Effect Of Nonmagnetic Impurities Research Articles

Magnetic Effects of Nonmagnetic Impurities in Gapped Short-Range Resonating Valence Bond Spin Liquids.

We study the effect of a small density n_{v} of quenched nonmagnetic impurities, i.e., vacancy disorder, in gapped short-range resonating valence bond (RVB) spin liquid states and valence bond solid (VBS) states of quantum magnets. We argue that a large class of short-range RVB liquids are stable to vacancy disorder at small n_{v} on the kagome lattice, while the corresponding states on triangular, square, and honeycomb lattices are unstable to vacancy disorder at any nonzero n_{v} due to the presence of emergent vacancy-induced local moments. In contrast, VBS states are argued to be generically unstable (independent of lattice geometry) to vacancy disorder at any nonzero n_{v} due to such a local-moment instability. Our arguments rely in part on an analysis of the statistical mechanics of maximally packed dimer covers of the diluted lattice, and are fully supported by our computational results on O(N) symmetric designer Hamiltonians. These arguments also imply that short-range RVB spin liquid states are generically unstable to bond dilution on all these lattices.

Impurity effect on magnetic and thermal properties of S = 3/2 spin gap system Ba3Ca(Ru1−xNbx)2O9

We have investigated the nonmagnetic impurity effects on magnetic and thermal properties for the spin gap system Ba3CaRu2O9, which has the Ru2O9 dimers composed of two Ru5+ spins (S = 3/2). The measurements of the magnetic susceptibility and specific heat have been carried out for the polycrystalline samples of Ba3Ca(Ru1−xNbx)2O9, where the Ru5+ spins are partially substituted by the non-magnetic Nb5+ ions. We have observed the magnetic behavior of the remained Ru5+ spins derived from breaking the singlet formation by the Nb-doping. These magnetic behaviors can be understood by the S = 3/2 free spin model under an internal magnetic field. Based on the obtained results, the mechanism of the singlet formation of Ba3CaRu2O9 is discussed.

Anomalous Hall effect from a non-Hermitian viewpoint

Non-Hermitian descriptions often model open or driven systems away from the equilibrium. Nonetheless, in equilibrium electronic systems, a non-Hermitian nature of an effective Hamiltonian manifests itself as unconventional observables such as a bulk Fermi arc and skin effects. We theoretically reveal that spin-dependent quasiparticle lifetimes, which signify the non-Hermiticity of an effective model in the equilibrium, induce the anomalous Hall effect, namely the Hall effect without an external magnetic field. We first examine the effect of nonmagnetic and magnetic impurities and obtain a non-Hermitian effective model. Then, we calculate the Kubo formula from the microscopic model to ascertain a non-Hermitian interpretation of the longitudinal and Hall conductivities. Our results elucidate the vital role of the non-Hermitian equilibrium nature in the quantum transport phenomena.

Nodeless Superconductivity in Kagome Metal CsV3Sb5 with and without Time Reversal Symmetry Breaking.

The kagome metal CsV3Sb5 features an unusual competition between the charge-density-wave (CDW) order and superconductivity. Evidence for time reversal symmetry breaking (TRSB) inside the CDW phase has been accumulating. Hence, the superconductivity in CsV3Sb5 emerges from a TRSB normal state, potentially resulting in an exotic superconducting state. To reveal the pairing symmetry, we first investigate the effect of nonmagnetic impurity. Our results show that the superconducting critical temperature is insensitive to disorder, pointing to conventional s-wave superconductivity. Moreover, our measurements of the self-field critical current (Ic,sf), which is related to the London penetration depth, also confirm conventional s-wave superconductivity with strong coupling. Finally, we measure Ic,sf where the CDW order is removed by pressure and superconductivity emerges from the pristine normal state. Our results show that s-wave gap symmetry is retained, providing strong evidence for the presence of conventional s-wave superconductivity in CsV3Sb5 irrespective of the presence of the TRSB.

