Universal conductivity of dirty bosons at the superconductor-insulator transition

Es, Sorensen; Wallin, Mats; Sm, Girvin; Ap, Young

doi:10.1103/physrevlett.69.828

Cited by 133 publications

(190 citation statements)

References 22 publications

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“…Strongly interacting bosonic systems have attracted a lot of recent interest [1][2][3][4] . Physical realizations include short correlation-length superconductors, granular superconductors, Josephson arrays, the dynamics of flux lattices in type II superconductors, and critical behavior of 4 He in porous media.…”

Section: Introductionmentioning

confidence: 99%

“…Physical realizations include short correlation-length superconductors, granular superconductors, Josephson arrays, the dynamics of flux lattices in type II superconductors, and critical behavior of 4 He in porous media. The bosonic systems are either tightly bound composites of fermions that act like effective bosonic particles with soft cores, or correspond to bosonic excitations that have repulsive interactions.…”

Section: Introductionmentioning

confidence: 99%

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Strong-coupling expansions for the pure and disordered Bose-Hubbard model

1996

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A strong-coupling expansion for the phase boundary of the (incompressible) Mott insulator is presented for the bose Hubbard model. Both the pure case and the disordered case are examined. Extrapolations of the series expansions provide results that are as accurate as the Monte Carlo simulations and agree with the exact solutions. The shape difference between Kosterlitz-Thouless critical behavior in one-dimension and power-law singularities in higher dimensions arises naturally in this strong-coupling expansion. Bounded disorder distributions produce a "first-order" kink to the Mott phase boundary in the thermodynamic limit because of the presence of Lifshitz's rare regions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Strong-coupling expansions for the pure and disordered Bose-Hubbard model

1996

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“…This has been the subject of a large body of work, including analytical arguments involving charge-vortex duality arguments, quantum Monte Carlo calculations in various representations, and experiments [1,4,16,23,[25][26][27][28][29][30][31][32]. It is often claimed that at the SIT σ * is finite and takes a universal value of the order of σ Q = 4e 2 /h, but there are large discrepancies between the "universal" values from various studies, and it is not clear whether there really is a universal value.…”

mentioning

confidence: 99%

Divergence of dynamical conductivity at certain percolative superconductor-insulator transitions

Loh¹,

Dhakal²,

Neis³

et al. 2014

J. Phys.: Condens. Matter

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Random inductor-capacitor (LC) networks can exhibit percolative superconductor-insulator transitions (SITs). We use a simple and efficient algorithm to compute the dynamical conductivity σ(ω, p) of one type of LC network on large (4000 × 4000) square lattices, where δ = p − pc is the tuning parameter for the SIT. We confirm that the conductivity obeys a scaling form, so that the characteristic frequency scales as Ω ∝ |δ| νz with νz ≈ 1.91, the superfluid stiffness scales as Υ ∝ |δ| t with t ≈ 1.3, and the electric susceptibility scales as χE ∝ |δ| −s with s = 2νz − t ≈ 2.52. In the insulating state, the low-frequency dissipative conductivity is exponentially small, whereas in the superconductor, it is linear in frequency. The sign of Im σ(ω) at small ω changes across the SIT. Most importantly, we find that right at the SIT Re σ(ω) ∝ ω t/νz−1 ∝ ω −0.32 , so that the conductivity diverges in the DC limit, in contrast with most other classical and quantum models of SITs. [4,5]. As a quantum phase transition occurring at zero temperature, this superconductor-insulator transition (SIT) has attracted much interest. Early work focused on the most easily measurable quantity, the DC conductivity.[1-3, 6-10] Recently, due to the availability of local scanning probes, attention has turned to the tunneling behavior [11][12][13][14][15]. In the case of the disorder-tuned SIT [15], it has become clear that the SIT is ultimately due to a bosonic mechanism [16] rather than a fermionic one [17]. The last step towards a full characterization of the SIT is to develop an understanding of the behavior of the AC conductivity. This is a powerful probe of fluctuations on both long and short length and time scales, and it is of great interest especially as recent technological developments begin to open up more windows of the electromagnetic spectrum for measurement [18][19][20][21].One of the most important questions concerns the AC conductivity in the "collisionless DC" limit [22,23] [52], σ * = lim ω→0 lim T →0 σ(ω, T ). This has been the subject of a large body of work, including analytical arguments involving charge-vortex duality arguments, quantum Monte Carlo calculations in various representations, and experiments [1,4,16,23,[25][26][27][28][29][30][31][32]. It is often claimed that at the SIT σ * is finite and takes a universal value of the order of σ Q = 4e 2 /h, but there are large discrepancies between the "universal" values from various studies, and it is not clear whether there really is a universal value.

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“…As a result, there were a number of analytic computations [71,72,75,76,77,78,79,80,81] and an exact diagonalization study [82] of the value of Σ(∞) in a variety of models which display a quantum-critical point in d = 2. Quantum Monte Carlo studies [72,74,83,84,85] determined the conductivity by analytic continuation from imaginary time data at ω = 2πnT i, with n ≥ 1 integer; as the smallest value of ω is 2πT i, these studies were effectively also in the regime |ω| ≫ T .…”

Section: Quantum Relaxational Transport In Two Dimensionsmentioning

confidence: 99%

Dynamics and Transport Near Quantum-Critical Points

Sachdev

1998

Dynamical Properties of Unconventional Magnetic Systems

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Abstract. The physics of non-zero temperature dynamics and transport near quantum-critical points is discussed by a detailed study of the O(N )-symmetric, relativistic, quantum field theory of a N -component scalar field in d spatial dimensions. A great deal of insight is gained from a simple, exact solution of the long-time dynamics for the N = 1 d = 1 case: this model describes the critical point of the Ising chain in a transverse field, and the dynamics in all the distinct, limiting, physical regions of its finite temperature phase diagram is obtained. The N = 3, d = 1 model describes insulating, gapped, spin chain compounds: the exact, low temperature value of the spin diffusivity is computed, and compared with NMR experiments. The N = 3, d = 2, 3 models describe Heisenberg antiferromagnets with collinear Néel correlations, and experimental realizations of quantum-critical behavior in these systems are discussed. Finally, the N = 2, d = 2 model describes the superfluid-insulator transition in lattice boson systems: the frequency and temperature dependence of the the conductivity at the quantum-critical coupling is described and implications for experiments in two-dimensional thin films and inversion layers are noted.

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Universal conductivity of dirty bosons at the superconductor-insulator transition

Cited by 133 publications

References 22 publications

Strong-coupling expansions for the pure and disordered Bose-Hubbard model

Strong-coupling expansions for the pure and disordered Bose-Hubbard model

Divergence of dynamical conductivity at certain percolative superconductor-insulator transitions

Dynamics and Transport Near Quantum-Critical Points

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