Universal conductivity of two-dimensional films at the superconductor-insulator transition

Cha, Min-Chul; Fisher, Matthew P. A.; Girvin, S. M.; Wallin, Mats; Young, A. P.

doi:10.1103/physrevb.44.6883

Cited by 365 publications

(478 citation statements)

References 60 publications

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“…In contrast, any computation of the conductivity performed at T = 0, in which the ω → 0 limit is taken subsequently will determine the number Σ(∞). It was argued quite generally by Cha et al [72] and Wallin et al [74] that Σ is in independent of ω/T , which therefore also implies that Σ(0) = Σ(∞). 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.…”

Section: Quantum Relaxational Transport In Two Dimensionsmentioning

confidence: 97%

“…The Eqns (72,73) are the central results of the N = ∞ theory; in spite of their extremely simple structure, these equations contain a great deal of information, and it takes a rather subtle and careful analysis to extract the universal information contained in them [7]. We will not go into these technical details here, but will be satisfied by describing the different physical regimes predicted by (72,73) and other analyses of H R .…”

Section: Continuum Theory and Large N Limitmentioning

confidence: 99%

“…Let us now turn to the computation of Σ for the specific model S. The T > 0 transport properties of S in d = 2 were considered briefly by Cha et al [72]. They concluded that the continuum model S had σ = ∞ for all T > 0, and that additional lattice umklapp scattering effects were needed to degrade the current carried by thermally excited carriers, and to yield a σ < ∞.…”

Section: Quantum Relaxational Transport In Two Dimensionsmentioning

confidence: 99%

“…For this we need the scaling and engineering dimensions of σ. Rather general arguments [71,72,73,68] show that in d = 2, σ has scaling dimension zero, and engineering dimensions of the quantum unit of conductance Q 2 /h. This leads to the scaling form…”

Section: Quantum Relaxational Transport In Two Dimensionsmentioning

confidence: 99%

“…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%

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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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Section: Quantum Relaxational Transport In Two Dimensionsmentioning

confidence: 97%

Section: Continuum Theory and Large N Limitmentioning

confidence: 99%

Section: Quantum Relaxational Transport In Two Dimensionsmentioning

confidence: 99%

Section: Quantum Relaxational Transport In Two Dimensionsmentioning

confidence: 99%

Section: Quantum Relaxational Transport In Two Dimensionsmentioning

confidence: 99%

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Dynamics and Transport Near Quantum-Critical Points

Sachdev

1998

Dynamical Properties of Unconventional Magnetic Systems

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Nonlinear Current-Voltage Characteristics of Locally Superconducting Elemental Films

Christiansen

Hernández

Goldman³

2002

phys. stat. sol. (b)

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Subject classification: 71.30.þh; 74.25.Dw; 74.76.Db; 74.80.Bj; S4 Nonlinear I-V characteristics have been observed in quench-condensed films which are locally superconducting. We suggest an interpretation of an apparent threshold phenomenon in terms of the enhancement of conduction by the depinning of a charge structure that may characterize this insulating regime. We propose that this is a more likely description than Coulomb blockade or charge-anticharge unbinding phenomena.In the context of the Bose-Hubbard model, zero-temperature superconductor-insulator (SI) transitions in two dimensions (2D), tuned by disorder or magnetic field, are direct, with metallic behavior only at a quantum critical point [1]. Recent experiments suggest that there may be a metallic phase separating the superconductor and insulator. This was observed in MoGe films at moderate magnetic fields at low temperatures, and attributed to dissipation [2]. A transition to "true" superconductivity was reported at low field [3]. It is well known that metallic behavior is found in quench-condensed granular films over a range of thicknesses intermediate between those for which films are insulating and superconducting [4]. Similar observations have been made for Josephson junction arrays [5]. Several new approaches to theory have yielded a metallic phase [6][7][8].Here our concern is with the insulating regime of granular quench-condensed films, which exhibit superconducting, metallic and insulating behaviors. In the past neither the insulating, nor the metallic regimes were the focus of investigation, as the main issue was determining the onset of superconductivity. Since local superconductivity exists in granular films when they are not globally superconducting [10] they should be good candidates for the application of the Bose-Hubbard model, in which there is nonvanishing order parameter amplitude. We focus on Ga films, which earlier exhibited the most striking metallic regime [4]. We propose that the nonlinear I-V characteristics found in the insulating regime may be evidence of a Bose insulating state, which could be either a Cooper-pair CDW, Cooper pair crystal, or for sufficient disorder, a Cooper pair glass. The nonlinearities are similar to those found in the depinning of charge density waves by a current [11]. The behavior of these films is different from that of nominally homogeneous films, where an orbital magnetoresistance linear in field was interpreted as evidence of vortices [12].Gallium films were grown on glazed alumina substrates held at liquid helium temperatures. This was done in an ultra high vacuum apparatus in which cyclic evaporations and in situ transport measurements [13] at temperatures down to 150 mK could be made.We show in Fig. 1 the evolution of RðTÞ with thickness of a-Ga films, adapted from Ref. [4]. The evidence for local superconductivity is the local minimum of RðTÞ.

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Superconductor‐Insulator Transition in Dark Matter Detection

Roychowdhury

Bhattacharyya

1995

Physica Status Solidi (b)

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Astrophysical observations suggest that 50% to 90% of the material in the universe is invisible, whose existence is solely inferred from gravitational effects. Various attempts to detect dark matter are reported, such as the Berkeley Stanford detectors (USA) [l] and the Komiokande detector (Japan). The latter recently reported neutralino dark matter heavier than the W-boson 121. The present note considers the possibility of a Stanford-like detector, in which dark matter incident on the superconducting film leads to universal conductivity at the critical point due to a superconductor-insulator transition.In the superconducting phase there are pinned vortices, so that the flux of vortices flowing across a superconducting material is zero. As a result, the voltage across the weak link Josephson junction is given by [3] where dq,ldt is the rate of change of the phase difference of the superconducting order parameter, qo the flux quantum, and 1, the characteristic length of the microbridge, while N , = JB -nB,l/cp,, defines the degree of mismatch between the vortex and the hole lattices. As dark matter is incident on the superconducting microbridges, the neutralino/neutrino flux causes an alternation of the hole lattice as a result of which the matching magnetic field is given by ( P~/ (~~" P ' ) where p is the spacing between the holes which is a sensitive function of the annihilation products of dark matter. This modulates the matching field which causes a variation of the magnetic field in the H -T (B-T ) phase diagram. As a result vortices are depinned and under matching conditions, there is a synchronization between the vortex lattice and the hole lattice. A simple model [4] accounts for the essential features of vortex motion in thickness modulated thin films. Assuming a harmonic film profile d(x, y) = d + (d, -d) sin qx (where q = 2n/J., J. being the period of thickness modulation and d , the critical thickness of the film) and neglecting background pinning effects, the motion of the vortex lattice is that of a single flux line (assuming that the extra vortex in a lattice of holes each filled with only I) Calcutta 700016, India. ' ) I/AF Bidhan Nagar,

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Universal conductivity of two-dimensional films at the superconductor-insulator transition

Cited by 365 publications

References 60 publications

Dynamics and Transport Near Quantum-Critical Points

Dynamics and Transport Near Quantum-Critical Points

Nonlinear Current-Voltage Characteristics of Locally Superconducting Elemental Films

Superconductor‐Insulator Transition in Dark Matter Detection

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