Session H10: Dirac/Weyl Semimetals -- Transport and Anomalies

Extremely high conductivity in the unconventional triple point fermion material MoP

Weyl and Dirac fermions have created much attention in condensed matter physics and materials science. Recently, several additional distinct types of fermions have been predicted. Depending on the inherent symmetry of a particular compound, the crossing points can be several-fold degenerate: two- and four-fold degenerate points are classified as Weyl and Dirac types, respectively. New materials going beyond Weyl and Dirac with higher band degeneracies have been proposed. MoP, a triple point Fermion material, shows characteristic like a correlated metal with anomalously high conductivity. Consistently, the momentum relaxing time of the electrons is found to be ~ 100 times larger than the momentum conserving time. We also find a strong violation of the Wiedemann-Franz law below ~ 40 K, the same temperature where a large magnetoresistance develops. These peculiar observations strongly indicate the role of hydrodynamic flow of charge carriers for extremely high conductivity in MoP. Our study opens a new window for hydrodynamic flow of fermions in low resistive topological metals.   

Negative magnetoresistance from the anomalous N=0 Landau level in topological materials

Negative longitudinal magnetoresistance (NLMR) is shown to occur in topological materials in the extreme quantum limit, when a magnetic field is applied parallel to the excitation current. We perform pulsed and dc field measurements on Pb1−xSnxSe epilayers where the topological state can be chemically tuned. The NLMR is observed in the topological state, but is suppressed and becomes positive when the system becomes trivial. In a topological material, the lowest N = 0 conduction Landau level disperses down in energy as a function of increasing magnetic field, while the N = 0 valence Landau level disperses upwards. This anomalous behavior is shown to be responsible for the observed NLMR. Our work provides an explanation of the outstanding question of NLMR in topological insulators and establishes this effect as a possible hallmark of bulk conduction in topological matter.   

Magnetotransport in Weyl semimetal nanowires

We theoretically study the band structure and the electronic transport in the Weyl semimetal nanowires in magnetic fields, and demonstrate that the interplay of the Fermi-arc surface states and the bulk Landau levels plays a crucial role in the magnetotransport. We show that a magnetic field perpendicular to the surface immediately hybridizes the counterpropagating surface modes into a series of dispersionless zeroth Landau levels, and it leads to a significant reduction of the traveling modes and a rapid decay of the conductance. On the contrary, a magnetic field parallel to the wire adds linearly dispersed zeroth Landau levels to the traveling modes and increases the conductance.   

Origin of the Butterfly Magnetoresistance in a Dirac Nodal-line System

We report a study on the geometry of the Fermi surface (FS) of ZrSi(Se,Te) \emph{via} the de Haas-van Alphen effect (dHvA), whose electronic dispersion was reported to display a line of Dirac nodes within their Brillouin zone. For both compounds we find that their FSs agree well with Density Functional Theory (DFT) calculations. In contrast to ZrSiTe, DFT finds that the nodal Dirac line is close to the Fermi level in ZrSiSe which displays a very small residual resistivity and pronounced four-fold symmetric magnetoresistivity as a function of field orientation. The transport lifetime in ZrSiSe is found to be 10E2-10E3 times larger than its quasiparticle lifetime indicating that its charge carriers are protected against backscattering under zero-field, as previously reported for Cd3As2. The quasiparticle lifetime in ZrSiSe is found to be angle-dependent displaying a minimum for fields along the \emph{c}-axis. Therefore, the ``butterfly" magnetoresistivity observed in ZrSiSe, but not in ZrSiTe, seems to result from the magnetic field-induced suppression of this protection against backscattering, with this effect becoming particularly effective as the field is aligned along the inter-planar direction.   

Anomalous transport properties of tilted Weyl semimetals

The anomalous transport properties of time-reversal-breaking Weyl semimetal with a tilted conical spectrum around the Weyl points will be discussed. In addition to the contribution coming from the relative location of the Weyl points, the tilting gives rise to anisotropic Fermi surface contribution to the observables. For example, the anomalous Hall conductivity is not universal and can change sign as a function of the parameters quantifying the tilts.

