Quantum Critical Scaling in Graphene

Sheehy, Daniel E.; Schmalian, Joerg

doi:10.1103/physrevlett.99.226803

Cited by 236 publications

(305 citation statements)

References 26 publications

Supporting

Mentioning

290

Contrasting

Order By: Relevance

“…Recently, it was shown that this material offers a unique opportunity to observe transport properties of a plasma of ultrarelativistic particles at moderately high temperatures [3]. Undoped graphene is located at a special point in parameter space where the Fermi surface shrinks to two points, and in many respects it behaves similarly as other systems close to more complex quantum critical points [4]. Due to its massless Dirac particles graphene also shares interesting properties with the ultrarelativistic quark gluon plasma.…”

mentioning

confidence: 99%

“…While effects due to electron-electron interactions only amount to very small additive corrections to the conductivity σ (ω, T ) in the collisionless optical regime ω k B T [3,4,11], collisions are crucial in the opposite regime ω k B T [3,12]. There they establish local equilibrium, the remaining low frequency dynamics being gov-…”

mentioning

confidence: 99%

“…The strength of the Coulomb interaction is characterized by the effective fine structure constant α = e 2 v 2.2/ , which is not small for realistic values of the substrate dielectric constant . Key for an understanding of clean, undoped graphene is the fact that it is a 'quantum critical' system with marginally irrelevant Coulomb interactions which renormalize logarithmically to zero [3,4,11,21,22,23,24]. This quantum critical behavior in undoped graphene is responsible for the distinctly different behavior of the collision-free and collision-dominated frequency regimes [25].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Graphene: A Nearly Perfect Fluid

2009

Self Cite

View full text Add to dashboard Cite

Hydrodynamics and collision dominated transport are crucial to understand the slow dynamics of many correlated quantum liquids. The ratio η/s of the shear viscosity η to the entropy density s is uniquely suited to determine how strongly the excitations in a quantum fluid interact. We determine η/s in clean undoped graphene using a quantum kinetic theory. As a result of the quantum criticality of this system the ratio is smaller than in many other correlated quantum liquids and, interestingly, comes close to a lower bound conjectured in the context of the quark gluon plasma. We discuss possible consequences of the low viscosity, including pre-turbulent current flow. PACS numbers: 67.90.+z,81.05.Uw Graphene [1,2], attracts a lot of attention due to the massless relativistic dispersion of its quasiparticles and their high mobility. Recently, it was shown that this material offers a unique opportunity to observe transport properties of a plasma of ultrarelativistic particles at moderately high temperatures [3]. Undoped graphene is located at a special point in parameter space where the Fermi surface shrinks to two points, and in many respects it behaves similarly as other systems close to more complex quantum critical points [4]. Due to its massless Dirac particles graphene also shares interesting properties with the ultrarelativistic quark gluon plasma. The latter, surprisingly, has an unexpectedly low shear viscosity, as was observed in the dense matter balls created at the relativistic heavy ion collider RHIC [5]. We show here that an analogous property can be found in undoped graphene, reflecting its quantum criticality.The shear viscosity η measures the resistance of a fluid to establishing transverse velocity gradients, see Fig. 1. The smaller the viscosity, the higher the tendency to turbulent flow dynamics. Viscosity, similarly as resistivity in a conductor, leads to entropy production by degrading inhomogeneities in the velocity field. While ideal fluids with η = 0 cannot exist, it is interesting to seek for perfect fluids which come as close as possible to this ideal.Viscosity has the units of n where n is some density. To quantify the magnitude of the viscosity, it is natural to compare η/ to the density of thermal excitations, n th , which can be estimated by the entropy density, s ∼ k B n th . Motivated by the nearly perfect fluid behavior seen in the RHIC experiments, Kovtun et al. have recently postulated a lower bound for the ratio of η and s for a wide class of systems [6]:Equality was obtained for an infinitely strongly coupled conformal field theory by mapping it to weakly coupled gravity using the AdS-CFT correspondence. While examples violating the bound (1)were found (see [7]), the existence of some lower bound with k B η/ s of order unity for a given family of fluids is not unexpected. It is analogous to the Mott-Ioffe-Regel limit for the minimum conductivity of poor metals [8,9], and to the saturation of the relaxation rate at τ −1 rel = k B T / · O(1) close to strongly coupled quantum cri...

