The electrons in graphene for energies close to the Dirac point have been found to form strongly interacting fluid. Taking this fact into account we have extended previous work on the transport properties of graphene by taking into account possible interactions between the currents and adding the external magnetic field directed perpendicularly to the graphene sheet. The perpendicular mag- netic field B severely modifies the transport parameters. In the present approach the quantization of the spectrum and formation of Landau levels is ignored. Gauge/gravity duality has been used in the probe limit. The dependence on the charge density of the Seebeck coefficient and thermo-electric parameters αij nicely agree with recent experimental data for graphene. The holographic model allows for the interpretation of one of the fields representing the currents as resulting from the dark matter sector. For the studied geometry with electric field perpendicular to the thermal gradient the effect of dark sector has been found to modify the transport parameters but mostly in a quantitative way only. This makes difficult the detection of this elusive component of the Universe by studying transport properties of graphene.
In this paper, we have investigated the Meissner effect of holographic superconductors in the presence of Dirac-Born-Infeld electrodynamics. The matching method is applied to obtain the critical magnetic field and the critical temperature. The critical magnetic field obtained from this investigation shows the effects of the DBI parameter $b$ and differs from that obtained from Born electrodynamics because of the extra $\vec{E}.\vec{B}$ term in the Dirac-Born-Infeld theory. It is observed that the critical magnetic field increases in Dirac-Born-Infeld theory compared to that in the Born theory.
We first point out that the Laia-Tong model realizes the Lieb lattice in the holographic setup. It generates a flat band of sharp particle spectrum together with a Dirac band of unparticle spectrum. We then construct a model which opens a gap to the Dirac band so that one can realize a well-separated flat band, which can play the role of the hydrogen atom of strongly correlated systems. We then study the phase transition between the gapped and gapless phases analytically. We also made methodological progress to find a few other quantizations and we express the Green functions in any quantizati…
In this paper we consider holographic model of exciton condensation in double monolayer Dirac semimetal. Excitons is a bound states of an electron and a hole. Being Bose particles, excitons can form a Bose-Einstein condensate. We study formation of two types of condensates. In first case both the electron and the hole forming the exciton are in the same layer (intralayer condensate), in the second case the electron and the hole are in different layers (interlayer condensate). We study how the condensates depend on the distance between layers and the mass of the quasiparticles in presence of a …
We study the thermodynamic properties of massless Dirac fermions in graphene under a uniform magnetic field and Rashba spin-orbit coupling with a $q-$deformed Heisenberg algebra calculus. The thermodynamic functions such as the Helmholtz free energy, total energy, entropy and heat capacity are obtained by using an approach based on the zeta function and Euler-Maclaurain formula. These functions will be numerically examined for different values of $η={1\over i}\ln(q)$. In particular, the heat capacity in the presence of deformation, all curves coincide and reach the fixed value $C=6K_B$ three t…
We extend the holographic Schwinger-Keldysh prescription introduced in arXiv:1812.08785 to charged black branes, with a view towards studying Hawking radiation in these backgrounds. Equivalently we study real-time fluctuations of the dual CFT held at finite temperature and finite chemical potential. We check our prescription using charged Dirac probe fields. We solve the Dirac equation in a boundary derivative expansion extending the results in arXiv:2011.07039. The Schwinger-Keldysh correlators derived using this prescription automatically satisfy the appropriate KMS relations with Fermi-Dira…
We demonstrate how self-sourced collective modes - of which the plasmon is a prominent example due to its relevance in modern technological applications - are identified in strongly correlated systems described by holographic Maxwell theories. The characteristic $ω\propto \sqrt{k}$ plasmon dispersion for 2D materials, such as graphene, naturally emerges from this formalism. We also demonstrate this by constructing the first holographic model containing this feature. This provides new insight into modeling such systems from a holographic point of view, bottom-up and top-down alike. Beyond that,…
We derive an effective dual holographic Einstein-Maxwell theory, applying renormalization group transformations to interacting Dirac fermions in a recursive way. In particular, we show how both background metric tensor and U(1) gauge fields become dynamical to describe the renormalization group flows of coupling functions and order parameter fields of the corresponding quantum field theory through natural emergence of an extra-dimensional space, respectively. Finally, we propose a prescription on how to calculate correlation functions in a non-perturbative way, where quantum fluctuations of bo…
We show that in bilayer graphene it is possible to achieve a very restrictive confinement of the massless Dirac fermions zero-modes by using inhomogeneous magnetic fields. Specifically, we show that, using a suitable nonuniform magnetic fields, the wave function may be restricted to a specific region of the space, being forbidden all transmission probability to the contiguous regions. This allows to construct mesoscopic structures in bilayer graphene by magnetic fields configurations.
The anomalous spin Hall conductivity in the holographic model of Dirac semimetals with two Dirac nodes protected by the crystal symmetry has been elaborated. Such system besides the chiral anomaly possesses another anomaly which is related to the $\mathbb{Z}_2$ topological charge of the system. The holographic model of the system contains matter action with two $U(1)$-gauge fields as well as the appropriate combination of the Chern-Simons gauge terms. We also allow for the coupling of two gauge fields {\it via} the kinetic mixing parametrised by the coupling $α$. The holographic approach in th…
The lattice studies in QCD demonstrate the nontrivial localization behavior of the eigenmodes of the 4D Euclidean Dirac operator considered as Hamiltonian of $4+1$ dimensional disordered system. We use the holographic viewpoint to provide the conjectural explanation of these properties. The delocalization of all modes in the confined phase is related to the $θ=π$ - like phenomena when the domain walls between degenerated vacua are possible. It is conjectured that the localized modes separated by mobility edge from the rest of the spectrum in deconfined QCD correspond to the near-horizon region…
Based on the gauge/gravity correspondence we have calculated the thermoelectric kinetic and transport characteristics of the strongly interacting materials in the presence of perpendicular magnetic field. The 3+1 dimensional system with Dirac-like spectrum is considered as a strongly interacting one if it is close to the particle-hole symmetry point. Transport in such system has been modeled by the two interacting vector fields. In the holographic theory the momentum relaxation is caused by axion field and leads to finite values of the direct current transport coefficients. We have calculated …
We study the confinement of Dirac fermions in armchair graphene nanoribbons by means of a quantum-dot-type electrostatic potential. With the use of specific projection operators, we find exact solutions for some bound states that satisfy appropriate boundary conditions. We show that the energies of these bound states belong either to the gap of valence and conducting bands or they represent BIC's (bound states in the continuum) whose energies are embedded in the continuous spectrum.
A mathematical formulation for particle states and electronic properties of a curved graphene sheet is provided, exploiting a massless Dirac spectrum description for charge carriers living in a curved bidimensional background. In particular, we study how the new description affects the characteristics of the sample, writing an appropriate conductivity Kubo formula for the modified background. Finally, we provide a theoretical analysis for the particular case of a cylindrical graphene sample.
We use the Wick-rotated time-dependent supersymmetry to construct models of two-dimensional Dirac fermions in presence of an electrostatic grating. We show that there appears omnidirectional perfect transmission through the grating at specific energy. Additionally to being transparent for incoming fermions, the grating hosts strongly localized states.
We provide an updated study of some electronic properties of graphene nanoscrolls, exploiting a related curved space Dirac equation for the charge carriers. To this end, we consider an explicit parametrization in cylindrical coordinates, together with analytical solutions for the pseudoparticle modes living on the two--dimensional background. These results are then used to obtain a compact expression for the sample optical conductivity, deriving from a Kubo formula adapted to the 1+2 dimensional curved space. The latter formulation is then adopted to perform some simulations for a cylindrical …