I will also comment on the study of the interplay of disorder and bandstructure topology in tilted Weyl semimetal. The spectrum of particles is given by the eigenvalues of non-Hermitian matrix which contains contributions from Weyl Hamiltonian and complex self-energy due to electron elastic scattering on disorder. The tilt induced matrix structure of the self-energy gives rise to a flat band at the interface of the electron and hole pockets depending on the Weyl cone inclination.

  

Angular dependence of negative magneto resistance in the Weyl semimetals

Three dimensional Weyl semimetals have recently been
observed to have negative magnetoresistance
with the magnetic field parallel to the electric field
and positive magnetoresistance with the magnetic field perpendicular
to the electric field.
It is understood that the negative magnetoresistance is due to a Berry
phase that causes the chiral anomaly,
while the positive magnetoresistnce can be understood in terms of
conventional semiclassical transport theory.
We solve the semiclassical Boltzmann equation with both the
Berry phase and Lorentz force terms present for an arbitrary angle
of the applied magnetic field relative to the electric field
within the relaxation time approximation.
The low field magnetoresistance does change from negative to positive
as one rotates the magnetic field away from the direction of the
electric field. As the magnetic field is increased we find in some
cases the magnetoresistance starts out negative and then become positive.
This is consistent with recent experimental data in $Cd_{3}As_{2}$.   

Behavior of Weyl Semimetals in the Hydrodynamic Electron Transport Regime

In solid state transport regimes where electron-electron scattering dominates over impurity scattering and other momentum-relaxing processes, electron flow is governed by the laws of hydrodynamics. This leads to a variety of surprising behaviors in different materials, such as breakdown of the Wiedemann-Franz law, appearance of electron vortices in graphene, and tunable viscosity via magnetic field in a Weyl semimetal. Here we report a new microscopic model of this behavior using a combination of ab initio scattering and transport methods and fluid dynamics techniques. Our work establishes a connection between the observed hydrodynamic phenomena in Weyl semi metals and their crystal structure and symmetry.   

Berry curvature-induced huge anomalous Nernst effect in the absence of magnetic field in the Weyl semimetal YbMnBi2

YbMnBi₂, a Type II time-reversal symmetry-breaking Weyl semimetal, yields a huge anomalous Nernst effect (ANE). This ANE is proven to be driven by Berry curvature and is present even in the absence of a magnetic field. The Seebeck thermopower, in contrast, is near zero. By combining magnetoresistance, Hall, Seebeck, and Nernst effects, the actual integral over the Fermi surface of the projection of the Berry phase can be derived. The ANE also results in transverse energy conversion ZT (thermoelectric figure of merit) values that compare favorably to those of conventional thermoelectric materials in the cryogenic temperature range.   

Chiral anomaly without Landau levels

We study the chiral anomaly in disordered Weyl semimetals, where the broken translational symmetry prevents the direct application of Nielson and Ninomiya’s mechanism. In the weak disorder regime, there exists rare regions of the random potential where the disorder strength is locally strong, this gives rise to quasi-localized resonances. These rare states are non-perturbative and thus their effect on the chiral anomaly is unknown. We numerically show that rare states do not affect the chiral anomaly only in the case of a single Weyl node, but weakens the anomaly in a quantized way when there are two nodes without inter-node scattering. When the disorder strength is strong and the system is deep in the diffusive regime, the chiral Landau level itself is not well defined. In this limit, we analytically use the supersymmetry method and find an additional Chern-Simons (CS) term in the effective action which is not present in non-topological systems. This CS term results in a non-zero average level velocity: using numerical calculations we show that this as an indicator of the chiral anomaly in the presence of strong disorder when the system can no longer be described using band theory.   

