Session L46: Metals II

Quantum oscillation signatures of Fermi arc surface states in Weyl semimetals

Weyl semimetal states and their crystalline symmetry protected Dirac- analogs have recently been discovered in a variety of materials. These new phases of matter offer an interesting example of topology in the absence of a protecting band- or correlation- gap. The bulk topological character of these materials is revealed upon the application of a magnetic field, which produces chiral Landau level modes that propagate along the field and which mediate inter-valley charge pumping associated with chiral anomaly physics. At a surface, the bulk topology manifests itself in unusual surface states whose Fermi surface consists of disjoint arcs. In this talk, I will describe magnetic field induced quantum oscillation signatures of both the surface and bulk topological features of these materials. These oscillations are associated with unusual magnetic orbits that start on the Fermi arc of one surface, propagate through the bulk on the chiral Landau level, and complete the orbit on the opposite surface. I also will describe some recent experimental evidence for these orbits in Dirac semimetal thin films.   

Optical properties of the perfectly compensated semimetal WTe$_{\mathbf{2}}$

The optical properties of layered tungsten ditelluride have been measured over a wide temperature and frequency range for light polarized in the \emph{a-b} planes. A striking low-frequency plasma edge develops in the reflectance at low temperature where this material is a perfectly compensated semimetal. The optical conductivity is described using a two-Drude model which treats the electron and hole pockets as separate electronic subsystems. At low temperature, one scattering rate collapses by over two orders of magnitude, while the other also undergoes a significant, but less dramatic, decrease; both scattering rates appear to display the quadratic temperature dependence expected for a Fermi liquid. First principles electronic structure calculations reveal that the low-lying optical excitations are due to direct transitions between the bands associated with the electron and hole pockets.\footnote{C. C. Homes, M. N. Ali, and R. J. Cava, Phys. Rev. B {\bf 92}, 161109(R) (2015).}   

Role of spin-orbit coupling and evolution of the electronic structure of WTe$_{2}$ under an external magnetic field

Here, we present a study on the temperature and angular dependence of the Shubnikov--de Haas (SdH) effect in the semimetal WTe$_{2}$. This compound has been shown to display a large, nonsaturating magnetoresistance which was attributed to nearly perfectly compensated densities of electrons and holes. We observe four fundamental SdH frequencies and attribute them to spin-orbit split, electron-like, and hole-like Fermi-surface (FS) cross-sectional areas. Their angular dependence is consistent with ellipsoidal FSs that suggest a modest excess in the density of electrons with respect to that of the holes. We show that DFT calculations fail to correctly describe the FSs of WTe$_{2}$ and find evidence for field-dependent FS cross-sectional areas. We also observe a pronounced field-induced renormalization of the effective masses. Our observations suggest that the electronic structure of WTe$_{2}$ evolves with the magnetic field due to the Zeeman splitting. This evolution is likely to contribute to its pronounced magnetoresistivity.   

Linear magnetoresistance and zero-field anomalies in HfNiSn single crystals

The Half-Heusler compound HfNiSn is probably best known as a candidate material for thermoelectric applications, and studies of its properties have mainly focused on polycrystalline samples and thin films. However, magnetotransport studies of HfNiSn show unusual transport properties like linear magnetoresistance (LMR) [1], where single-crystalline samples of HfNiSn exhibit unexpected LMR at very low fields. In this work, we optimized the solution growth of HfNiSn to obtain high-quality single crystals, where electrical transport measurements show that it is a compensated semimetal below $\approx200$ K, where the Hall voltage is zero. At higher temperatures, we see a finite Hall contribution from activated excess carriers. In the semimetallic regime, we observe transport anomalies like resistive signals that strongly depend on contact configuration, and LMR below 5 K. Both low-field DC and low frequency AC magntization measurements show pronounced diamagnetic behavior and the onset of paramagnetism below 4 K. High-frequency diamagnetic screening may be attributed to a decreased skin depth with decreased resistance, but this scenario seems unlikely in HfNiSn since the measured resistance increases steeply at the lowest temperatures. [1] K. Ahilan et al., PRB 69, 245116 (2004).   

