Weyl equation | EPFL Graph Search

In physics, particularly in quantum field theory, the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles called Weyl fermions. The equation is named after Hermann Weyl. The Weyl fermions are one of the three possible types of elementary fermions, the other two being the Dirac and the Majorana fermions. None of the elementary particles in the Standard Model are Weyl fermions. Previous to the confirmation of the neutrino oscillations, it was considered possible that the neutrino might be a Weyl fermion (it is now expected to be either a Dirac or a Majorana fermion). In condensed matter physics, some materials can display quasiparticles that behave as Weyl fermions, leading to the notion of Weyl semimetals. Mathematically, any Dirac fermion can be decomposed as two Weyl fermions of opposite chirality coupled by the mass term. History The Dirac equation was published in 1928 by Paul Dirac, and was first used to mo

Anisotropic and nonlinear transport in microstructured 3D topological semimetals

Xiangwei Huang

Topological semimetals are frequently discussed as materials platforms for future electronics that exploit the remarkable properties of their quasiparticles. These ideas are mostly based on dispersion relations that mimic relativistic particles, such as Weyl Fermions, and the nontrivial quantum phase evolution in a Berry curvature landscape. These ideas are fascinating, yet so-far entirely theoretical. This thesis is concerned with experimentally investigating these prospects using Focused Ion Beam prototyping. Three science cases are pursued in its course:The first project involves searching for the chiral zero sound in microstructuredWeyl semimetals. The chiral zero sound mode is a collective excitation of the Fermi surface, that is predicted to lead to giant magnetic quantum oscillations in the thermal conductivity. We developed a technique based on the idea of the 3w method and successfully measured the thermal conductivity of a TaAs microbar at cryogenic temperatures. We found that the third harmonic voltage of the material within the magnetic field showed large quantum oscillations without the magnetoresistance background as in the regular Shubnikov-de Haas (SdH) effect. We demonstrated this effect comprehensively in topological semimetal CoSi, due to its simpler oscillation frequencies. Third harmonic voltage is related to the derivative of the resistance due to the nonlinear current-voltage relation of a semimetal under self-heating. The enhanced quantum oscillations appear because the derivative of the resistance reacts more sensitive to Landau quantization than the resistance. This alternative way of measuring quantum oscillations may improve the sensitivity with which we probe topological semimetals.The aim of the second experiment is the search for nonlocal voltages in microstructured Cd3As2 devices. Theory predicts non-local voltages to appear due to a quantum process combining Fermi arc states with bulk chiral Landau levels, known as the Weyl orbit. We demonstrate that due to the field-induced giant conductivity anisotropy in semimetals, the current path is strongly altered, forming two long-ranged current beams propagating along the magnetic field. This phenomenon sometimes referred to as "current jetting", is a general property of high mobility semimetals. It can also cause nonlocal signals, leaving it impossible to unequivocally identify the nonlocal voltages from topological effects. Finite element simulations of the current jetting effect in Cd3As2 microstructures quantitatively capture the current path in the devices. This experiment presents a significant step towards understanding the microscopic current patterns in 3D Dirac semimetal microdevices.In the third experiment, we report a thorough study on the transport properties of the recently discovered Kagome superconductor CsV3Sb5, which is considered an ideal platform to study the interplay between topology and correlations. By designing a unique membrane-based low-strain microstructure, we are able to detect the intrinsic properties of this material. This allows us to settle the ongoing debate about the existence of 3D ellipsoidal Fermi surfaces and to uncover the unexpected absence of magnetoresistance at moderately high temperatures, which violates Kohler scaling. Our results indicate that the electrical properties of CsV3Sb5 have mixed dimensionality, and the 3D nature has to be considered in the physical description of this material.

EPFL2022

Observation of Weyl Nodes in Robust Type-II Weyl Semimetal WP2

Gabriel Albert Autes, Joël Mesot, Quansheng Wu, Oleg Yazyev

Distinct to type-I Weyl semimetals (WSMs) that host quasiparticles described by the Weyl equation, the energy dispersion of quasiparticles in type-II WSMs violates Lorentz invariance and the Weyl cones in the momentum space are tilted. Since it was proposed that type-II Weyl fermions could emerge from (W, Mo)Te-2, and (W, Mo)P-2 families of materials, a large number of experiments have been dedicated to unveiling the possible manifestation of type-II WSMs, e.g., surface-state Fermi arcs. However, the interpretations of the experimental results are very controversial. Here, using angle-resolved photoemission spectroscopy supported by the first-principles calculations, we probe the tilted Weyl cone bands in the bulk electronic structure of WP2 directly, which are at the origin of Fermi arcs at the surfaces and transport properties related to the chiral anomaly in type-II WSMs. Our results ascertain that, due to the spin-orbit coupling, the Weyl nodes originate from the splitting of fourfold degenerate band-crossing points with Chem numbers C = +/- 2 induced by the crystal symmetries of WP2, which is unique among all the discovered WSMs. Our finding also provides a guiding line to observe the chiral anomaly that could manifest in novel transport properties.

AMER PHYSICAL SOC2019

Robust Type-II Weyl Semimetal Phase in Transition Metal Diphosphides XP2 (X = Mo, W)

Gabriel Albert Autes, Oleg Yazyev

The recently discovered type-II Weyl points appear at the boundary between electron and hole pockets. Type-II Weyl semimetals that host such points are predicted to exhibit a new type of chiral anomaly and possess thermodynamic properties very different from their type-I counterparts. In this Letter, we describe the prediction of a type-II Weyl semimetal phase in the transition metal diphosphides MoP2 and WP2. These materials are characterized by relatively simple band structures with four pairs of type-II Weyl points. Neighboring Weyl points have the same chirality, which makes the predicted topological phase robust with respect to small perturbations of the crystalline lattice. In addition, this peculiar arrangement of the Weyl points results in long topological Fermi arcs, thus making them readily accessible in angle-resolved photoemission spectroscopy.

Amer Physical Soc2016

Anisotropic and nonlinear transport in microstructured 3D topological semimetals

Xiangwei Huang

EPFL2022