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Graphene: A Nearly Perfect Fluid

2009

Self Cite

View full text Add to dashboard Cite

show abstract

“…For the latter, neutral or intrinsic graphene embodies the paradigm of a marginal Fermi liquid (FL). [13][14][15] While graphene in the presence of electronelectron interactions (EEI) establishes a finite Fermi surface at high doping, it crosses over to a relativistic Dirac liquid at lower densities and manifests non-FL relaxation rates [16][17][18] and transport characteristics. 6,15,19 Another interesting interaction-dominated transport phenomenon is Coulomb drag in graphene double layer systems [20][21][22] which is determined by the peculiar interaction-induced interlayer relaxation.…”

Section: Introductionmentioning

confidence: 99%

Relaxation of optically excited carriers in graphene: Anomalous diffusion and Lévy flights

2014

View full text Add to dashboard Cite

We present a theoretical analysis of the relaxation cascade of a photoexcited electron in graphene in the presence of RPA screened electron-electron interaction. We calculate the relaxation rate of high energy electrons and the jump-size distribution of the random walk constituting the cascade which exhibits fat tails. We find that the statistics of the entire cascade are described by Lévy flights with constant drift instead of standard drift-diffusion in energy space. The Lévy flight manifests nontrivial scaling relations of the fluctuations in the cascade time, which is related to the problem of the first passage time of Lévy processes. Furthermore we determine the transient differential transmission of graphene after an excitation by a laser pulse taking into account the fractional kinetics of the relaxation dynamics.

show abstract

“…In contrast, armchair strain has very little effect on the electronic structure, so we will restrict ourselves to zig-zag strain hereafter. Though scarcely studied 9,10 , e − e interactions FIG. 1.…”

mentioning

confidence: 99%

Quantum phase transitions in strained graphene due to the interplay between spin fluctuations and anisotropic band structure

Arya¹,

Laad²,

Hassan³

2017

Phys. Rev. B

View full text Add to dashboard Cite

Strain tuning is increasingly being recognized as a clean tuning parameter to induce novel behavior in quantum matter. Motivated by the possibility of straining graphene up to 20 percent, we investigate novel quantum criticality due to interplay between strain-induced anisotropic band structure and critical antiferromagnetic spin fluctuations (AFSF) in this setting. We detail how this interplay drives (i) a quantum phase transition (QPT) between the Dirac-semimetal-incoherent pseudogapped metal-correlated insulator as a function of strain ( ), and (ii) critical AFSF-driven divergent nematic susceptibility near critical strain ( c) manifesting as critical singularities in magneto-thermal expansion and Grüneisen co-efficients. The correlated band insulator at large strain affords realization of a two-dimensional dimerized spin-singlet state due to this interplay, and we argue how doping such an insulator can lead to a spin-charge separated metal, leading to anomalous metallicity and possible unconventional superconductivity. On a wider front, our work serves to illustrate the range of novel states realizable by strain-tuning quantum materials.PACS numbers: 25.40. Fq, 71.10.Hf, 63.20.Dj, 63.20.Ls, 74.25.Ha, 74.20.Rp The exciting discovery of single-layer graphene has spawned a tremendous burst of activity 1 on fundamental and applied grounds. It is the strongest electronic material, capable of sustaining reversible elastic deformations in excess of 20 percent. 2 . Besides, graphene possesses rich electronic properties, originating from gapless, linearly dispersing Dirac-like excitations 3 . Attractive features like high mobility, absence of backscattering and strong field effects hold out the promise for future devices, but such possibilities are hindered by the gapless spectrum. Inducement of a gap by quantum confinement is possible, but this also gives rise to edge roughness, with deleterious effect on electronic properties.Recently, strain engineering has been studied 4 as a way to profitably unite seemingly independent mechanical and electronic properties of graphene. Experimental studies indicate that reversible and controlled strain up to 20 percent can be produced in graphene 5 , opening a unique opportunity to realize this aspect. While detailed investigation of this interplay within one-electron band structure has been carried out 4 , possibility of novel physics arising due to interplay between strain-modified electronic structure and electron-electron interactions has not received much attention. Observed breakdown of the Wiedemann-Franz law 6 near the charge neutrality point betrays the effect of sizable e − e interactions in graphene. In this light, one may anticipate that a strainmodified band structure could give rise to novel quantum phase transition(s) and novel physical responses as a result of interplay between an anisotropic electronic structure and local Coulomb interactions. In this letter, we explore the possibility of inducing novel quantum phase transitions in (20 percent) strained graph...

show abstract

Quantum Critical Scaling in Graphene

Cited by 236 publications

References 26 publications

Graphene: A Nearly Perfect Fluid

Graphene: A Nearly Perfect Fluid

Relaxation of optically excited carriers in graphene: Anomalous diffusion and Lévy flights

Quantum phase transitions in strained graphene due to the interplay between spin fluctuations and anisotropic band structure

Contact Info

Product

Resources

About