Low Carrier Density Systems Research Articles

Phonon-mediated superconductivity in low carrier-density systems

Motivated by the observation of superconductivity in SrTiO$_3$ and Bi, we analyze phonon-mediated superconductivity in three-dimensional systems at low carrier density, when the chemical potential $\mu$ (equal to Fermi energy at $T=0$) is comparable to or even smaller than the characteristic phonon frequency $\omega_L$. We consider the attractive part of the Bardeen-Pines pairing interaction, in which the frequency-dependent electron-phonon interaction is dressed by the Coulomb potential. This dressing endows the pairing interaction with momentum dependence. We argue that the conventional Migdal-Eliashberg (ME) approximation becomes invalid when $\mu \leq \omega_L$ chiefly because the dominant contribution to pairing comes from electronic states away from the Fermi surface. We obtain the pairing onset temperature, which is equal to $T_c$ in the absence of phase fluctuations, as a function of $\mu/\omega_L$. We find both analytically and numerically that $T_c$ increases as the ratio $\mu/\omega_L$ becomes smaller. In particular, in the dilute regime, $\mu \rightarrow 0$, it holds that $T_c\propto\omega_L\left(\frac{Ry}{\omega_L}\right)^\eta$, where $\text{Ry}$ is the Rydberg constant and $\eta \sim 0.2$.

Field-insensitive heavy fermion features and phase transition in the caged-structure quasi-skutterudite Sm3 Ru4 Ge13

The robust field-insensitive heavy fermion features in Sm3 Ru4 Ge13 and the magnetic phase transition at TN ≈ 5 K are studied using magnetization M(T), specific heat Cp(T), resistivity ρ(T) and thermal conductivity κT(T). The average crystal structure of Sm3 Ru4 Ge13 conforms to the cubic space group Pm3¯n however, signatures of subtle structural distortions are obtained from the x ray data. The magnetic susceptibility, χ(T), follows a modified Curie–Weiss law indicating the presence of crystal fields of Sm3+ and the significance of van Vleck terms. No sign of ferromagnetism is observed in M(H) of Sm3 Ru4 Ge13 which yields only 0.025 μB/f.u.-Sm at 2 K, 7 T. The Sommerfeld coefficient, γ≈ 220 mJ/mol-Sm K2, estimated from the analysis of low temperature specific heat suggests the formation of heavy quasi particles at low temperature. Though a lnT dependence of ρ(T) is observed till 60 K, the resistivity behavior is accounted for by assuming a two-band model for activated behavior of charge carriers. The field scans of resistivity, ρ(H), below TN display significant nonlinearity while those above the TN are more metal-like. Low values of thermal conductivity, κT(T), are observed in Sm3 Ru4 Ge13 however, displaying an anomaly at TN which signifies magnetoelastic coupling. A fairly high value of Seebeck coefficient, S ≈ 40 μV/K is observed at 300 K. We identify Sm3 Ru4 Ge13 as a low charge carrier density system with unusual field-insensitive heavy fermion features very similar to the filled skutterudites.

Superconductivity in Y3Ru4Ge13 and Lu3Os4Ge13: A comparative study

A variety of unconventional superconductors have low carrier density as a common factor. However, the underlying mechanism of superconductivity in such low carrier density systems is not well understood. Besides, small carrier density is an unfavourable component for conventional superconductivity as described by the Bardeen-Cooper-Schrieffer (BCS) theory. Therefore, studying low carrier density systems can lead to a better understanding in such systems. In this paper, we report superconductivity property studies in low carrier density systems, Y3Ru4Ge13 and Lu3Os4Ge13, using various experimental techniques. Single crystals of Y3Ru4Ge13 and Lu3Os4Ge13 have been grown using the Czochralski crystal pulling method in a tetra-arc furnace. The x-ray diffraction experiment reveals that both compounds crystallize in cubic structure (space group Pm3n, no. 223). The transport, magnetization and heat capacity measurements show that Y3Ru4Ge13 single crystal undergoes a superconducting transition at 2.85 K, whereas, Lu3Os4Ge13 becomes superconductor at 3.1 K.

Superconductivity in a low carrier density system: A single crystal study of cubic Y3Ru4Ge13

We have successfully grown the single crystal of a low carrier density system Y3Ru4Ge13 which crystallises in the cubic crystal structure with the space group Pm3n. Y3Ru4Ge13 exhibits superconductivity below 2.85K as determined from the electrical resistivity, magnetic susceptibility and heat capacity measurements. The bulk measurements indicate multi-band superconductivity in this low carrier system. Hall effect measurements show that the Hall coefficient RH is positive and it decreases rapidly with temperature which is highly unusual. The simple estimation of the carrier concentration gives a value (1020/cm3) which is 2–3 orders of magnitude lower than that of a conventional metal like Cu which seems to suggest that Y3Ru4Ge13 is a semimetal that display multiband superconductivity.

