Stability of the superfluid state in a disordered one-dimensional ultracold fermionic gas

Tezuka, Masaki; García-García, Antonio M.

doi:10.1103/physreva.82.043613

Cited by 32 publications

(28 citation statements)

References 44 publications

(60 reference statements)

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“…Our disordered superfluids are characterized by a certain concentration of pointlike impurities 47,50 , each one of strength V randomly placed along the chain, such that there are sites with impurity V and non-impurity sites (). For each set of parameters, , we generate samples to avoid features due to specific impurity configurations.…”

Section: The Theoretical Model and Computational Methodsmentioning

confidence: 99%

“…However, none of the previous studies i) has considered fermionic superfluid systems (with both charge and spin degrees of freedom) and ii) none has found entanglement as an unambiguous signature of the SIT: the typical fingerprints of a quantum phase transition (non-monotonicity, discontinuity or saturation) were missing. Furthermore, important features of the SIT are in current debate, as the existence or not of a critical disorder intensity for localization in 1D and 2D systems 5,43–47 , as well as the nature of the transition, whether it is a more pronounced transition or a crossover 6,48 .…”

Section: Introductionmentioning

confidence: 99%

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Superfluid-Insulator Transition unambiguously detected by entanglement in one-dimensional disordered superfluids

Canella

França

2019

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We use entanglement to track the superfluid-insulator transition (SIT) in disordered fermionic superfluids described by the one-dimensional Hubbard model. Entanglement is found to have remarkable signatures of the SIT driven by i) the disorder strength V, ii) the concentration of impurities C and iii) the particle density n. Our results reveal the absence of a critical potential intensity on the SIT driven by V, i.e. any small V suffices to decrease considerably the degree of entanglement: it drops ∼50% for V = −0.25t. We also find that entanglement is non-monotonic with the concentration C, approaching to zero for a certain critical value CC. This critical concentration is found to be related to a special type of localization, here named as fully-localized state, which can be also reached for a particular density nC. Our results show that the SIT driven by n or C has distinct nature whether it leads to the full localization or to the ordinary one: it is a first-order quantum phase transition only when leading to full localization. In contrast, the SIT driven by V is never a first-order quantum phase transition independently on the type of localization reached.

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Section: The Theoretical Model and Computational Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Superfluid-Insulator Transition unambiguously detected by entanglement in one-dimensional disordered superfluids

Canella

França

2019

Sci Rep

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“…Similar kind of quasi-periodic lattice has been already used to study the Anderson localization in Refs. [21][22][23]. Strictly, k 1 /k 2 should an irrational number for the quasi-periodic case, however, by using two coprime positive integers 2k 1 and 2k 2 we can still induce some weak disorder effect as shown in Fig.…”

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confidence: 98%

Possible Anderson localization in a holographic superconductor

Zeng

2013

Phys. Rev. D

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We study the effect of disorder in a holographic superconductor by introducing a quasi-periodic chemical potential. When the condensation of the superconductor is sufficiently small compared with the strength of disorder, we find that there exists a discontinuous phase transition from superconducting state to normal state with increasing disorder strength. For relatively large condensation, we find that disorder suppress but not completely destroy superconductivity.Introduction.-The effect of disorder in superconductor has intrigued scientists for several decades. Soon after the BCS theory [1], Anderson found that weak disorder cannot destroy the superconductivity [2]. Until now, both theories and experiments have confirmed that a strong disorder will eventually destruct superconductivity, driving the system into an insulating state or a normal metal state [3][4][5][6][7][8][9][10]. However, the effect of interactions in a disordered superconductors is still not well understood. As a natural way to study a strongly coupled quantum field theory systems, the AdS/CFT correspondence [17] has been used to study the interplay of disorder and interaction [11][12][13][14][15][16]. The holographic correspondence has also been proved to be successful to study various properties of superconductors [18,19]. In reference [20] the authors firstly studied a dirty holographic superconductor, the found that the disordered superconductor always has a larger critical temperature relative to the to the T c for the uniform one. In this paper we focus on understanding another important issue, the possible Anderson localization in a holographic superconductor. Technically, the weak disorder effect is introduced by a quasi-periodic chemical potential on the boundary field theory, the strength of the disorder is controlled by a parameter α. By tuning

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“…The density matrix renormalization group analysis of ref. [31] showed that phase coherence in a one dimensional disordered Hubbard model with attractive interactions at zero temperature is enhanced for weak coupling and disorder close to but below the superconductor-insulator threshold. In Refs.…”

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confidence: 99%

Global critical temperature in disordered superconductors with weak multifractality

Mayoh

García-García

2015

Phys. Rev. B

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There is growing evidence, from experiments and numerical simulations, that a key feature of sufficiently disordered superconductors is the spatial inhomogeneity of the order parameter. However not much is known analytically about the details of its spatial distribution or the associated global critical temperature that signals the breaking of long-range order. Here we address this problem for disordered systems around an Anderson transition characterized by multifractal one-body eigenstates. In the limit of weak multifractality and for weakly coupled superconductors we compute the superconducting order parameter analytically, including its energy dependence and statistical distribution in space. The spatial distribution of the order parameter is found to be always lognormal. The global critical temperature, computed by percolation techniques and neglecting phase fluctuations, is enhanced with respect to the clean limit only for very weakly coupled superconductors. Some enhancement still persists even in the presence of moderate phase fluctuations crudely modelled by increasing the percolation threshold. Our results are also consistent with experiments, where enhancement of the critical temperature is observed in Al thin films, a very weakly coupled metallic superconductor, but not in more strongly coupled materials.PACS numbers: 74.78. Na, 75.10.Pq For many years the role of disorder in superconductivity was believed to be well understood. According to the so called Anderson theorem [1], also stated independently by Gor'kov and Abrikosov [2], the critical temperature of a conventional weakly-coupled superconductor is not affected by weak non-magnetic impurity scattering. These results are based on the assumption that the local density of states in the material is unaffected by weak disorder [3,4]. However with the development of the Bogoliubovde Gennes theory of superconductivity [5] it became clear that the order parameter becomes increasingly inhomogeneous with increasing disorder.Experimentally it is well established [6][7][8][9][10][11][12][13][14], especially for conventional superconducting thin films, that the critical temperature decreases monotonically as disorder increases. Analytic results [15,16], obtained using mesoscopic techniques, confirmed that the interplay between weak disorder and Coulomb interactions could explain this suppression of the critical temperature. For stronger disorder around the superconductor insulator transition there is recent numerical [17,18] evidence that, even in the absence of Coulomb interactions, phase fluctuations are enhanced [19] and the superconducting order parameter becomes highly inhomogeneous [20,21]. Close to the Berezinski-Kosterlitz-Thouless transition phase correlation only persist along a ramified network, reminiscent of a percolation transition [22]. This is consistent with experimental observations of a universal scaling of the order parameter amplitude distribution function [23], emergent granularity [24,25] and reports of glassy features [26], with...

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Stability of the superfluid state in a disordered one-dimensional ultracold fermionic gas

Cited by 32 publications

References 44 publications

Superfluid-Insulator Transition unambiguously detected by entanglement in one-dimensional disordered superfluids

Superfluid-Insulator Transition unambiguously detected by entanglement in one-dimensional disordered superfluids

Possible Anderson localization in a holographic superconductor

Global critical temperature in disordered superconductors with weak multifractality

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