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Analytical calculation on critical magnetic field in holographic superconductors with backreaction
High Energy Physics - Theory · Submitted 22 May 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We derive the analytical expression for the upper critical magnetic field up to $\mathcal{O}(\kappa^2)$ order and find that backreaction makes the upper critical magnetic field stronger.
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The abstract, sentence by sentence
We investigate the effect of spacetime backreaction on the upper critical magnetic field for s-wave holographic superconductors by using the matching method. The backreaction of the constant external magnetic field and the electric field to the background geometry leads to a dyonic black hole solution. The magnetic fields as well as the electric fields acting as gravitational sources tend to depress the critical temperature of the superconductor. We derive the analytical expression for the upper critical magnetic field up to $\mathcal{O}(\kappa^2)$ order and find that backreaction makes the upper critical magnetic field stronger. The result is consistent with the previous numerical and analytical results.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate the effect of spacetime backreaction on the upper critical magnetic field for s-wave holographic superconductors by using the matching method. | contribution 0.99 | 0.95 | 0.07 | asserted 0.89 |
| s1 | The backreaction of the constant external magnetic field and the electric field to the background geometry leads to a dyonic black hole solution. | method 0.67 | 0.61 | 0.04 | asserted 1.00 |
| s2 | The magnetic fields as well as the electric fields acting as gravitational sources tend to depress the critical temperature of the superconductor. | result 0.94 | 0.51 | 0.07 | asserted 0.99 |
| s3 | We derive the analytical expression for the upper critical magnetic field up to $\mathcal{O}(\kappa^2)$ order and find that backreaction makes the upper critical magnetic field stronger. | result 0.99 | 0.97 | 0.85 | asserted 1.00 |
| s4 | The result is consistent with the previous numerical and analytical results. | interpretation 0.71 | 0.27 | 0.04 | hedged possibility 0.73 |
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The paper
Original abstract
We investigate the effect of spacetime backreaction on the upper critical magnetic field for s-wave holographic superconductors by using the matching method. The backreaction of the constant external magnetic field and the electric field to the background geometry leads to a dyonic black hole solution. The magnetic fields as well as the electric fields acting as gravitational sources tend to depress the critical temperature of the superconductor. We derive the analytical expression for the upper critical magnetic field up to $\mathcal{O}(\kappa^2)$ order and find that backreaction makes the upper critical magnetic field stronger. The result is consistent with the previous numerical and analytical results.
Human review
How the literature uses it
15 arXiv papers cite this in 19 sentences
Papers citing it · 9 sentences without a confident label
Builds on it 1 paper
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So, it can be generalize to the case with external magnetic field [ref] .
Holographic superconductor in a deformed four-dimensional STU model · Introduction · 0.82
Uses its method or tool 5 papers
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Therefore, we get to the first order differential equation as follows, [equation] Defining a turning point $z_*$ such that $z'|_z=z_*=0$, one can obtain the following minimal path for $x(z)$ as: [equation] Let us regard $f(z)=f_0(z)+ϵ^2 f_2(z)+...$, $β(z)=ϵ^2β_2(z)+...$, and $μ=μ_0+ϵ^2δμ_2+...$ where $ϵ$ is interpreted as the coherence length in a superconductor which is considered small and $δμ_2≪μ_0$ [ref] .
Holographic Complexity in Gauge/String Superconductors · Holographic complexity and phase transitions · 0.91
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Since $ϵ$ is so small, we can expand the model functions as [ref] [ It is expected that when the sign of $ϵ$ changes, the sign of scalar filed which leads to order parameter, changes too.
One-dimensional backreacting holographic superconductors with exponential nonlinear electrodynamics · Analytical Study · 0.84
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Since we are interested in solutions where $ψ(r)$ is small, therefore from Eqs. ([ref]) and ([ref]) we can expand the scalar field $ψ$ and the gauge field $ϕ$ as [ref] [equation] [equation] where $ϵ≪1$.
Analytical study of holographic superconductor in Born-Infeld electrodynamics with backreaction · Analytical Investigation of the Holographic Superconductor · 0.83
Cites it as background 4 papers
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Recently some analytical approaches have been proposed to address the universal properties of second order phase transitions in holographic superconductors [ref] .