Nearly frozen Coulomb liquids

We show that very long range repulsive interactions of a generalized Coulomb-like form $V(R)\sim R^{-\alpha}$, with $\alpha<d$ ($d$-dimensionality), typically introduce very strong frustration, resulting in extreme fragility of the charge-ordered state. An \textquotedbl{}almost frozen\textquotedbl{} liquid then survives in a broad dynamical range above the (very low) melting temperature $T_{c}$ which is proportional to $\alpha$. This \textquotedbl{}pseudogap\textquotedbl{} phase is characterized by unusual insulating-like, but very weakly temperature dependent transport, similar to experimental findings in certain low carrier density systems.

Electronic structure and transport properties of SrAl2Si2: Effect of yttrium substitution

We report the results of yttrium substitution on the electrical resistivity (ρ), the thermal conductivity (κ), as well as the Seebeck coefficient (S) of the Sr1−xYxAl2Si2 alloys with 0 ≤ x ≤ 0.20. Both ρ(T) and S(T) data suggest that SrAl2Si2 is a semimetallic, low charge carrier density system with a pseudogap at the Fermi level density of states (DOS). Upon substituting Y onto the Sr sites, the electrical resistivity and the absolute value of the Seebeck coefficient decrease significantly. Such an observation can be associated with the modification of the electronic band structure due to electron doping via Y substitution. Analysis of the thermal conductivity reveals the contribution of various thermal scattering mechanisms through chemical substitution. Theoretical studies with density functional theory are also employed to investigate the electronic band structure of Sr1−xYxAl2Si2. It is revealed that SrAl2Si2 possesses a shallow DOS at the Fermi level with both n-type and p-type charge carriers. Upon Y substitution a shift in the Femi level occurs such that the Sr1−xYxAl2Si2 system becomes more metallic with increasing x, being consistent with the experimental findings.

Quantum percolation transition in Eu1−xCaxB6

AbstractThe study of transport and magnetic properties performed on Eu1−xCaxB6 single crystals with nominal Ca content 0 ≤ x ≤ 0.4 at temperatures 1.8–300 K in magnetic fields up to 80 kOe provides the direct experimental evidence of metal‐to‐insulator transition (MIT) earlier proposed for the system by V. M. Pereira et al. [Phys. Rev. Lett., 93, 147202 (2004)]. A giant enhancement of magnetoresistance up to the values of (ρ(0) − ρ(H))/ρ(H) ∼ 7 × 107% was detected for x = 0.4 in the wide vicinity of the ferromagnetic insulating state. The field induced crossover from hole‐like to electron‐like regime of charge transport observed for the first time in the paramagnetic phase of Eu0.6Ca0.4B6 is discussed in terms of quantum percolation transition predicted for this low carrier density system within double exchange model.

A giant enhancement of CMR in Eu0.6Ca0.4B6

The transport and magnetic properties of Eu0.6Ca0.4B6 single crystals have been studied at temperatures 1.8-300 K in magnetic fields up to 80 kOe. It was found that lowering of temperature results in a drastic increase of magnetoresistance up to the values of ρ(0)/ρ(H)≈7·105 detected below 6K. The Hall and Seebeck effect measurements showed that colossal magnetoresistance (CMR) observed in Eu0.6Ca0.4B6 is accompanied by a crossover from hole-like to electron-like regime of charge transport induced by applied magnetic field. Hall mobility values μH~200–350 cm2/(Vs) estimated for the high conductive state of Eu0.6Ca0.4B6 in the presence of strong substitutional disorder were proved to be comparable with these ones measured for undoped EuB6. The anomalous behaviour of transport and magnetic parameters is discussed in terms of metal-insulator transition earlier predicted for this low carrier density system within double exchange model by V M Pereira et al., Phys. Rev. Lett. 93 147202 (2004).

Anomalous Magnetism in Eu(Ca)B&lt;sub&gt;6&lt;/sub&gt;

The transport and magnetic properties of the Eu1-xCaxB6 (0x0.4) single crystals were studied in the wide ranges of temperatures (1.8-300 K) and magnetic fields (up to 8 T). The experimental data allow to identify a metal-insulator transition (MIT) at the critical Ca concentration xMIT≈0.3, which agrees well with the predictions of double exchange model (V.M. Pereira et al. Phys. Rev. Lett., 93 (2004) 147202). A significant enhancement of magnetoresistive effect is observed below 100K for Eu1-xCaxB6 compounds corresponding to the metallic side of the MIT (xxMIT). The drastic decrease of paramagnetic Curie temperature evaluated from the magnetic and magnetotransport data is discussed in terms of quantum MIT scenario recently proposed for this low carrier density system.

