Dissipation-driven phase transitions in superconducting wires

Lobos, Alejandro M.; Iucci, Anı́bal; Müller, Markus; Giamarchi, Thierry

doi:10.1103/physrevb.80.214515

Cited by 12 publications

(18 citation statements)

References 49 publications

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“…Interestingly, recent theoretical works have shown the possibility to stabilize a 1D SC through a weak coupling to a dissipative environment [4][5][6][7][8][9] that suppresses fluctuations and restore phase coherence 10 . Experimentally, restoration of phase coherence has been recently observed in thin Zn 11,12 and Al 13 nanowires by increasing the coupling of the wire to dissipative electrodes.…”

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confidence: 99%

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Restoring phase coherence in a one-dimensional superconductor using power-law electron hopping

2013

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In a one-dimensional (1D) superconductor, zero temperature quantum fluctuations destroy phase coherence. Here we put forward a mechanism which can restore phase coherence: power-law hopping. We study a 1D attractive-U Hubbard model with power-law hopping by Abelian bosonization and density-matrix renormalization group (DMRG) techniques. The parameter that controls the hopping decay acts as the effective, non-integer spatial dimensionality d eff . For real-valued hopping amplitudes we identify analytically a range of parameters for which power-law hopping suppress fluctuations and restore superconducting long-range order for any d eff > 1. A detailed DMRG analysis fully supports these findings. These results are also of direct relevance to quantum magnetism as our model can be mapped onto a S=1/2 XXZ spin-chain with power-law decaying couplings, which can be studied experimentally by cold ion-trap techniques.PACS numbers: 74.78. Na, 75.10.Pq According to the Mermin-Wagner-Hohenberg theorem quantum and thermal fluctuations in low dimensions prevent the spontaneous breaking of a continuous symmetry 1,2 . A paradigmatic example is a onedimensional (1D) superconductor (SC), where fluctuations of the SC order parameter result in quasi long-range order at zero temperature, i.e., the algebraic decay of the order parameter correlation function 3 . By contrast superconducting long-range order (LRO), equivalent to phase coherence in this context, occurs if the correlation function does not decay even for arbitrarily large distances.Therefore one of the main theoretical challenges in the field is to identify mechanisms that are capable to restore phase coherence in 1D. Interestingly, recent theoretical works have shown the possibility to stabilize a 1D SC through a weak coupling to a dissipative environment 4-9 that suppresses fluctuations and restore phase coherence 10 . Experimentally, restoration of phase coherence has been recently observed in thin Zn 11,12 and Al 13 nanowires by increasing the coupling of the wire to dissipative electrodes.The increase of the effective spatial dimensionality is another appealing choice. In the context of noninteracting 1D weakly disordered systems 14 , it is wellknown that power-law hopping ∝ 1/|i − j| α (with α > 1/2) effectively mimics the properties of a system in d eff = 2/ (2α − 1) spatial dimensions with short-range hopping. This effect seems to be robust to the presence of interactions 15 . Similar effects are also well-known in 1D spin chains with ferromagnetic (FM) 16-21 or with non-frustrating antiferromagnetic (AFM)22-24 power-law exchange couplings where LRO can occur at sufficiently low temperatures.In this Letter we study the role of power-law singleparticle hopping in 1D SCs. We focus on the 1D attractive-U Hubbard model with real-valued power-law hoppings t lm ∝ t/|l − m| α , where α is the parameter controlling the decay. We study the quantum phases of the system at zero temperature by analytical (Abelian bosonization and a variational approach) and numerical dens...