The chiral anomaly in the Dirac semimetal Na3Bi and the half-Heusler GdPtBi*

The Dirac semimetal Na₃Bi has two protected 3D Dirac nodes. In a magnetic field B, each node splits into two Weyl nodes. The lowest Weyl Landau levels are chiral with velocity v||B determined by the chirality χ. Alignment of the electric field E with B violates conservation of the axial charge density. The resulting “axial” current J⁵ leads to a large, negative, longitudinal magnetoresistance (MR) known as the “chiral anomaly.” This is the analog of the process π⁰→2γ in the physics of pion decay. The negative MR has been observed in Na₃Bi and in GdPtBi (where field-induced band crossings create twin Weyl nodes). Here we report new test results that distinguish the chiral anomaly MR from spurious current-jetting effects. In high-mobility semimetals, the "squeezing" of the current density into a narrow beam || B increases dissipation along the beam axis (“the spine”), but lowers it at the edge of the sample. In Bi, we indeed observe a voltage (difference) that increases rapidly with B along the spine, but decreases along the edge. By contrast, in both Na₃Bi and GdPtBi, both voltage differences decrease. The chiral anomaly causes the spine voltage to decrease despite the increased dissipation. In a second test based on the planar angular MR, we find that the parametric plots of the angular MR voltages V_yx vs. V_xx define concentric orbits in the chiral anomaly systems. In Bi, however, the orbits expand in a strongly skewed fashion. The difference brings out a crucial difference in the conductance anisotropy. The separation of the Weyl nodes in Na₃Bi also creates anomalies in the Hall signal in weak B.   

Large, nonsaturating thermopower of nodal semimetals in a quantizing magnetic field

The thermoelectric effect is the generation of an electrical voltage from a temperature gradient in a solid material. Identifying materials with large thermoelectric response is pivotal for the development of novel electric generators and coolers. In this talk we consider theoretically the thermopower of Dirac/Weyl semimetals subjected to a quantizing magnetic field. We show that, under a sufficiently large magnetic field, the thermopower grows linearly with the field strength without saturation and can reach extremely high values. Our results suggest an immediate pathway for achieving record-high thermopower and thermoelectric figure of merit, and compare well with recent experiments.   

Electronic Interactions and Transport in Weyl Semimetals

The viscous electron phase of graphene is a well-known phenomenon which occurs at the charge neutrality point due to the dominance of electron-electron scattering processes. Recent experiments have shown evidence of an analogous state of electron viscosity in tungsten phosphide (WP2), a known Weyl semimetal (WSM). WSMs are materials where electrons effectively interact as massless relativistic particles (Weyl fermions) and in 3-dimensions the conduction and valence bands touch at isolated points. Hydrodynamics in such systems has typically been studied via kinetic theory. This talk will show ab initio linked hydrodynamic simulations of electron flow in WP2 with a focus on the role of electron-phonon interactions and the suppression of momentum non-conserving processes in the hydrodynamic phase of WP2.   

High Surface Conductivity of Fermi Arc Electrons in Weyl semimetals

Weyl semimetals (WSMs) have attracted great interest recently due to their unusual electronic states and intriguing transport properties. These systems are close cousins of topological insulators (TIs) which are known for their disorder tolerant surface states. Similarly, WSMs exhibit unique topologically protected Fermi arcs surface states. We have analyzed electron-phonon scattering as a function of the shape of the Fermi arc and find that the impact on surface transport disappears in the limit of a straight arc. Likewise, we have determined the effect of strong surface disorder on the resistivity by simulating a tight-binding model with the presence of quenched surface vacancies using the Coherent Potential Approximation (CPA) and Kubo-Greenwood formalism. We find that the limit of a straight arc is remarkably disorder tolerant, producing a surface conductivity 50 times larger than a comparable setup with surface states of TI. Finally I will discuss our simulations of the effects of surface vacancies on TaAs using the DFT + CPA method, illustrating the disorder tolerance of the topological surface states in a recently discovered WSM material.