Defects and transport in complex oxide thin films

Epitaxial oxide thin films are at the heart of new “oxide electronic” applications, such as excitonic ultraviolet light-emitting diodes and resistive switching memories. Complex oxide films are often grown by pulsed laser deposition (PLD) because the technique is believed to be material agnostic. Here, we show that one of the fundamental premises used to justify the use of PLD, that material is transferred from an ablation target to the film without stoichiometry deviations, is incorrect even when no volatile elements are involved. Even more importantly, the commonly used solution of increasing the laser energy density above a material-specific threshold value to obtain stoichiometric films cannot be used in the case of low carrier density systems such as SrTiO3, where even minute 1018 cm−3 order cation nonstoichiometry can have a dramatic effect on transport. Lattice parameter deviations in oxide films, which are often incorrectly ascribed to oxygen loss, correlate very well with cation nonstoichiometry. We show that proper simultaneous choice of ablation laser fluence and ablation area is essential and often more important than the growth temperature and oxygen pressure for obtaining bulklike properties in oxide heterostructures.

P31Knight shifts and spin dynamics in Si:P at temperatures comparable to the Fermi temperature

Meintjes, Danielson, and Warren (MDW) have recently reported the results of high-temperature NMR and Hall effect experiments using samples of Si:P with P concentrations at, and above, the metal-insulator transition value of $3.7\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. MDW interpret their measurements of the $^{31}\mathrm{P}$ Knight shift $(K)$ and relaxation rate $(1∕{T}_{1})$ in terms of a model that emphasizes the role of impurity bands for just-metallic samples. We show that a number of features of the MDW data can be usefully explored by use of a less elaborate approach. An extension of the Korringa relation, which relates $K$ and $1∕{T}_{1}$, into regimes where ${k}_{B}T$ is comparable to, or greater than, the Fermi energy ${E}_{F}$ confirms that the electron-nucleus hyperfine interaction does, indeed, control Knight shift and relaxation rate in this high-$T$ regime. We also explore insights gained by comparison of the MDW data with the extensive earlier NMR data at $4.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and below. The extended Korringa relation provides a method for analyzing high-$T$ NMR data in other low carrier density systems.

Direct observation of the modulation of the 4f-electron orbital state by strong p-f mixing in CeSb.

Low-temperature x-ray diffraction experiment has been carried out to investigate the 4 f-electron state of the low carrier density system CeSb which shows complicated magnetic phase diagrams at low temperatures. The scattering pattern of the satellite peaks observed in the magnetically ordered state AFP3 is explained well by the model which takes into account both the lattice and charge modulations corresponding to the complex magnetic structure. The present result gives direct evidence for the strong modulation of the 4 f-electron orbital state in CeSb due to the combined effect of the strong p-f mixing and carrier localization.

Mechanism of anomalously weak magnetic scattering in Gd monopnictides

It was found that the ferromagnetic enhancement in the paramagnetic Curie temperature in Gd monopnictides is very weak compared with doped Eu chalcogenides with the similar amount of electrons. Magnetic resistivity is also unusually small with nearly equal amount of mobilities for electrons and holes. This anomalous behavior was explained by near cancellation of the d-f exchange interaction and the p-f scattering through p-f mixing with opposite sign. The cancellation dose not occur in metals but occurs in low carrier density systems with small scattering wave vectors. Symmetry conserving characteristics is also significant for the mixing process in low carrier density systems.

Mass Reduction in Low Carrier Density Systems

The cyclotron masses observed by the de Haas-van Alphen effect in semimetallic LaSb and particularly in small flat pockets in LaB 6 , are substantially smaller than those evaluated by band calculations. As a common mechanism for low-carrier-density-systems, the mass reduction mechanism by the exchange interaction was first studied for an electron gas based on a simple model including Wigner crystal type screening. This model reproduces the result of high-density expansion and extends the result to the much lower density region of the Wigner liquid. The model was applied to the band electrons by dividing the band state into a plane wave part and a core part within a muffin-tin-sphere. It is shown that the mass reduction effect is enhanced particularly in the case of a small Fermi surface with strong anisotropy, which is in good agreement with the results obtained for the above materials.

