Vortex correlations in a fully frustrated two-dimensional superconducting network

Serret, E.; Butaud, P.; Pannetier, B.

doi:10.1209/epl/i2002-00230-6

Cited by 41 publications

(43 citation statements)

References 27 publications

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“…One of the most intriguing systems in this respect is the fully frustrated XY model on a dice lattice, which exhibits a similar degeneracy between its classical ground states [23], and has been the subject of recent experiments [24] and numerical simulations [25]. In particular, one of the main reasons for the absence of vortex ordering in magnetic decoration experiments on Josephson junction arrays [24], as well as in numerical simulations of Ref. 25 is very likely to be a not sufficent system size.…”

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confidence: 99%

Fluctuations and Vortex-Pattern Ordering in the Fully FrustratedXYModel on a Honeycomb Lattice

Douçot

2004

Phys. Rev. Lett.

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The accidental degeneracy of various ground states of a fully frustrated XY model with a honeycomb lattice is shown to survive even when the free energy of the harmonic fluctuations is taken into account. The reason for that consists in the existence of a hidden gauge symmetry between the Hamiltonians describing the harmonic fluctuations in all these ground states. A particular vortex pattern is selected only when anharmonic fluctuations are taken into account. However, the observation of vortex ordering requires relatively large system size L ≫ Lc > ∼ 10 5 .PACS numbers: 74.81. Fa, 64.60.Cn, A fully frustrated XY model can be defined by the Hamiltonianwhere J > 0 is the coupling constant, the fluctuating variables ϕ i are defined on the sites i of some regular two-dimensional lattice, and the summation is performed over the pairs of nearest neighbors (ij) on this lattice. The non-fluctuating (quenched) variables A ij ≡ −A ji defined on lattice bonds have to satisfy the constraint A ij = π (mod 2π) (where the summation is performed over the perimeter of a plaquette) on all plaquettes of the lattice.For two decades such models (on various lattices) have been extensively studied [1] in relation with experiments on Josephson junction arrays [2], in which ϕ i can be associated with the phase of the superconducting order parameter on the i-th superconducting grain, and A ij is related to the vector potential of a perpendicular magnetic field, whose magnitude corresponds to a half-integer number of superconducting flux quanta per lattice plaquette. Planar magnets with odd number of antiferromagnetic bonds per plaquette [3] are also described by fully frustrated XY models. Recently, the active interest in fully frustrated Josephson arrays has been related to their possible application for creation of topologically protected quantum bits [4,5].The ground states of the fully frustrated XY models are characterized by the combination of the continuous U (1) degeneracy (related with the possibility of the simultaneous rotation of all phases) and discrete degeneracy related with the distribution of positive and negative half-vortices between the lattice plaquettes. Since vortices of the same sign repel each other, the energy is minimized when the vorticities of the neighboring plaquettes are of the opposite sign. In the case of a square lattice this requirement is fulfilled for all pairs of neigboring plaquettes when the vortices of different signs form a regular checkerboard pattern [3]. Analogous pattern, in which the vorticities of the neighboring plaquettes are always of the opposite sign, can be constructed in the case of a triangular lattice [6,7].In the case of a honeycomb lattice it is impossible to construct a configuration in which the vorticities are of the opposite sign for all pairs of neighboring plaquettes. As a consequence, the discrete degeneracy of the ground state turns out to be much more developed [8,9], and can be described in terms of formation of zero-energy domain walls in parallel to each other [10]...

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confidence: 99%

Fluctuations and Vortex-Pattern Ordering in the Fully FrustratedXYModel on a Honeycomb Lattice

Douçot

2004

Phys. Rev. Lett.

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“…Let us, for definiteness, consider the C-C case. Substituting the general solution (8) into conditions ψ C (y = 0) = ψ C (y = L) = 0, we find the following system of equations for constants C 1 and C 2 :…”

Section: Zigzag Terminationmentioning

confidence: 99%

Electronic states of pseudospin-1 fermions in $\boldsymbol {\alpha-\mathcal{T}_3}$ lattice ribbons in a magnetic field