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“…0 stands for the average with respect to the trial action S 0 . Minimizing F var with respect to g 0 (q), i.e., ∂F var /∂g 0 (q) = 0, results in a self-consistent equation for g 0 (q) 3,4,6 . In the regime 1/2 < α < 3/2, L → ∞, T → 0, an approximate solution, asymptotically correct in the limit k → 0, is given by the expression…”

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Restoring phase coherence in a one-dimensional superconductor using power-law electron hopping

2013

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“…We adopt a Gaussian ansatz S 0 = 1 2βL ∑ q g −1 0 (q) θ * q θ q for the Euclidean action of the system, with q = (k, −ω m ), ω m = 2πT m being the bosonic Matsubara frequencies at temperature T [16], and the functions g −1 0 (q) being unknown variational parameters which must be chosen to minimize the variational free energy F var = F 0 + T S − S 0 0 . Then we obtain a self-consistent equation for g 0 (q) [4,8,17,18] …”

Section: Bosonization Analysis Of the Hard-core Boson Modelmentioning

confidence: 99%

“…For SC LRO to be stabilized, a finite η > 0 is needed. A selfconsistent equation for η [17][18][19] is obtained by combining (5) with (4). In the limit of λ → 0, a solution with η > 0 exists only for α < 3/2 − 1/(4K) [8].…”

Section: Bosonization Analysis Of the Hard-core Boson Modelmentioning

confidence: 99%

Restoring Long-Range Order in One-Dimensional Superconductivity by Power-Law Hopping

Tezuka

Lobos²,

García-García³

2014

Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2013)

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Quantum fluctuations destroy phase coherence and thus long-range order in one-dimensional (1D) superconductivity as long as all interactions are short-ranged. Here we discuss the possibility of restoring phase coherence by power-law hopping. A 1D attractive-U Hubbard model with powerlaw hopping having the power-law exponent α is studied by Abelian bosonization and density-matrix renormalization group (DMRG). For 1/2 < α < 3/2, the system has an effective spatial dimensionality d eff > 1. We demonstrate that long-range superconducting order is restored for 1/2 < α < α c , with 5/4 < α c < 3/2. This conclusion is supported by a DMRG analysis of the model.

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“…23,24 Therefore, a better understanding of the screening effects occurring in superconducting wires and the consequences to their superconducting properties is needed. This issue is particularly relevant to recent theoretical 13,25,26 and experimental 27,28 works showing evidence of stabilization of superconductivity in low-dimensional systems due to the presence of tunneling contacts with normal metallic leads, which suppress fluctuations of the superconducting order parameter. It would be desirable to investigate to what extent the same leads introduce additional sources of dissipation prejudicial to superconductivity.…”

Section: Introductionmentioning

confidence: 98%

Dissipative phase fluctuations in superconducting wires capacitively coupled to diffusive metals

Lobos¹,

Giamarchi²

2010

Phys. Rev. B

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We study the screening of the Coulomb interaction in a quasi-one-dimensional superconductor by the presence of either a one-or a two-dimensional electron gas nearby. To that end, we derive an effective low-energy phase-only action, which amounts to treating the Coulomb and superconducting correlations in the random-phase approximation. We concentrate on the study of dissipation effects in the superconductor, induced by the effect of Coulomb coupling to the diffusive modes in the electron gas, and study its consequences on the behavior of the one-dimensional plasma mode, and the static and dynamical conductivity. Our results point toward the importance of the dimensionality of the screening metal in the behavior of the superconducting plasma mode of the wire at low energies. In absence of topological defects, and when the screening is given by a one-dimensional electron gas, the superconducting plasma mode is completely damped in the limit k → 0, and consequently superconductivity is lost in the wire. In contrast, we recover a Drude-type response in the conductivity when the screening is provided by a two-dimensional electron gas.

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Dissipation-driven phase transitions in superconducting wires

Cited by 12 publications

References 49 publications

Restoring phase coherence in a one-dimensional superconductor using power-law electron hopping

Restoring phase coherence in a one-dimensional superconductor using power-law electron hopping

Restoring Long-Range Order in One-Dimensional Superconductivity by Power-Law Hopping

Dissipative phase fluctuations in superconducting wires capacitively coupled to diffusive metals

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