Dulmage-Mendelsohn Percolation: Geometry of Maximally Packed Dimer Models and Topologically Protected Zero Modes on Site-Diluted Bipartite Lattices

A new kind of quantum percolation phenomenon---of particles hopping on a lattice with missing sites---has implications for the effect of nonmagnetic impurities in quantum antiferromagnets and could aid the search for Majorana excitations in solid-state devices.

Changes in the Structural Parameters and Effective Magnetic Moment of Eu2−xCexCuO4+α−δ by Zn Substitution

The effect of nonmagnetic Zn impurities on the structural parameters and effective magnetic moment of electron-doped superconducting cuprates Eu2−xCexCu1−yZnyO4+α−δ (ECCZO) with x = 0.10 and 0.15 and y = 0 and 0.01 has been investigated using XRD and SQUID measurements. From XRD measurements, it is found that the lattice parameter of c and the Cu-O bond length increase with increasing y. The crystallite size of ECCZO samples was relatively smaller than the sample without impurities determined by the Debye–Scherrer equation and the W-H Plot method. Changes in the lattice parameters of c and Cu-O bond length can affect the appearance of superconductivity (Tc). The smaller the value of the lattice parameter of c and the Cu-O bond length causes the distance between the conducting layer and the charge reservoir to be close enough so that the charge transfer process becomes easier. From the magnetic susceptibility measurement, paramagnetic characteristics were observed for samples with x = 0.10. Meanwhile, for samples with x = 0.15, diamagnetic characteristics can be identified in sample with y = 0. The onset of Tc was observed around 11 K, as indicated by a change from paramagnetic to diamagnetic characteristics. The superconductivity phase disappears with y = 0.01. The effective magnetic moments in samples with y = 0 are smaller than those in samples with y = 0.01. The effective magnetic moment in ECCZO can be contributed by Cu2+. When the amount of Cu2+ decreases due to the addition of nonmagnetic Zn2+ atoms, the overall effective magnetic moment value also decreases. Another possibility that causes a decrease in the value of the magnetic moment of the ECCZO is the existence of stripe-pinning model, which results in suppressed superconductivity by Zn.

The Gor'kov and Melik‐Barkhudarov Correction to an Imbalanced Fermi Gas in the Presence of Impurities

AbstractThe effects of induced interactions are calculated in both clean and dirty situations, for balanced and imbalanced Fermi gases. The effects of nonmagnetic impurities on the induced interactions corrections to the transition temperature in the case of a balanced gas, and to the tricritical point in the case of an imbalanced Fermi gas at unitarity are investigated. It is found that impurities act in detriment of the induced interactions, or particle–hole fluctuations, for the transition temperature and the tricritical point. For large impurity parameter, the particle–hole fluctuations are strongly suppressed. The Chandrasekhar–Clogston limit of an imbalanced Fermi gas at unitarity considering the effects of the induced interactions, both in the pure and impurity regimes have also been found.

Effects of Nonmagnetic Impurities and Subgap States on the Kinetic Inductance, Complex Conductivity, Quality Factor, and Depairing Current Density