Bugaiko

Oriekhov²

2019

J. Phys.: Condens. Matter

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The electronic states on a finite width α−T3 ribbon in a magnetic field are studied in the framework of low-energy effective theory. Both zigzag and armchair types of boundary conditions are analyzed. The analytical solutions are compared with the results of numerical tight-binding calculations. It is found that the flat band of zero energy survives for all types of boundary conditions. The analytical estimates for the spectral gap in a weak magnetic field are discussed. For zigzag type boundary conditions the approximate expressions for the edge and bulk electron states in the strong magnetic field are found. I. INTRODUCTIONAfter the experimental discovery of graphene [1] the systems with relativisticlike quasiparticle spectrum attracted a great interest. In addition, it was shown [2] that in crystals with special space groups one can obtain fermionic excitations with no analogues in high-energy physics. One of the remarkable features of such quasiparticles is a possibility to possess strictly flat bands [3] (for a recent review of artificial flat band systems, see Ref.[4]). The dice model is probably historically the first example of such a system with a flat band which hosts pseudospin-1 fermions [5].Recently the α − T 3 model attracted a significant interest as an interpolation between graphene and dice model [6]. The α − T 3 model is a tight-binding model of two-dimensional fermions living on the T 3 (or dice) lattice where atoms are situated at both the vertices of a hexagonal lattice and the hexagons centers [5,7]. The parameter α describes the relative strength of the coupling between the honeycomb lattice sites and the central site. Since the α − T 3 model has three sites per unit cell, the electron states in this model are described by three-component pseudospin-1 fermions. It is natural then that the spectrum of the model is comprised of three bands. The two of them form a Dirac cone as in graphene, and the third band is completely flat and has zero energy [6]. All three bands meet at the K and K ′ points, which are situated at the corners of the Brillouin zone. The T 3 lattice has been experimentally realized in Josephson arrays [8] and its optical realization by laser beams was proposed in Ref. [9]. Recently, a 2D model for Hg 1−x Cd x Te at critical doping has been shown to map onto the α − T 3 model with an intermediate parameter α = 1/ √ 3 [10]. The presence of completely flat energy band results in surprisingly strong paramagnetic response in a magnetic field in the dice model (α = 1) [6]. The minimal conductivity and topological Berry winding were analyzed in threeband semi-metals in Ref. [11]. The dynamic polarizability of the dice model was calculated in the random phase approximation [12] and it was found that the plasmon branch due to strong screening in the flat band is pinched to the point ω = |k| = µ. In addition, the singular nature of the Lindhard function leads to a much faster decay of the Friedel oscillations. Recently several physical quantities have been studied in the α − T 3 latt...

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“…The existence of these cages is due to destructive interference along all paths that particles could walk on, when the phase shift around a rhombic plaquette is π. Following the original paper by Vidal et al, several experimental 13,14,15 and theoretical works 16,17,18,19,20,21 analyzed the properties of the AB cages. In the case of superconducting networks most of the attention has been devoted to classical arrays with the exception of Refs.…”

Section: Introductionmentioning

confidence: 99%

“…The location and the properties of the phase diagram will be analyzed by a variety of approximate analytical methods (mean-field, variational Gutzwiller approach, strong coupling expansion) and by Monte Carlo simulations. The T 3 lattice has been experimentally realized in Josephson arrays 14 . In addition we show that it is possible to realize it experimentally also with optical lattices.…”

Section: Introductionmentioning

confidence: 99%

Phase diagram of the Bose-Hubbard model withT3symmetry

2006

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In this paper we study the quantum phase transition between the Insulating and the globally coherent superfluid phases in the Bose-Hubbard model with T3 structure, the "dice lattice". Even in the absence of any frustration the superfluid phase is characterized by modulation of the order parameter on the different sublattices of the T3 structure. The zero-temperature critical point as a function of a magnetic field shows the characteristic "butterfly" form. At fully frustration the superfluid region is strongly suppressed. In addition, due to the existence of the Aharonov-Bohm cages at f = 1/2, we find evidence for the existence of an intermediate insulating phase characterized by a zero superfluid stiffness but finite compressibility. In this intermediate phase bosons are localized due to the external frustration and the topology of the T3 lattice. We name this new phase the Aharonov-Bohm (AB) insulator. In the presence of charge frustration the phase diagram acquires the typical lobe-structure. The form and hierarchy of the Mott insulating states with fractional fillings, is dictated by the particular topology of the T3 lattice. The results presented in this paper were obtained by a variety of analytical methods: mean-field and variational techniques to approach the phase boundary from the superconducting side, and a strongly coupled expansion appropriate for the Mott insulating region. In addition we performed Quantum Monte Carlo simulations of the corresponding (2+1)D XY model to corroborate the analytical calculations with a more accurate quantitative analysis. We finally discuss experimental realization of the T3 lattice both with optical lattices and with Josephson junction arrays.

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Vortex correlations in a fully frustrated two-dimensional superconducting network

Cited by 41 publications

References 27 publications

Fluctuations and Vortex-Pattern Ordering in the Fully FrustratedXYModel on a Honeycomb Lattice

Fluctuations and Vortex-Pattern Ordering in the Fully FrustratedXYModel on a Honeycomb Lattice

Electronic states of pseudospin-1 fermions in $\boldsymbol {\alpha-\mathcal{T}_3}$ lattice ribbons in a magnetic field

Phase diagram of the Bose-Hubbard model withT3symmetry

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