Magnetoresistance (MR), the change of a material's electrical resistance in response to an applied magnetic field, is a technologically important property that has been the topic of intense study for more than a quarter century. We report the observation of an unusual "butterfly"-shaped titanic angular magnetoresistance (AMR) in the nonmagnetic Dirac material, ZrSiS, which we find to be the mos...

Transport due to spin-helical massless Dirac fermion surface state is of paramount importance to realize various new physical phenomena in topological insulators, ranging from quantum anomalous Hall effect to Majorana fermions. However, one of the most important hallmarks of topological surface states, the Dirac linear band dispersion, has been difficult to reveal directly in transport measurem...

Fermi liquid theory is remarkably successful in describing the transport and optical properties of metals; at frequencies higher than the scattering rate, the optical conductivity adopts the well-known power law behavior σ1(ω) ∝ ω(-2). We have observed an unusual non-Fermi liquid response σ1(ω) ∝ ω(-1±0.2) in the ground states of several cuprate and iron-based materials which undergo electronic...

In a magnetic field, electrons in metals repeatedly traverse closed magnetic orbits around the Fermi surface. The resulting oscillations in the density of states enable powerful experimental techniques for measuring a metal's Fermi surface structure. On the other hand, the surface states of Weyl semimetals consist of disjoint, open Fermi arcs raising the question of whether they can be observed...

A quantization method of a gauge theory on a canonical noncommutative space is presented utilizing the path integral formalism. As tools to quantize, we construct the Dixmier trace that is the special trace for the infinite-dimensional matrices and the Dirac operator which behaves as a line element of the noncommutative space. We refer to a suggestion of solving the cosmological constant proble...

An elliptic Fourier integral operator of order 0, associated to a homogeneous canonical diffeomorphism, on a compact manifold is Fredholm on L2. The index may be expressed as the sum of a term, which we call the contact degree, associated to the canonical diffeomorphism and a term, computable by the Atiyah-Singer theorem, associated to the symbol. The contact degree is shown to be defined for a...

A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the dynamics of the spin and the chirality flips. The problems to overcome in order to find a c-number path integral representation for the solution of the Dirac e...

The polarizational stopping power of an electron fluid is studied within the quantum random-phase approximation using canonical solutions Hamburger moment problem for loss function. function not even here frequency as in, example, non-magnetized one-component plasma. Since proportional to inverse longitudinal dielectric we can deduce that it a response possessing consequtive properties. moments...

This manuscript concerns two definite integrals that could be connected to the Bose-Einstein and Fermi-Dirac functions in integrands, separately, with numerators slightly modified a difference expressions contain Fourier kernel multiplied by polynomial its complex conjugate. In this work, we use our contour integral method derive these integrals, which are given ∫0∞ie−imx(log(a)−ix)k−eimx(log(a...

We study a single two-dimensional Dirac fermion at finite density, subject to quenched random magnetic field. At low energies and sufficiently weak disorder, the theory maps onto an infinite collection of 1D chiral fermions (associated each point on Fermi surface) coupled by vector potential. This low-energy exhibits exactly solvable fixed line, along which we directly compute various disorder-...