Related papers: Competition of density waves and quantum multicrit…
Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature…
This review aims at a theoretical discussion of Dirac points in two-dimensional systems. Whereas Dirac points and Dirac fermions are prominent low-energy electrons in graphene (two-dimensional graphite), research on Dirac fermions in…
We study the quantum phase transition of $U(1)$ - charged Dirac fermions Yukawa-coupled to the Kekul\'e valence bond solid order parameter with $Z_3$ symmetry of the honeycomb lattice. The symmetry allows for the presence of the term in the…
We revisit the problem of two dimensional metals in the vicinity of a quantum phase transition to incommensurate $\mathbf{Q}=2k_F$ charge density wave order, where the order parameter wave vector $\mathbf{Q}$ connects two hot spots on the…
Dirac and Weyl fermions appear as quasi-particle excitations in many different condensed-matter systems. They display various quantum transitions which represent unconventional universality classes related to the variants of the Gross-Neveu…
In two dimensions chaotic level-statistics is expected for massless Dirac fermions in the presence of disorder. For weakly disordered graphene flakes with zigzag edges the obtained level-spacing distribution in the Dirac region is neither…
We investigate the relativistic SO(2)- and SO(3)-invariant Gross-Neveu-Yukawa field theories for real, rank-two, symmetric, traceless tensor order parameters coupled to $N_{\text{f}}$ flavors of two-component Dirac fermions. These field…
We report on numerical study of the Dirac fermions in partially filled N=3 Landau level (LL) in graphene. At half-filling, the equal-time density-density correlation function displays sharp peaks at nonzero wavevectors $\pm {\bf q^{*}}$.…
We study the critical properties of the QED$_3$-Gross-Neveu model with $2N$ flavors of two-component Dirac fermions coupled to a massless scalar field and a U(1) gauge field. For $N=1$, this theory has recently been suggested to be dual to…
Understanding the influence of quenched random potential is crucial for comprehending the exotic electronic transport of non-Fermi liquid metals near metallic quantum critical points. In this study, we identify a stable fixed point…
Recently, the most intensely studied objects in the electronic theory of solids have been strongly correlated systems and graphene. However, the fact that the Dirac bands in graphene are made up of $sp^{2}$-electrons, which are subject to…
Inspired by our recent works[1, 2] of SU(2) and SU(4) Dirac fermions subjected to plaquette interactions on square lattice, here we extend the large-scale quantum Monte Carlo investigations to the phase digram of correlated Dirac fermions…
We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalisation group. Their critical behaviour is of special interest in condensed matter systems, in particular graphene. To derive the…
Quantum critical phenomena may be qualitatively different when massless Dirac fermions are present at criticality. Using our recently-discovered fermion-sign-free Majorana quantum Monte Carlo (MQMC) method introduced by us in Ref. [1], we…
We establish the universal torus low-energy spectra at the free Dirac fixed point and at the strongly coupled chiral Ising fixed point and their subtle crossover behaviour in the Gross-Neuveu-Yukawa field theory with ${n_\text{D}=4}$…
Quantum point contacts (QPCs) are cornerstones of mesoscopic physics and central building blocks for quantum electronics. Although the Fermi wave-length in high-quality bulk graphene can be tuned up to hundreds of nanometers, the…
In an ideal graphene sheet charge carriers behave as two-dimensional (2D) Dirac fermions governed by the quantum mechanics of massless relativistic particles. This has been confirmed by the discovery of a half-integer quantum Hall effect in…
Motivated by many contemporary problems in condensed matter physics where matter particles experience random gauge fields, we investigate the physics of fermions on a square lattice with $\pi$-flux (that realizes Dirac fermions at low…
We investigate the ground state phase diagram of an extended Hubbard model with $\pi$-flux hopping term at half-filling on a square lattice, with unbiased large-scale auxiliary-field quantum Monte Carlo simulations. As a function of…
We predict the magnetic and electronic properties of a novel metal-organic framework. By combining density functional theory and density matrix renormalization group approaches, we find the diatomic Kagome crystal structure of the…