr\"{o}dinger equation. We show that the Born approximation can underestimate the localization length by four orders of magnitude at low energies, while exact cross sections and scaling theory provide an upper bound. Achievable experimental parameters for observing localization in this system are proposed.

Electromagnetic Properties of Melt-Grown YBaCuO Superconductors Doped by Gd and Sm

Electromagnetic properties of YBa2Cu3Oy samples melt-grown in air and doped with small amounts of light rare earth (LRE) ions Gd and Sm were studied. The LRE doping creates a point-like disorder contributing to the second peak on the magnetization curve. In the eld range of the second peak the average magnetic moment, Mav, deduced from the magnetization curves exhibited strong uctuations. Mav is commonly regarded as an equilibrium moment close to the thermodynamic reversible one, obeying in intermediate elds a logarithmic eld dependence. However, in our experiments Mav(B) curves failed to follow such a dependence below irreversibility line. Mav(B) curves deduced from rather static measurements, done by SQUID magnetometer still showed the disturbance but signi cantly weaker. It indicates that this feature re ects the vortex dynamics in the second peak region. Its scaling with temperature was found to coincide with that of the pinning force.

Diffusion at the surface of topological insulators

We consider the dc transport properties of topological insulator surface states in the presence of uncorrelated point-like disorder, both in the classical and quantum regimes. The dc conductivity of those two-dimensional surface states depends strongly on the amplitude of the hexagonal warping of their Fermi surface. A perturbative analysis of the warping is shown to fail to describe the transport in Bi2Se3 over a broad range of experimentally available Fermi energies, and in Bi2Te3 for the higher Fermi energies. Hence we develop a fully non-perturbative description of these effects. In particular, we find that the dependence of the warping amplitude on the Fermi energy manifests itself in a strong dependence of the diffusion constant on this Fermi energy, leading to several important experimental consequences. Moreover, the combination of a strong warping with an in-plane Zeeman effect leads to an attenuation of conductance fluctuations in contrast to the situation of unwarped Dirac surface states.

Effect of point-like disorder on the vortex phase diagram in Bi2Sr2CaCu2O8−δ in oblique field

The phase diagram of vortex matter in the layered superconductor Bi2Sr2CaCu2O8−δ exposed to a magnetic field oblique to the crystalline c-axis contains two first order transition (FOT) lines [1]. The first, HFOTm, separates the vortex solid from the vortex liquid, the second, HFOTct, separates the combined lattice state in the vortex solid from a tilted lattice state. The angular dependence of HFOTm in the tilted lattice region follows the anisotropic Ginzburg–Landau model [2], allowing for the determination of the anisotropy factor γeff and the contribution of magnetic coupling to the mutual interaction of “pancake” vortices in the crossed lattice limit. The later parameter is directly related to the in-plane penetration depth λab. We investigate the evolution of the phase diagram of Bi2Sr2CaCu2O8−δ in oblique fields with point-like disorder, introduced by irradiation with 2.3MeV electrons. Apart from the depression of Tc, point-like disorder induces an increase of γeff and a depression of the superfluid density.

Vortex matter in Bi2Sr2CaCu2O8 with pointlike disorder

We investigate the effect of point-like disorder, introduced by irradiation with 2.3 MeV electrons, on the mixed state phase diagram of Bi2Sr2CaCu2O8 single crystals. We focus on the higher irradiation doses that produce a significant depression of the critical temperature Tc, to as low as 2/3 of the initial value. Surprisingly, the first order phase transition (FOT) of the vortex ensemble, from a crystal to the pancake vortex liquid, persists in those highly disordered samples. The second peak in the irreversible magnetization, observed at low temperatures, is equally observed after high irradiation doses, but at much lower magnetic fields. A simple scaling of the phase diagram for samples with various degrees of disorder is not possible, indicating that several fundamental parameters of the superconductor are affected. From the analysis of the angular dependence of the FOT, we deduce that the effective anisotropy factor increases after irradiation.

