Split degenerate states and stable p $$+i$$ + i p phases from holography

Nie, Zhang-Yu; Pan, Qiyuan; Zeng, Hua-Bi; Zeng, Hui

doi:10.1140/epjc/s10052-017-4643-x

Cited by 18 publications

(26 citation statements)

References 66 publications

(85 reference statements)

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“…In current paper we have only worked in the probe limit. Although this probe limit can reveal some main properties of superconductor, it was shown that new phases such as zeroorder phase transition and the retrograde phase can emerge once the backreaction is taken into account [16,58,59]. Therefore, it is interesting to build the superconductor model by including the backreaction from the C 2 F 2 correction to the AdS metric via both numerical shooting method [17,22,31,40] and analytical S-L method [21,38,64,68,69].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Over the past years, the AdS/CFT correspondence(or its generalized version, the gauge/gravity a e-mail: lujunwang.2008@163.com b e-mail: ybwu61@163.com duality) has been intensively applied in many aspects in condensed systems [3][4][5][6][7][8][9], especially the high T c superconductor (s-wave), which was realized successfully via an Einstein-Maxwell theory coupled to a complex scalar field in the Schwarzschild-AdS black hole in the probe limit [10,11]. After that, the holographic superconductor model was extended to the SU (2) p-wave superconductor model [12], d-wave superconductor model [13], the insulator/superconductor model [14], the competition and coexistence of two order parameters [15][16][17][18], Sturm-Liouville (S-L) method [19][20][21], the backreaction from the matter field to the gravitational background [22], the effects of external magnetic field [23,24] as well as the lattice effects [25][26][27][28][29], see, for example, Refs. [30][31][32] for reviews.…”

Section: Introductionmentioning

confidence: 99%

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Holographic p-wave superconductor with $$C^2F^2$$ correction

Dong

2020

Eur. Phys. J. C

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Via numerical and analytical method, we construct the holographic p-wave conductor/superconductor model with C 2 F 2 correction (where C 2 F 2 = C αβ μν C μν αβ F ρσ F ρσ , and C αβ μν and F ρσ denotes the Weyl tensor and gauge field strength, respectively.)in the four-dimensional Schwarzschild-AdS black hole, and mainly study the effects of C 2 F 2 correction parameter denoted by γ on the properties of superconductors. The results show that for all values of the C 2 F 2 parameter, there always exists a critical temperature below which the vector hair appears. Meanwhile, the critical temperature increases with the improving C 2 F 2 parameter γ , which suggests that the improving C 2 F 2 parameter enhances the superconductor phase transition. Furthermore, at the critical temperature, the real part of conductivity reproduces respectively a Drude-like peak and an obviously pronounced peak for some value of nonvanishing C 2 F 2 parameter. At the low temperature, a clear energy gap can be observed at the intermediate frequency and the ratio of the energy gap to the critical temperature decreases with the increasing C 2 F 2 parameter, which is consistent with the effect of the C 2 F 2 parameter on the critical temperature. In addition, the analytical results agree well with the numerical results, which means that the analytical Sturm-Liouville method is still reliable in the grand canonical ensemble.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Holographic p-wave superconductor with $$C^2F^2$$ correction

Dong

2020

Eur. Phys. J. C

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“…Therefore it is interesting to study possible new phases in holographic p-wave model. Previous studies [8,26] already imply that p + ip solutions can be realized in both the two typical holographic p-wave models. However, the p + ip solution in the SU(2) p-wave model is unstable even in the probe limit.…”

Section: Introductionmentioning

confidence: 92%

“…This is because the non-Abelien coupling term between the p and ip components raises the thermodynamic potential of the p + ip solution with respect to the p-wave solution. In the massive vector p-wave model, the p-wave and p + ip solution get the same value of grand potential and thus form a degenerate state in probe limit [26]. However, when back-reaction on the metric is turned on, the p + ip solution always get a larger value of grand potential than the p-wave solution which is more stable [26].…”

Section: Introductionmentioning

confidence: 99%

The holographic p + ip solution failed to win the competition in dRGT massive gravity

Nie

Zeng

2020

Eur. Phys. J. C

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In this paper, the holographic p-wave superfluid model with charged complex vector field is studied in dRGT massive gravity beyond the probe limit. The stability of p-wave and p + ip solutions are compared in the grand canonical ensemble. The p-wave solution always get lower value of grand potential than the p + ip solution, showing that the holographic system still favors an anisotropic (p-wave) solution even with considering a massive gravity theory in bulk. In the holographic superconductor models with dRGT massive gravity in bulk, a key scaling symmetry is found to be violated by fixing the reference metric parameter $$c_0$$ c 0 . Therefore, in order to get the dependence of condensate and grand potential on temperature, different values of horizon radius should be considered in numerical work. With a special choice of model parameters, we further study the dependence of critical back-reaction strength on the graviton mass parameter, beyond which the superfluid phase transition become first order. We also give the dependence of critical temperature on the back reaction strength b and graviton mass parameter $$m^2$$ m 2 .

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“…One of the more interesting extensions of this duality consists in the study of quantum critical systems that belong to the realm of condensed matter physics [7,8,9,10,11,13,12,14,15]. These quantum critical models are scale invariant where space and time scale in a different way [16].…”

Section: Introductionmentioning

confidence: 99%

Anisotropic Lifshitz holography in Einstein–Proca theory with stable negative mass spectrum

et al. 2020

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In this article we focus on constructing a new family of spatially anisotropic Lifshitz spacetimes with arbitrary dynamical exponent z and constant negative curvature in d + 1 dimensions within the framework of the Einstein-Proca theory with a single vector field. So far this kind of anisotropic spaces have been constructed with the aid of a set of vector fields. We also consider the spatially isotropic case as a particular limit. The constructed metric tensor depends on the spacetime dimensionality, the critical exponent and the Lifshitz radius, while the curvature scalar depends just on the number of dimensions. We also obtain a novel spectrum with negative squared mass, we compute the corresponding Breitenlohner-Freedman (BF) bound and observe that the found family of spatially anisotropic Lifshitz spaces respects this bound. Hence these new solutions are stable and can be useful within the gravity/condensed matter theory holographic duality, since the spectrum with negative squared mass is complementary to the positive ones already known in the literature. We also examine the null energy condition (NEC) and show that it is essentially satisfied along all the boundary directions, i.e. along all directions, except the r one, of our Lifshitz spacetime with the corresponding consistency conditions imposed on the scaling exponents.

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Split degenerate states and stable p $$+i$$ + i p phases from holography

Cited by 18 publications

References 66 publications

Holographic p-wave superconductor with $$C^2F^2$$ correction

Holographic p-wave superconductor with $$C^2F^2$$ correction

The holographic p + ip solution failed to win the competition in dRGT massive gravity

Anisotropic Lifshitz holography in Einstein–Proca theory with stable negative mass spectrum

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