Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the \emph{collisionless} regime ($\hbar ω\gg k_B T$) in the vicinity of a relativistic quantum critical point, separating two-dimensional ($d=2$) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such critical point gapless fermionic and bosonic excitations are strongly coupled, leading to a \emph{universal} suppression of the inter-band OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in $1/N_f$- and $ε$-expansions, where $N_f$ counts fermion flavor number and $ε=3-d$. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from non-pertubative gauge-gravity duality, for example.
We provide detailed calculation of the a.c. conductivity in the case of 1/r-Coulomb interacting massless Dirac particles in graphene in the collisionless limit when ω>> T. The analysis of the electron self-energy, current vertex function and polarization function, which enter into the calculation of physical quantities including the a.c. conductivity, is carried out by checking the Ward-Takahashi identities associated with the electrical charge conservation and making sure that they are satisfied at each step. We adopt a variant of the dimensional regularization of Veltman and t'Hooft by takin…
The impact of the electron-electron Coulomb interaction on the optical conductivity of graphene has led to a controversy that calls into question the universality of collisionless transport in this and other Dirac materials. Using a lattice calculation that avoids divergences present in previous nodal Dirac approaches, our work settles this controversy and obtains results in quantitative agreement with experiment over a wide frequency range. We also demonstrate that dimensional regularization methods agree, as long as the scaling properties of the conductivity and the regularization of the the…
We numerically demonstrate that the topological corner states residing in the corners of higher-order topological insulator possess non-Abelian braiding properties. Such topological corner states are Dirac fermionic modes other than Majorana zero-modes. We claim that Dirac fermionic modes protected by nontrivial topology also support non-Abelian braiding. An analytical description on such non-Abelian braiding is conducted based on the vortex-induced Dirac-type fermionic modes. The braiding operator for Dirac fermionic modes is also analytically derivated and compared with the Majorana zero-mod…
Materials with non-trivial topology in their electronic structures enforce the existence of helical Dirac fermionic surface states. We discovered emergent topological phases in the stacked structures of topological insulator and band insulator layers where the surface Dirac fermions interact to each other with particular helicity ordering. Using first-principles calculations and a model Lagrangian, we explicitly demonstrated that such helicity ordering occurs in real materials of ternary chalcogen compounds and determines their topological insulating phase. Our results reveal the rich collecti…
We study the emergence of Dirac fermionic field in the low energy description of non-relativistic dynamical models on graphs admitting continuum limit. The Dirac fermionic field appears as the effective field describing the excitations above point-like Fermi surface. Together with the Dirac fermionic field an effective space-time metric is also emerging. We analyze the conditions for such Fermi points to appear in general, paying special attention to the cases of two and three spacial dimensions.
Measurement of gravitational Hawking radiation of black hole (BH) is prohibitive because of an extremely low Hawking temperature (TH). Here we demonstrate a fermionic analog of BH with a super high TH ~ 3 K, which is several orders of magnitude higher than previous works. We propose that Floquet-Dirac states, formed in a periodically laser driven two-dimensional black phosphorous thin film, can be designed with a spatial gradient to mimic the "gravity" felt by fermionic quasiparticles as that for a Schwarzschild BH (SBH). Quantum tunneling of electrons from a type-II Dirac cone (inside BH) to …
The elastic response of an electron fluid at finite frequencies is defined by the electron viscosity $η(ω)$. We determine $η(ω)$ for graphene at the charge neutrality point in the collisionless regime, including the leading corrections due to the electron-electron Coulomb interaction. We find interaction corrections to $η(ω)$ that are significantly larger if compared to the corresponding corrections to the optical conductivity. In addition, we find comparable contributions to the dynamic momentum flux due to single-particle and many-particle effects. We also demonstrate that $η(ω)$ is directly…
We study characteristic band structures of the fermions on a square kagome lattice, one of the two-dimensional lattices hosting a corner-sharing network of triangles. We show that the band structures of the nearest-neighbor tight-binding model exhibit many characteristic features, including a flat band which is ubiquitous among frustrated lattices. On the flat band, we elucidate its origin by using the molecular-orbital representation and also find localized exact eigenstates called compact localized states. In addition to the flat band, we also find two spin-1 Dirac cones with different energ…