We investigate how a combination of a nonmagnetic-impurity scattering rate $\gamma$ and finite subgap states parametrized by Dynes $\Gamma$ affects various physical quantities relevant to to superconducting devices: kinetic inductance $L_k$, complex conductivity $\sigma$, surface resistance $R_s$, quality factor $Q$, and depairing current density $J_d$. All the calculations are based on the Eilenberger formalism of the BCS theory. We assume the device materials are extreme type-II $s$-wave superconductors. It is well known that the optimum impurity concentration ($\gamma/\Delta_0 \sim 1$) minimizes $R_s$. Here, $\Delta_0$ is the pair potential for the idealized ($\Gamma\to 0$) superconductor for the temperature $T\to 0$. We find the optimum $\Gamma$ can also reduce $R_s$ by one order of magnitude for a clean superconductor ($\gamma/\Delta_0 < 1$) and a few tens $\%$ for a dirty superconductor ($\gamma/\Delta_0 > 1$). Also, we find a nearly-ideal ($\Gamma/\Delta_0 \ll 1$) clean-limit superconductor exhibits a frequency-independent $R_s$ for a broad range of frequency $\omega$, which can significantly improve $Q$ of a very compact cavity with a few tens of GHz frequency. As $\Gamma$ or $\gamma$ increases, the plateau disappears, and $R_s$ obeys the $\omega^2$ dependence. The subgap-state-induced residual surface resistance $R_{\rm res}$ is also studied, which can be detected by an SRF-grade high-$Q$ 3D resonator. We calculate $L_k(\gamma, \Gamma,T)$ and $J_d(\gamma, \Gamma,T)$, which are monotonic increasing and decreasing functions of $(\gamma, \Gamma,T)$, respectively. Measurements of $(\gamma, \Gamma)$ of device materials can give helpful information on engineering $(\gamma, \Gamma)$ via materials processing, by which it would be possible to improve $Q$, engineer $L_k$, and ameliorate $J_d$.

Superconductivity in Cu-doped Bi2Se3 with potential disorder

We study the effects of random nonmagnetic impurities on superconducting transition temperature ${T}_{c}$ in a Cu-doped ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, for which four types of pair potentials have been proposed. Although all the candidates belong to $s$-wave symmetry, two orbital degrees of freedom in electronic structures enrich the symmetry variety of a Cooper pair such as even-orbital-parity and odd-orbital-parity. We consider realistic electronic structures of Cu-doped ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ by using a tight-binding Hamiltonian on a hexagonal lattice and consider effects of impurity scatterings through the self-energy of the Green's function within the Born approximation. We find that even-orbital-parity spin-singlet superconductivity is basically robust even in the presence of impurities. The degree of the robustness depends on the electronic structures in the normal state and on the pairing symmetry in orbital space. On the other hand, two odd-orbital-parity spin-triplet order parameters are always fragile in the presence of potential disorder.

The Superconductivity Mechanism in Nd-1111 Iron-Based Superconductor Doped by Calcium

We describe the effect of nonmagnetic impurity on the superconductivity behavior of the NdFeAsO0.8F0.2 iron-based superconductor. The resistivity measurements show that the superconductivity is suppressed upon increasing the low amounts of calcium impurity (x ≤ 0.05). Also, the TC decreases with the increase in the residual resistivity. Such behavior is qualitatively described by the Abrikosov–Gorkov theory and confirms that these impurities act as scattering centers. Moreover, we present the phase diagram of our synthesized samples for the various calcium dopings. We find that according to the increase in the calcium impurities and the decrease in the spin-density wave transition tempeθrature (TSDW), Fe ions are arranged stripe-antiferromagnetic at lower temperatures and also the superconducting transition temperature (TC) declines. Based on our results and in agreement with the available theories as is explained in the text, since the S++ state has no effect on the impurity-doped samples, and for low amounts of calcium, the S± state that is attributed to the spin-fluctuations causes the superconductivity suppression. So, it confirms the role of the spin-fluctuations as a dominant pairing mechanism in our synthesized samples.

Variation of zero-energy density of states of a d -wave superconductor in a rotating in-plane magnetic field: Effect of nonmagnetic impurities

Oscillation of zero-energy density of states under the rotation of an in-plane magnetic field is used to identify node positions of the superconducting gap. Based on Eilenberger theory that can capture the vortex core contribution appropriately, we quantitatively study the effects of nonmagnetic impurity scattering on the oscillation in a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductor, as a function of the magnetic field and the scattering rate in the Born and the unitary limits. We find that the sign of the oscillation can be changed by the impurity scattering at low fields, indicating that impurity effect is an important factor in the analysis of angle-resolved specific heat measurements.

