Two interacting current model of holographic Dirac fluid in graphene

Abstract

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 magnetic 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 α ij 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. PACS numbers: 11.25.Tq, 04.50.-h, 98.80.Cq I. INTRODUCTIONThe crossroads between gravity theory and condensed matter physics have recently become an intense field of research with at least two-fold goal. On one side, the expectation of the condensed matter community is that the approach providing strong coupling analysis of problems will shed some light on those aspects being difficult to access by other means [1,2]. On the other hand, such studies can shed the light on the question whether the holographic approach is able to describe real phenomena observed in experiments.The exploit of the gauge/gravity correspondence [3][4][5] in studying strongly correlated systems resulted, among others, in establishing the lower bound /4π on the ratio of the shear viscosity η s to entropy density s in holographic fluid [6]. This interesting result has contributed to the deeper understanding of the state of strongly interacting quark-gluon plasma obtained at RHIC [7]- [9]. Related studies based on the gauge/gravity duality [10,11] have also triggered the shear viscosity measurements in the ultra-cold Fermi gases [12], and more recently in the condensed matter systems such as graphene [13,14] and strongly correlated oxide [15]. The comprehensive discussion of this novel set of experiments is given in [16].Recently, a great resurgence of the interests in holographic lattice studies of the thermoelectric DC transport has been observed. Breaking of the translation invariance provides the mechanism of momentum dissipation in the underlying field theory and disposes to the finite values of holographic DC kinetic coefficients including thermoelectric matrix elements.The number of results have already been obtained by this technique for a similar model of dissipation and valid in principle for arbitrary value of temperature and the ...

Holographic charged fluid with chiral electric separation effect

“…On the other hand, the exotic topological states of metal, such as Dirac and Weyl semi-metals, provide an experimental playground to study potential observable effects of CESE and other anomalous transports in a controllable way. See [27,[35][36][37] for recent progress on this topic, as well as the relevant investigations from holographic models [54][55][56][57][58][59][60][61][62].…”

DC conductivities and Stokes flows in Dirac semimetals influenced by hidden sector

“…However, there still exists room for improvements. In [48] the model with two interacting U (1)-gauge currents (α = 0) was proposed, where the thermoelectric transport properties, Hall effect geometry with the magnetic field perpendicular to the graphene plane and with the electric field and temperature gradients in the plane but being perpendicular to each other, were studied. Among all, the DC-transport coefficients were found by the introduction of the axionic field which on the condensed matter side provides a momentum relaxation mechanism related to the mobility of the material.…”

“…In Ref. [49], the extension of the previous analysis [47,48] of transport in graphene in three directions was provided. The interaction between the two currents and the application of an external magnetic field enable one to calculate the transport coefficients in the model under consideration.…”

AC conductivities of a holographic Dirac semimetal

“…The study of Dirac semimetals with holographic techniques can be approached using either bottom-up (see for instance [6][7][8] for recent applications) or, as we do in this paper, top-down models, based on D-branes constructions. In particular we consider the well studied D3/probe-D5-brane system, where the D5-probes intersect the D3-branes on a (2+1)-dimensional defect, as depicted in Figure 1.…”