Optical conductivity (OC) can serve as a measure of correlation effects in a wide range of condensed matter systems. We here show that the long-range tail of the Coulomb interaction yields a universal correction to the OC in a three-dimensional Weyl semimetal $σ(Ω)=σ_0(Ω)\left[ 1+\frac{1}{N+1} \right]$, where of $σ_0(Ω)=Ne^2_0 Ω/(12 h v)$ is the OC in the non-interacting system, with $v$ as the actual (renormalized) Fermi velocity of Weyl quasiparticles at frequency $Ω$, and $e_0$ is the electron charge in vacuum. Such universal enhancement of OC, which depends only on the number of Weyl nodes…
A doublet of three-dimensional Dirac fermions can effectively describe the low energy spectrum of a fermionic cubic lattice. We employ this fermion doubling to encode a non-Abelian SU(2) charge in the fundamental representation. We explicitly demonstrate that suitable distortion of the tunnelling couplings can introduce a scalar and a Yang-Mills field in the effective low energy description, both coupled to the Dirac fermions. As an application we simulate Yang-Mills monopoles that give rise to localized zero-modes and fermion fractionalization. The generation of the non-Abelian field in the t…
We consider the gapless modes along the vortex line of the fully gapped, momentum independent paired states of three-dimensional Dirac fermions. For this, we require the solution of fermion zero modes of the corresponding two-dimensional problem in the presence of a point vortex, in the plane perpendicular to the vortex line. Based on the spectral symmetry requirement for the existence of the zero mode, we identify the appropriate generalized Jackiw-Rossi Hamiltonians for different paired states. A four-dimensional generalized Jackiw-Rossi Hamiltonian possesses spectral symmetry with respect t…
We examine the low energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in honeycomb lattice structure. Using the example of graphene we present the evidence for the engineered Dirac nodes in the bosonic excitations: the spectra of the collective bosonic modes cross at the K and K points in the Brillouin zone and form Dirac nodes. We show how two different types of collective phase oscillations are obtained and that they are analogous to the Leggett and the Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. …
Among the quantum materials that gained interest recently are the topological Dirac/Weyl semimetals, where conduction and valence bands touch at points in reciprocal (k)-space, and the Dirac nodal-line semimetals, where these bands touch along a line or a loop in k-space. However, the coexistence of multiple fermion phases in one and the same material has not been verified yet. Using angle-resolved photoemission spectroscopy (ARPES) and first-principles electronic structure calculations, we systematically study the metallic topological quantum material, Hf2Te2P. Our investigations discover var…
Interaction driven symmetry breaking in a metallic (doped) Dirac system can manifest in the spontaneous gap generation at the nodal point buried below the Fermi level. Across this transition linear conductivity remains finite making its direct observation difficult in linear transport. We propose the nonlinear Hall effect as a direct probe of this transition when inversion symmetry is broken. Specifically, for a two-dimensional Dirac material with a tilted low-energy dispersion, we first predict a transformation of the characteristic inter-band resonance peak into a non-Lorentzian form in the …
The Osp(2|2) current algebra at level k=-2 is known to describe the IR fixed point of 2D Dirac fermions, subject to a random SU(2) gauge potential. We show that this theory has a simple free-field representation in terms of a compact, and a non-compact free scalar field, as well as a free fermionic ghost, at c=-2. The fermionic twist fields are crucial for the construction. The logarithmic current-algebra primary field with vanishing scaling dimension, transforming in an indecomposable representation, appears as a consequence of familiar logarithmic operators at c=-2.
Topological Dirac semimetals with accidental band touching between conduction and valence bands protected by time reversal and inversion symmetry are at the frontier of modern condensed matter research. Theoretically one can get Weyl and/or nodal-line semimetals by breaking either one of them. Most of the discovered topological semimetals are nonmagnetic i.e respect time reversal symmetry. Here we report the experimental observation of a topological nodal-line semi metallic state in GdSbTe using angle-resolved photoemission spectroscopy. Our systematic study reveals the detailed electronic str…
The response of fermionic system to external gauge fields in presence of non-quantized magnetic field is determined by current-current correlation function $Π_{μν}({\bf B})$. We study $2D$ dimensional Dirac electron system and calculate current-current correlation function in a presence of magnetic field $B$, chemical potential $η$ and gap $m$.