Relation of Superconducting Pairing Symmetry and Non-Magnetic Impurity Effects in Vortex States

Non-magnetic impurity scattering effects on the vortex core states are theoretically studied to clarify the contributions from the sign-change of the pairing function in anisotropic superconductors. The vortex states are calculated by the Eilenberger theory in superconductors with p x -wave pairing symmetry, as well as the corresponding anisotropic s-wave symmetry. From the spatial structure of the pair potential and the local electronic states around a vortex, we examine the differences between anisotropic superconductors with and without sign-change of the pairing function, and estimate how twofold symmetric vortex core images change with increasing the impurity scattering rate both in the Born and the unitary limits. We found that twofold symmetric vortex core image of zero-energy local density of states changes the orientation of the twofold symmetry with increasing the scattering rate when the sign change occurs in the pairing function. Without the sign change, the vortex core shape reduces to circular one with approaching dirty cases. These results of the impurity effects are valuable for identifying the pairing symmetry by observation of the vortex core image by the STM observation.

Compensation in the spin-1/2 site diluted Ising ferrimagnet: a Monte Carlo study

ABSTRACTA two-dimensional spin-1/2 trilayer magnetic system with quenched non-magnetic impurity is studied. The lattice is formed by alternate layers of two different theoretical atoms A and B arranged in a particular fashion A–B–A. The compensation point appears below the critical temperature, for which total magnetization of the system becomes zero even though the sublattice magnetization has a nonzero value. For a range of values of the relative interaction strength in the Hamiltonian, a compensation point is observed. We considered the Ising mechanics and employed the Monte Carlo method to determine the compensation point and critical temperature of the system. However, the effects of impurity in such systems are still not well studied. With that in mind, we address the effects of random non-magnetic impurity in the trilayer system. We also investigate the lattice morphologies in the presence of compensation and dilution and finally obtain the three-dimensional phase diagram for selected Hamiltonian parameters and impurity concentration.

Impurity Effects in Nodal Extendeds- and Nodelessd-Wave Superconductors: Gap Symmetry of BiS2-Based Layered Superconductors

In BiS$_2$-based layered superconductors,the existence of gap nodes on Fermi-surface curves has been suggested from angle-resolved photoemission spectroscopy measurements, whereas the conventional $s$-wave gap has been proposed from measurements of superfluid density and thermal conductivity. To reconcile these two distinct experimental results of the gap node, we investigate nonmagnetic impurity effects in the superconductor with a disconnected pocketlike Fermi-surface structure. Then, we claim that the seemingly contradictory situation concerning the gap node is resolved by a concept of dirty nodal extended $s$-wave superconductivity. Provided that it is unnecessary to consider the nodes of the gap, at first glance, the conventional $s$-wave gap seems to be a unique solution, but in the pocketlike Fermi-surface topology, a nontrivial possibility of a nodeless $d$-wave superconductor is pointed out. To clarify the gap symmetry, we propose to perform experiments on nuclear magnetic relaxation rate $T_{1}^{-1}$ in BiS$_2$-based layered superconductors.

Nonmagnetic impurity effect on magnetic correlation in the triangular-lattice antiferromagnet Ba3Mn1−xZnxSb2O9(0 < x < 0.16)

The nonmagnetic impurity effects on the triangular-lattice antiferromagnet (TLAF) Ba3Mn1−xZnxSb2O9 () by Zn2+ () dilutions are investigated based on magnetic susceptibility, specific heat and electron spin resonance (ESR) measurements. The ac susceptibility and specific heat result reveal that the two-dimensional (2D) antiferromagnetic (AFM) ground state is stable rather than forming a spin-glass (SG) phase for Zn2+ substitution up to , where the AFM transition temperature (TN) shifts slowly from 10.2 K () to 8.2 K (). For all samples, the divergence of the temperature-dependent linewidth of ESR can be well described in terms of the Berezinskii-Kosterlitz-Thouless (BKT) scenario. The evolution of ESR spectra suggests that the nonmagnetic impurity does not induce magnetic defects decoupled with AFM matrix but rather change the bulk AFM properties.

