By combining the Dirac equation of relativistic quantum mechanics with the Bogoliubov-de Gennes equation of superconductivity we investigate the electron-hole conversion at a normal-metal-superconductor interface in graphene. We find that the Andreev reflection of Dirac fermions has several unusual features: (1) the electron and hole occupy different valleys of the band structure; (2) at normal...

Landau's Fermi-liquid theory is the standard model for metals, characterized by the existence of electron quasiparticles near a Fermi surface as long as Landau's interaction parameters lie below critical values for instabilities. Recently this fundamental paradigm has been challenged by the physics of strong spin-orbit coupling, although the concept of electron quasiparticles remains valid near...

We study a class of Dirac semimetals that feature an eightfold-degenerate double Dirac point. We show that 7 of the 230 space groups can host such Dirac points and argue that they all generically display linear dispersion. We introduce an explicit tight-binding model for space groups 130 and 135. Space group 135 can host an intrinsic double Dirac semimetal with no additional states at the Fermi...

The band structure of strongly correlated two-dimensional (2D) semimetal systems is found to be significantly affected by the spin-orbit coupling (SOC), resulting in SOC-induced Fermi surfaces. Dirac, Weyl and Majorana representations are used for the description of different semimetals, though the band structures of all these systems are very similar. We develop a theoretical approach to the b...

This article explains how to apply the deterministic annealing (DA) and simulated annealing (SA) methods to fuzzy entropy based fuzzy c-means clustering. By regularizing the fuzzy c-means method with fuzzy entropy, a membership function similar to the Fermi-Dirac distribution function, well known in statistical mechanics, is obtained, and, while optimizing its parameters by SA, the minimum of t...

We study the thermal and electric transport of a fluid of interacting Dirac fermions as they arise in single-layer graphene. We include Coulomb interactions, a dilute density of charged impurities and the presence of a magnetic field to describe both the static and the low frequency response as a function of temperature T and chemical potential μ . In the critical regime μ . T where both bands ...

Quantum point contacts are cornerstones of mesoscopic physics and central building blocks for quantum electronics. Although the Fermi wavelength in high-quality bulk graphene can be tuned up to hundreds of nanometres, the observation of quantum confinement of Dirac electrons in nanostructured graphene has proven surprisingly challenging. Here we show ballistic transport and quantized conductanc...

The Landau-Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal such as graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the long-standing puzzles in this field. Here we pres...

Spin and pseudospin in graphene are known to interact under enhanced spin-orbit interaction giving rise to an in-plane Rashba spin texture. Here we show that Au-intercalated graphene on Fe(110) displays a large (∼230 meV) bandgap with out-of-plane hedgehog-type spin reorientation around the gapped Dirac point. We identify two causes responsible. First, a giant Rashba effect (∼70 meV splitting) ...

We extend the semiclassical study of fermionic particle-hole symmetric semi-Dirac (more appropriately, semiDirac semi-Weyl) dispersion of quasiparticles, εK = ± √ (k2 x/2m) + (vky)) = ±ε0 √ K4 x +K2 y in dimensionless units, discovered computationally in oxide heterostructures by Pardo and collaborators. This unique system is a highly anisotropic sister phase of both (symmetric) graphene and wh...