Nonmagnetic impurities in aS=12frustrated triangular antiferromagnet: Broadening ofC13NMR lines inκ−(ET)2Cu2(CN)3

We study effects of nonmagnetic impurities in a spin-1/2 frustrated triangular antiferromagnet with the aim of understanding the observed broadening of $^{13}$C NMR lines in the organic spin liquid material $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$. For high temperatures down to $J/3$, we calculate local susceptibility near a nonmagnetic impurity and near a grain boundary for the nearest neighbor Heisenberg model in high temperature series expansion. We find that the local susceptibility decays to the uniform one in few lattice spacings, and for a low density of impurities we would not be able to explain the line broadening present in the experiments already at elevated temperatures. At low temperatures, we assume a gapless spin liquid with a Fermi surface of spinons. We calculate the local susceptibility in the mean field and also go beyond the mean field by Gutzwiller projection. The zero temperature local susceptibility decays as a power law and oscillates at $2 k_F$. As in the high temperature analysis we find that a low density of impurities is not able to explain the observed broadening of the lines. We are thus led to conclude that there is more disorder in the system. We find that a large density of point-like disorder gives broadening that is consistent with the experiment down to about 5K, but that below this temperature additional mechanism is likely needed.

Pinning performance of (Nd,Eu,Gd)-123 superconductors: Comparison of melt-textured pellet and single crystal

We studied pinning homogeneity and the content fluctuation of light rare earth ions in a (Nd 0.33Eu 0.38Gd 0.28)Ba 2Cu 3O y melt-textured (MT) pellet 16 mm in diameter, doped by 0.035 mol% ZnO. The pinning performance was compared to that of the recently grown (Nd 0.33Eu 0.2Gd 0.47)Ba 2Cu 3O y single crystal. While magnetic properties of most test samples cut from the MT pellet were surprisingly uniform, two samples from the pellet center behaved significantly different. This anomaly was found to correlate with the significant departure of the Eu:Nd ratio from the average. Nearly all MT samples showed a high-field shoulder on J c( B) curve that was attributed to the pinning effect of a nanoscopic correlated lamellar substructure filling channels between regular twin boundaries. As a result, the irreversibility field at 77 K reached in all 20 measured MT samples 9 T. In the single crystal no high-field J c( B) shoulder was observed, and the irreversibility field at 77 K was about 6 T. The strip-like structure observed on the crystal surface was evidently of another origin than the lamellar substructure in the MT samples and did not significantly contribute to vortex pinning. The secondary peak in J c( B) of the single crystal was quite strong, showing a well set point-like disorder. All magnetic characteristics of the single crystal were strongly affected by twin-plane channeling effect.

C-axis coupling in underdopedBi2Sr2CaCu2O8+δwith varying degrees of disorder

The dependence of the Josephson plasma resonance (JPR) frequency in heavily underdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ on temperature and controlled pointlike disorder, introduced by high-energy electron irradiation, is cross-correlated and compared to the behavior of the $ab$-plane penetration depth. It is found that the square of the zero-temperature plasma frequency, representative of the superfluid component of the $c$-axis spectral weight, decreases proportionally with ${T}_{c}$ when the disorder is increased. The temperature dependence of the JPR frequency is the same for all disorder levels, including pristine crystals. The reduction of the $c$-axis superfluid density as function of disorder is accounted for by pair breaking induced by impurity scattering in the $\mathrm{Cu}{\mathrm{O}}_{2}$ planes, rather than by quantum fluctuations of the superconducting phase. The reduction of the $c$-axis superfluid density as function of temperature follows a ${T}^{2}$ law and is accounted for by quasiparticle hopping through impurity-induced interlayer states.

Influence of point-like disorder on the guiding of vortices in a rotating current scheme

Explicit current-dependent expressions for anisotropic longitudinal and transverse (with respect to the current direction) nonlinear magnetoresistivities are represented and analyzed on the basis of a Fokker–Planck approach for two-dimensional single-vortex dynamics in a washboard pinning potential in the presence of point-like disorder. Graphical analysis of the nonlinear resistive responses is presented in the rotating current scheme.

Influence of point-like disorder on the guiding of vortices in anisotropic superconductors

It is shown that guiding of vortices caused by anisotropy of a superconductor can lead to the appearance of new nonlinear anisotropic Hall voltages in the presence of point-like disorder. The magnetoresistivity tensor of the problem is calculated and analyzed. New anisotropic “scaling” relation for the Hall conductivity (which generalize the well-known scaling relation ρ xy ∼ ( ρ xx ) 2 for isotropic media) is derived and related experiment for its observation is proposed.