Lifshitz scaling effects on the holographic p-wave superconductors coupled to nonlinear electrodynamics

Abstract

We employ gauge/gravity duality to study the effects of Lifshitz scaling on the holographic p-wave superconductors in the presence of Born–Infeld nonlinear electrodynamics. By using the shooting method in the probe limit, we calculate the relation between critical temperature $$T_\mathrm{{c}}$$ T c and $$\rho ^{z/d}$$ ρ z / d numerically for different values of mass, nonlinear parameter b and Lifshitz critical exponent z in various dimensions. We observe that critical temperature decreases by increasing b, z or the mass parameter m which makes conductor/superconductor phase transition harder to form. In addition, we analyze the electrical conductivity and find the behavior of the real and the imaginary parts as a function of frequency, which depend on the model parameters. However, some universal behaviors are seen. For instance at low frequencies, the real part of conductivity shows a delta function behavior, while the imaginary part has a pole, which means that these two parts are connected to each other through the Kramers–Kronig relation. The behavior of the real part of the conductivity in the large frequency regime can be achieved by $$\mathrm{{Re}}[\sigma ]=\omega ^{D-4}$$ Re [ σ ] = ω D - 4 . Furthermore, with increasing the Lifshitz scaling z, the energy gap and the minimum values of the real and imaginary parts become unclear.

Lifshitz symmetry: Lie algebras, spacetimes and particles

“…Let us consider the case g = a z 3 , thought of as Killing vector fields (3) in the Lifshitz spacetime (M d+2 , g) for the metric g given in equation ( 2). 5 Let γ(s) = (t(s), r(s), x a (s)) be an affinely parametrised geodesic. As discussed in Section 6.1, γ defines an element α γ = (∆, ℓ, k, E) ∈ g * , where…”

“…Since the 1980s, numerous examples of condensed matter systems without a quasiparticle description have been found [1,2]. These systems cannot be described using traditional Landau-Fermi liquid theory; therefore, these non-Fermi liquids, such as cuprate superconductors [3][4][5], heavy fermion systems near a quantum phase transition [6][7][8] and graphene in metallic states [9][10][11] require a new set of tools for understanding their thermodynamic and transport properties [12,13]. In particular, there is great interest in understanding the universal behaviour of certain physical properties near quantum critical points [13][14][15].…”

Higher-dimensional holographic superconductors in Born–Infeld electrodynamics and f(R) gravity

“…in an external magnetic field [10][11][12][13][14][15], with Weyl corrections [16][17][18], in Horava-Lifshitz gravity [19][20][21][22], Gauss-Bonnet gravity [7,9,12,[23][24][25][26][27][28][29][30][31][32][33][34][35][36], and f (R) gravity [37,38]. Some studies also include non-linear electrodynamics [13,14,30,31,[38][39][40][41][42][43][44][45]. In particular, Born-Infeld electrodynamics is especially interesting: it has finite self energies for charged point particles, and is the only non-linear electromagnetic theory that possesses invariance under electromagnetic duality and has no birefringence.…”

Bose-Einstein condensation in Hořava-Lifshitz theory

“…The great interest in the HL model for gravity lies in the fact that the gravity becomes power counting renormalizable when z = 3, since the dimension of the gravitational coupling constant goes to zero. After Hořava's seminal paper [2], several studies were done within the context of gravity [6][7][8][9], black holes [10][11][12][13], cosmology [14][15][16][17], holography [18][19][20] and so on.…”