Hyperuniversality in quantum critical phenomena

Kim, Kihong; Weichman, Peter B.

doi:10.1103/physrevb.43.13583

Cited by 46 publications

(70 citation statements)

References 22 publications

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“…This behavior is in agreement with experiments on the magnetic field-tuned IST in disordered indium-oxide thin films [1]. However, these results are in disagreement with the suggestion of Kim and Weichman that the conductivity saturates with increasing field [14]. This discrepancy can be explained by the fact that for η = 0 in the general universal scaling function,…”

Section: Three Limiting Regimes Follow From Eq (4) 1) If T √contrasting

confidence: 51%

“…The former is the collisionless limit, apparently considered in Ref. (14), in which the conductivity is likely to experience a crossover between two universal values depending on the ratio √ H/∆ [18]. However, it is the collision-dominated limit that is experimentally relevant and hence the main subject of our treatment.…”

Section: Three Limiting Regimes Follow From Eq (4) 1) If T √mentioning

confidence: 96%

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Magnetotransport properties near the superconductor-insulator transition in two dimensions

Dalidovich

Phillips

2001

Phys. Rev. B

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We analyze here the behavior near the 2D insulator-superconductor quantum critical point in the presence of a perpendicular magnetic field. We show that with increasing field H, the quantum disordered and quantum critical regimes, in which vortex degrees of freedom are suppressed, crossover to a new magnetically activated (MA) regime, where the correlation length ξ ∼ 1/ √ H. In this regime, we show that the conductivity decreases monotonically as opposed to the anticipated saturation predicted from hyperuniversality arguments. This discrepancy arises from the lack of commutativity of the frequency and temperature tending to zero limits of the conductivity. In the low-field regime such that √ H ≪ ∆, and in the absence of Ohmic dissipation, where ∆ is a measure of the distance from the quantum critical point, the resistivity saturates to the Bose metal value found previously for Cooper pairs lacking phase coherence.From the earliest experiments [1-3] on superconducting thin metal alloy films, a simple picture emerged for the magnetic-field tuned transition to the insulating state. Namely, the transition is continuous with a welldefined critical field, H c , below which superconductivity occurs and above which an insulator obtains. At the critical field, the resistivity is independent of temperature. Within the dirty boson model [4] in an applied magnetic field, these results follow naturally as a direct consequence of the inherent duality between Cooper pairs and vortices: above H c , vortices condense while Cooper pairs remain localized but below H c it is the Cooper pair condensation and vortex localization that affords the zero-resistance state. At criticality, Cooper pairs on the brink of forming a phase coherent state diffuse with the quantum of conductance σ Q = 4e 2 /h for charge 2e bosons. However, more recent experiments have shown that this simple picture breaks down dramatically at and below H c . In particular, a metallic phase [6,7] emerges below H c with the zero-resistance state occurring only at a much smaller field H M ≪ H c [8]. On phenomenological grounds, it has been suggested that the metallic phase arises from the quantum tunneling of field-induced vortices in the presence of dissipation [9].As the metallic phase has been observed at zero-field [10] in the disorder-tuned insulator-superconductor transition as well, we reinvestigated the conductivity of the standard quantum-disordered regime in zero field. We found that quite generally Cooper pairs lacking phase coherence form a Bose metal phase [11]. This result arises from the fact that in the quantum-disordered regime the elementary excitations obey Boltzmann statistics. Hence, their concentration n is exponentially suppressed. As a consequence, so is the inverse scattering time 1/τ that is determined by the probability that two quasiparticles collide. But because the conductivity is a product of the density and the scattering time, the exponentials cancel one another, thereby leading to a finite conductivity as T → 0. In the current study,...

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Section: Three Limiting Regimes Follow From Eq (4) 1) If T √contrasting

confidence: 51%

Section: Three Limiting Regimes Follow From Eq (4) 1) If T √mentioning

confidence: 96%

Magnetotransport properties near the superconductor-insulator transition in two dimensions

Dalidovich

Phillips

2001

Phys. Rev. B

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“…To substantiate this conjecture we begin, following Ref. [16], with a short sketch of the scaling theory of quantum critical phenomena. This also serves to derive Eq.…”

Section: Universal Critical Quantum Properties Of Cuprate Superconducmentioning

confidence: 99%

“…As there is a phase transition line with two end points at T = 0 (1 and 2), a 2d to 3d crossover, and strong evidence of the importance of critical fluctuations at finite temperature [14,15], it seems natural to explore the problem of a consistent description of the doping dependence of various superconducting properties with the scaling theory of quantum critical phenomena [16]. Using this approach we show that at the critical end point 1 the relations are universal, provided that the order parameter is a complex scalar in d = 2 and the London relation between superfluid number density and magnetic penetration depth holds.…”