Analytical study of critical magnetic field in a holographic superconductor · Introduction · 0.81
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Along this line, there has been accumulated interest in studying the effects of the backreaction on the holographic $s$-wave [ref] $p$-wave [ref] and $d$-wave [ref] dual models.
Backreacting holographic superconductors from the coupling of a scalar field to the Einstein tensor · Introduction · 0.94
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Apart from the points mentioned above there are several other non-trivial issues, such as the study of the effects of dynamical magnetic fields as well as of backreaction[The author thanks Hong-Qiang Leng for bringing this to attention.] [ref] , [ref] on the properties of the $s$-wave Lifshitz superconductor, the effects of various non-linear corrections in the gauge and/or gravity sector on this superconductor and the study of the holographic model considered here in higher dimensions, that we wish to illuminate in the future.
Magnetic response of holographic Lifshitz superconductors:Vortex and Droplet solutions · Conclusions and future scopes · 0.81
What it cites · 19 sentences without a confident label
Builds on 2 papers
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As an analytical approach for deriving the upper critical magnetic field, an expression was found in the probe limit by extending the matching method first proposed in [ref] to the magnetic case [ref] , which is shown to be consistent with the Ginzburg-Landau theory.
Analytical study on holographic superconductors in external magnetic field · Introduction · 0.86
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As an analytical approach for deriving the upper critical magnetic field, an expression was found in the probe limit by extending the matching method first proposed in [ref] to the magnetic case [ref] , which is shown to be consistent with the Ginzburg-Landau theory.
Holographic Superconductors with Higher Curvature Corrections · Introduction · 0.86
Uses the method or tool of 3 papers
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The main idea of [ref] is to work in the small backreaction approximation $κ^2≪1$ together with the matching method so that all the functions can be expanded by $κ^2$ and the $κ^4$ term in the above equation can be neglected.
A Note on Gauss-Bonnet Holographic Superconductors · Critical temperature with backreaction in the absence of magnetic fields · 0.96
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In this paper, we have investigated the effect of backreaction to the upper critical magnetic field of $(2+1)$-dimensional holographic superconductors in Einstein gravity by using the analytical method developed in [ref] .
Holographic Superconductors with Higher Curvature Corrections · Conclusion · 0.99
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We will impose that $ρ$ is fixed and take $<𝒪_Δ_->=0$ as in [ref] .
Building an AdS/CFT superconductor · Critical temperature with backreaction in the absence of magnetic fields · 0.91
Compares with 4 papers
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One may find that when $κ^2=0$, the result exactly agrees with [ref] , which is also consistent with the Ginzburg-Landau theory where $B_c2∝(1-T/T_c)$.
Analytical study on holographic superconductors in external magnetic field · The upper critical magnetic field with backreaction · 0.96
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As a consistent check, we have derived the critical temperature with backreaction in four-dimensional Einstein gravity and confirmed the numerical result given in [ref] that backreaction makes the condensation harder to form.
General holographic superconductor models with backreactions · Conclusion · 0.95
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It is easy to check that when $m^2l^2=-2$, $z_m=1/2$ and thus $Δ_+=2$, we have $T_1=3 √(ρ)/4 πl√(2√(7))$, the exact result obtained in [ref] for $(2+1)$-dimensional superconductors and $T_2=5/6$.
Holographic Superconductors with Higher Curvature Corrections · Critical temperature with backreaction in the absence of magnetic fields · 0.89
Cites as background 23 papers
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The behavior of holographic superconductors in the presence of an external magnetic field has been widely studied in the probe limit [ref] .
A Holographic Superconductor in an External Magnetic Field · Introduction · 0.98
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The behavior of holographic superconductors in the presence of an external magnetic field has been widely studied in the probe limit [ref] .
Analytical study on holographic superconductors in external magnetic field · Introduction · 0.98
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The behavior of holographic superconductors in the presence of an external magnetic field has been widely studied in the probe limit [ref] .
Vortex and Droplet Engineering in Holographic Superconductors · Introduction · 0.98
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