Landau level quantization and almost flat modes in three-dimensional semimetals with nodal ring spectra

We investigate Landau level structures of semimetals with nodal ring dispersions. When the magnetic field is applied parallel to the plane in which the ring lies, there exist almost nondispersive Landau levels at the Fermi level ($E_F = 0$) as a function of the momentum along the field direction inside the ring. We show that the Landau levels at each momentum along the field direction can be described by the Hamiltonian for the graphene bilayer with fictitious interlayer couplings under a tilted magnetic field. Near the center of the ring where the interlayer coupling is negligible, we have Dirac Landau levels which explain the appearance of the zero modes. Although the interlayer hopping amplitudes become finite at higher momenta, the splitting of zero modes is exponentially small and they remain almost flat due to the finite artificial in-plane component of the magnetic field. The emergence of the density of states peak at the Fermi level would be a hallmark of the ring dispersion.   

Observation of the Thermal Hall Effect Using Capacitive Thermometers in Bismuth

The thermal Hall effect is the thermal analog of the electrical Hall effect. Rarely observed in normal metals, thermal Hall signals were argued to be a key property for a number of strongly correlated materials, such as high temperature superconductors, correlated topological insulators, and quantum magnets. The observation of the thermal Hall effect requires precise measurement of temperature in intense magnetic fields. Particularly at low temperature, resistive thermometers have a strong dependence on field, which makes them unsuitable for this purpose. We have created capacitive thermometers which instead measure the dielectric constant of stontium titanate (SrTiO$_3$). SrTiO$_3$ approaches a ferroelectic transition, causing its dielectric constant to increase by a few orders of magnitude at low temperature. As a result, these thermometers are very sensitive at low temperature while having very little dependence on the applied magnetic field, making them ideal for thermal Hall measurements. We demonstrate this by making measurements of the thermal Hall effect in Bismuth in magnetic fields of up to 10T.   

Gyrotropic magnetic effects in chiral metals

We consider two conjugate transport effects occuring in chiral metals as the low-frequency limit of natural optical activity (optical gyrotropy). One occurs in the clean limit where $\omega$ is small compared to the minimum energy for interband transitions, but large compared to the scattering rate $1/\tau$. It consists of a dissipationless current induced by a magnetic field, $J_i = \alpha'_{ij}B_j$, and is different from the chiral magnetic effect requiring a static ${\bf B}$ and an electric-field pulse ${\bf E}\parallel {\bf B}$. In the inverse effect a magnetization is generated by a dissipative current, $M_i =(1/\omega)\alpha''_{ji}E_j$, with ${\bf E}$ the field driving the current and $\omega \ll 1/\tau$, as discussed by Yoda {\it et al.}, Sci. Rep.~{\bf 5}, 12024 (2015). The low-frequency gyrotropic responses $\alpha'$ and $\alpha''$ in the clean and dirty limits can be combined into a complex tensor $\alpha=\alpha'+i\alpha''$ given by the Fermi-surface integral of the total (orbital plus spin) intrinsic magnetic moment of the Bloch electrons, with a prefactor proportional to $1-i\omega\tau$. Without spin-orbit coupling, only the orbital moment contributes.   

Anomalous optical properties of a multiband metal due to thermal redistribution: The case of SrMnSb$_{\mathrm{2}}$

We report an optical spectroscopic study of SnMnSb$_{\mathrm{2}}$, a low carrier density metal. As temperature is decreased, our measurements reveal a large increase in the free carrier plasma frequency, which is unusual for a metal. This seemingly anomalous behavior can be accounted for using a `three band' model of the multiband electronic structure of SrMnSb$_{\mathrm{2}}$ that includes two conduction bands and one valence band close to the Fermi level. The temperature dependence of the low-lying interband optical transitions and the Hall number can also be understood using our model. Our results provide a possible explanation for the puzzling optical properties that have been reported in a number of topical low carrier density metals and semimetals.   

Optical Spectroscopy of anomalous Fermi Liquids.