Study of structure and resistivity of electron-doped superconducting cuprates Eu1.85Ce0.15Cu1-yZnyO4+α-δ

Partially Zn-substituted for Cu in electron-doped superconducting cuprates of Eu1.85Ce0.15Cu1-yZny4+α-δ (ECCZO) with y = 0, 0.01, 0.02, 0.05 and various δ values have been studied in order to elucidate the effect of nonmagnetic impurity of Zn to their structure and resistivity properties in the electron-doped cuprates. It has been found that the main peaks of T’ structures are clearly observed in all samples. Superconductivity disappeared with Zn substitution for Cu in electron-doped system of ECCZO.

Green's-function theory of dirty two-band superconductivity

We study the effects of random nonmagnetic impurities on the superconducting transition temperature $T_c$ in a two-band superconductor, where we assume the equal-time spin-singlet s-wave pair potential in each conduction band and the hybridization between the two bands as well as the band asymmetry. In the clean limit, the phase of hybridization determines the stability of two states: called $s_{++}$ and $s_{+-}$. The interband impurity scatterings decrease $T_c$ of the two states exactly in the same manner when the Hamiltonian preserves time-reversal symmetry. We find that a superconductor with larger hybridization shows more moderate suppression of $T_c$. This effect can be explained by the presence of odd-frequency Cooper pairs which are generated by the band hybridization in the clean limit and are broken by impurities.

Dirty two-band superconductivity with interband pairing order

We study theoretically the effects of random nonmagnetic impurities on the superconducting transition temperature Tc in a two-band superconductor characterized by an equal-time s-wave interband pairing order parameter. Because of the two-band degree of freedom, it is possible to define a spin-triplet s-wave pairing order parameter as well as a spin-singlet s-wave order parameter. The former belongs to odd-band-parity symmetry class, whereas the latter belongs to even-band-parity symmetry class. In a spin-singlet superconductor, Tc is insensitive to the impurity concentration when we estimate the self-energy due to the random impurity potential within the Born approximation. On the other hand in a spin-triplet superconductor, Tc decreases with the increase of the impurity concentration. We conclude that Cooper pairs belonging to odd-band-parity symmetry class are fragile under the random impurity potential even though they have s-wave pairing symmetry.

Coexistence of topological charge density waves and superconductivity in a two-dimensional topological superconductor

We perform microscopic mean-field studies of topological order in a two-dimensional s-wave topological superconductor with Rashba spin-orbit coupling and Zeeman field by solving the Bogoliubov-de Gennes equations. By solving for the spin-dependent Hartree potential self-consistently along with the superconducting order parameter, we show that topological charge density waves (TCDW) can coexist with topological superconductivity (TSC) at half filling just as in a conventional s-wave superconductor. Furthermore, we examine the effects of nonmagnetic impurities – which tend to create spin-polarised midgap excitation and pin the phase of charge density modulations – on possible interplay of TCDW and TSC.

Magnetic and nonmagnetic impurity effects on Cu3Mo2O9

We compare the magnetic (Ni) substitution effects in Cu3Mo2O9 to the nonmagnetic (Zn) ones. Changes in the lattice constants show similar behaviours for both impurity substituted samples. In specific heat measurements, we observe the anomalous specific heat at the phase transition temperature TN. TN in the Ni substituted sample increases to 8.8 K; while TN in the Zn substituted sample decreases to 4.0 K. In magnetization measurement on the Ni substituted sample, we obtain the Van-Vleck type constant magnetization. We suggest the existence of the single-ion anisotropy of the substituted Ni2+ ions, which is a possible candidate for the origin of the increment of TN in the Ni substituted sample.