Section: Isotropy Characterized By Y = √ M/ M I N O P T I Ma L L Y Dmentioning

confidence: 99%

Universal Critical Quantum Properties of Cuprate Superconductors

Schneider

1997

Acta Phys. Pol. A

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Using the scaling theory of quantum critical phenomena we explore the occurrence of universal critical behavior at the insulator-to-superconductor and superconductor-to-normal state transitions at zero temperature. Experimentally, these phase transitions are driven by doping and correspond to critical end points of the phase transition łine in the temperature-hole concentration plane. Provided that the order parameter is a complex scalar in two dimensions, and that the London relation between superfluid number density and magnetic penetration depth holds, the scaling theory predicts universal behavior close to the insulator-to-superconductor transition. In particular, transition temperature and zero temperature penetration depth are universally related and the sheet resistance adopts a universal value. These predictions agree remarkably well with available experimental data and provide useful constraints for a microscopic theory.PACS numbers: 74.62.Dh Many physical properties of cuprate superconductors depend on hole doping. The generic doping dependence of the transition temperature Tc is depicted in Fig. 1. At a certain doping level, the so-called underdoped limit, these materials undergo at the hole concentration x" and T > O a transition from insulator to anomalous metal, and at T = O a transition from insulator to superconductor. As x is increased, Tc rises and reaches its maximum at x m . This behavior is shared by many cuprates, . In some compounds a further increase in the doping level leads to more metallic normal-state properties [8,9], but T, decreases and vanishes in the overdoped limit xo. Here, these materials undergo at T = O a superconductor-to-normal-state transition. A prominent example is La2_x S rx C uO4 _ δ [2].Another essential and doping-dependent property is the effective mass an-

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“…Here the materials correspond to a stack of independent sheets of thickness d s As there is a phase transition line with an endpoint T c (x = x u ) = 0, one expects a doping driven 2D-XY insulator to superconductor transition at T = 0. For such a transition the scaling theory of quantum critical phenomena predicts [19][20][21] …”

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confidence: 99%

D-XY critical behavior in cuprate superconductors

Schneider¹,

Singer²

2000

Physica C: Superconductivity

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We outline the universal and finite temperature critical properties of the 3D-XY model, extended to anisotropic extreme type-II superconductors, as well as the universal quantum critical properties in 2D. On this basis we review: (i) the mounting evidence for 3D-XY behavior in optimally doped cuprate superconductors and the 3D to 2D crossover in the underdoped regime; (ii) the finite size limitations imposed by inhomogeneities; (iii) the experimental evidence for a 2D-XY quantum critical point in the underdoped limit, where the superconductor to insulator transition occurs; (iv) the emerging implications and constraints for microscopic models.The starting point of the phenomenological theory of superconductivity is the GinzburgLandau HamiltonianD is the dimensionality of the system, the complex scalar Ψ (R) is the order parameter, M the effective mass of the pair and A the vector potential. The pair carries a non-zero charge in addition to its mass. The charge (Φ 0 = hc/2e) couples the order parameter to the electromagnetic field via the first term in H. If Ψ and A are treated as classical fields, the relative probability P of finding a given configuration [Ψ, Ψ * , A] is thenThe free energy F follows fromwhere the partition function on the right hand side corresponds to an integral over all possible realizations of the vector potential A, the order parameter Ψ and its complex conjugate Ψ * . Setting e = 0, the free energy reduces to that for a normal to neutral superfluid transition, which is one of the best understood continuous phase transitions with unparalleled agreement between theory, simulations and experiment [1]. In extreme type-II superconductors, however, the coupling to vector potential fluctuations appears to be weak [2], but nonetheless these fluctuations drive the system -very close to criticality -to a charged critical point [3,4]. In any case, inhomogeneities prevent cuprate superconductors from entering this regime, due to the associated finite size effect. For these reasons, the neglect of vectorpotential fluctuations appears to be a reasonable starting point. In this case the vectorpotential in Hamiltonian Eq. (1) can be replaced by its most probable value. The critical properties at finite temperature are then those of the 3D-XY model, reminiscent to the lamda transition in superfluid helium, but extended to take the effective mass anisotropy into account [5,6]. The universal properties of the 3D-XY universality class are characterized by a set of critical exponents, describing the asymptotic behavior of the correlation length ξ ± i , magnetic penetration depth λ i , specific heat A ± , etc., in terms ofwhere 3ν = 2 − α. As usual, in the above expression ± refer to t = T /T c −1 > 0 and t < 0, respectively. The critical amplitudes ξ ± i,0 , λ 2 i,0 , A ± , etc., are nonuniversal, but there are universal critical

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Hyperuniversality in quantum critical phenomena

Cited by 46 publications

References 22 publications

Magnetotransport properties near the superconductor-insulator transition in two dimensions

Magnetotransport properties near the superconductor-insulator transition in two dimensions

Universal Critical Quantum Properties of Cuprate Superconductors

D-XY critical behavior in cuprate superconductors

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