It is customary to classify a metallic conductor as a Fermi liquid if, at low temperatures, the electrical resistivity varies as the square of the absolute temperature. Fermi liquid theory shows that if umklapp scattering dominates then, independent of a particular band structure, this T squared dependence is accompanied by a quadratic frequency dependence where $\rho ({\rm T},\omega )=C(\omega^{2\thinspace }+b(\pi {\rm T})^{2})$ where the scaling constant $b=$4 for a Fermi liquid[1,2]. A survey of literature shows that where spectroscopic data exist$, b=$4 has not been generally observed[3]. We find that, surveying the recent literature, that in heavy fermion systems the scaling coefficient $b=$1, pointing to a resonant scattering mechanism [2]. In most other systems an unknown mechanism yields a value of $b$ of around 2. 1. R. N. Gurzhi, Sov. Phys. JETP \textbf{14}, 886 (1962). 2. D.L. Maslov and A.V. Chubukov, Phys. Rev. B \textbf{86}, 155137 (2012). 3. U. Nagel \textit{et al}. PNAS \textbf{109}, 19161 (2012).   

Origin of large electron-phonon coupling in the metallic hydride TiH$_2$

The recent discovery of large superconducting transition temperature of $T_c=190$ K in metallic H$_2$S under high pressures of 200 GPa, has renewed the interest in the superconducting properties of metal-hydrogen systems. These materials are expected to be electron-phonon superconductors and hydrogen with its low mass can contribute new optic phonons that may couple with the conduction electrons. Often, though not always, a large electron-phonon coupling parameter $\lambda$ (and consequently high $T_c$) can result from a high electronic density of states at the Fermi level ($N(E_F)$) and the presence of soft phonons. With the help of first-principles calculations within density functional theory, we studied the cubic TiH$_2$ which has a large $3d$ $N(E_F)=2.8$ states/eV/f.u. Our calculated phonon dispersions show that Ti modes active below frequencies of 10 THz whereas much lighter H modes are active between 32 and 40~THz. Electron-phonon coupling calculations reveal a $\lambda=0.98$ which corresponds to a $T_c=6.1$ K. However, the large $N(E_F)$ also leads to a tetragonal instability at low temperatures in TiH$_2$, which may be overcome by a uniaxial strain, potentially making it a candidate for electron-phonon superconductor.   

Structure and dynamics of bulk liquid iron at pressures up to 58 GPa. A first-principles study

The static and dynamic properties of bulk liquid Fe at a several high pressure states, have been studied by using first-principles molecular dynamics simulations based on the density functional theory and the projector augmented wave technique. Results are reported for four thermodynamic states at pressures of 27, 42, 50 and 58 GPa for which x-ray scattering data are available. The calculated static structure shows very good agreement with the available experimental data, including an asymmetric second peak which becomes more marked with increasing pressure. The dynamical structure reveals the existence of propagating density fluctuations and the associated dispersion relation has also been determined. The relaxation mechanisms for the density fluctuations have been analyzed in terms of a model with two decay channels (fast and slow, respectively). We found that the thermal relaxation proceeds along the slow decaying channel whereas the fast one is that of the viscoelastic relaxation. Finally, results are also reported for some transport coefficients.   

Thermodynamic properties by Equation of state of liquid sodium under pressure.

Isothermal bulk modulus, molar volume and speed of sound of molten sodium are calculated through an equation of state of a power law form within good precision as compared with the experimental data. The calculated internal energy data show the minimum along the isothermal lines as the previous result but with slightly larger values. The calculated values of isobaric heat capacity show the unexpected minimum in the isothermal compression. The temperature and pressure derivative of various thermodynamic quantities in liquid Sodium are derived. It is discussed about the contribution from entropy to the temperature and pressure derivative of isothermal bulk modulus. The expressions for acoustical parameter and nonlinearity parameter are obtained based on thermodynamic relations from the equation of state. Both parameters for liquid Sodium are calculated under high pressure along the isothermal lines by using the available thermodynamic data and numeric derivations. By comparison with the results from experimental measurements and quasi-thermodynamic theory, the calculated values are found to be very close at melting point at ambient condition. Furthermore, several other thermodynamic quantities are also presented.