Physics in low carrier strongly correlated systems: Kondo insulator magnetic polaron and high Tc

It is shown that in low carrier density systems a strong tendency to form the Wigner crystal, or electron localization, is clearly seen through long-range Coulomb interaction. The Kondo insulator is one typical example, in which the Kondo electron is localized and an excitondashlike excitation is observed. The magnetic polaron liquid and lattice is another typical example and is seen most typically in Ce and Yb monopnictides. A detailed study on Cesb is shown. In this system, an enhanced Kondo state due to tendency of localization coexists. High T c CuO 2 layered materials are also another typical example belonging to the present category. A description by the magnetic polaron picture is given. It is shown that, due to strong antiferromagnetic short-range order, a modified magnetic polaron with a singlet core is formed at high temperature and at lower temperature a pair magnetic polaron is formed. The superconductivity occurs due to their Bose condensation.

Comparison between Ce-monopnictides and An-monopnictides: strong mixing effect

The present situation with respect to understanding rare earth and transition metal compounds is reviewed briefly. Ideas essential to the understanding of anomalous heavy fermion rare earth compounds are described in detail by selecting Ce-monopnictides as a typical example. The Kondo state is considered as a typical charge screening mechanism. In the low carrier density systems, the magnetic polaron liquid is shown to play an important role. In general, the unrestricted Hartrec-Fock band picture is applicable to the 4f states. General ideas to explain the anomalous heavy fermion U-compounds are presented by borrowing ideas from the 4f and 3d systems. For the anomalous U-compounds, the unrestricted Hartree-Fock picture is proposed to be applicable. Anomalous properties in U-monopnictides and U-monochalcogenides are studied in detail based on the above described ideas, in particular the unrestricted Hartree-Fock picture. It is shown that the main anomalous properties are explained consistently.

Magnetic polarons in magnetic low carrier density systems

In magnetic low carrier density systems, in addition to the strong intra-atomic correlation, a strong correlation due to the long-range Coulomb interaction becomes important, causing a tendency to Wigner crystal or liquid system. In magnetic systems, the tendency to localization is further enhanced by magnetic polarization, and the magnetic polaron liquid and lattice are fairly easily formed. This is most clearly seen in CeP and CeAs; a detailed description is given in this paper. A weak Γ8 hole magnetic polaron is formed in a liquid state even at room temperature. The population of the magnetic polaron decreases with decreasing population of 4f Γ8 but persists even at the lowest temperatures. An applied field and pressure change the weak magnetic polaron liquid to a strong magnetic polaron lattice with nearly saturated moment.

Bose condensation and high-T c superconductivity in La 2−xSr xCuO 4

The Wigner-liquid model developed recently in strongly correlated low carrier density systems with 4f-electrons was applied to the high- T c CuO 2 layer systems. It is expected that pair formation of up- and down-spin holes inducing magnetic polarons occurs through Coulomb interaction as well as enhancing the exchange energy gain and the superconductivity occurs as Bose condensation. Temperature and the hole concentration dependences of the spin-spin correlation length are explained very well by this model.

Impurity-spin screening in low-density Fermi liquids.

We consider the problem of a magnetic impurity, described by the Anderson impurity model, in a low carrier density system. Such a system might be realized experimentally in strongly doped semiconductors containing magnetic impurities. We focus on the simple cases of a one-hole impurity (e.g., ${\mathrm{Cu}}^{2+}$) or a one-electron impurity (like ${\mathrm{Ce}}^{3+}$) hybridizing with a nearly filled or nearly empty band. We show that the physics of these systems is in various respects distinct from the Kondo effect of systems with partly filled valence bands. Although the local susceptibility is strongly enhanced by the interactions, we find at low doping (\ensuremath{\delta}) a mass reduction of the quasiparticles at the Fermi energy (${\mathit{E}}_{\mathit{F}}$), if a (singlet) bound state is stable at zero doping. We show analytically that this is caused by band-edge effects. We show further that vastly different behavior can be expected, depending on the filling of the impurity. For a one-electron impurity (Ce) interacting with an almost-filled valence band in the U=\ensuremath{\infty} limit, there is a one-particle-like bound state close to ${\mathit{E}}_{\mathit{F}}$. As the doping is increased this state turns into a traditional Kondo resonance. In the case of a nearly filled impurity, however, the gap state is a two-particle singlet bound state, causing a singularity in the vertex function of the diagrammatic approach to the Kondo problem. In this limit the so-called noncrossing approximation breaks down. At intermediate doping levels it is no longer possible to identify a small parameter and for small and intermediate dopings we argue that the system is not characterized by a single energy scale.