Renormalization group theory of nematic ordering in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-wave superconductors

Huh, Young Eun; Sachdev, Subir

doi:10.1103/physrevb.78.064512

Cited by 112 publications

(315 citation statements)

References 15 publications

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“…(3.20) in Ref. 36 holds to all orders in 1/N. The low energy theory (2.7) has two continuous global U(1) symmetries.…”

Section: B Ward Identitiesmentioning

confidence: 99%

“…This paper provides a scaling theory of the Ising-nematic quantum critical point in twodimensional metals, satisfying the requirements stated above. Our theory builds upon the work in the d-wave superconductor 35,36 , and also on advances by Polchinski 37 , Altshuler, Ioffe, and Millis 38 , and Sung-Sik Lee 39,40 on a closely-related problem: the dynamics of a…”

Section: -9mentioning

confidence: 99%

“…A fairly complete understanding of the Ising-nematic transition in d-wave superconductors has been reached in recent work 35,36 using a large-N expansion, where N is the number of fermion components. This paper provides a scaling theory of the Ising-nematic quantum critical point in twodimensional metals, satisfying the requirements stated above.…”

Section: -9mentioning

confidence: 99%

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Quantum phase transitions of metals in two spatial dimensions. I. Ising-nematic order

2010

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We present a renormalization group theory for the onset of Ising-nematic order in a Fermi liquid in two spatial dimensions. This is a quantum phase transition, driven by electron interactions, which spontaneously reduces the point-group symmetry from square to rectangular. The critical point is described by an infinite set of 2+1 dimensional local field theories, labeled by points on the Fermi surface. Each field theory contains a real scalar field representing the Ising order parameter, and fermionic fields representing a time-reversed pair of patches on the Fermi surface. We demonstrate that the field theories obey compatibility constraints required by our redundant representation of the underlying degrees of freedom. Scaling forms for the response functions are proposed, and supported by computations up to three loops. Extensions of our results to other transitions of two-dimensional Fermi liquids with broken point-group and/or time-reversal symmetry are noted.Our results extend also to the problem of a Fermi surface coupled to a U(1) gauge field.

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“…(3.20) in Ref. 36 holds to all orders in 1/N. The low energy theory (2.7) has two continuous global U(1) symmetries.…”

Section: B Ward Identitiesmentioning

confidence: 99%

Section: -9mentioning

confidence: 99%

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Quantum phase transitions of metals in two spatial dimensions. I. Ising-nematic order

2010

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“…To proceed, we need to integrate out the modes defined in the momentum shell bΛ < k < Λ, where b can be written as b = e −l . Under the scaling transformation k i = k ′ i e −l and ω = ω ′ e −l , the fermion field and disorder potential should transform as follows [59] …”

Section: Rg Calculations In Disordered Dirac Semimetalsmentioning

confidence: 99%

Superconductivity in two-dimensional disordered Dirac semimetals

et al. 2017

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In two-dimensional Dirac semimetals, Cooper pairing instability occurs only when the attractive interaction strength |u| is larger than some critical value |uc| because the density of states vanishes at Dirac points. Disorders enhance the low-energy density of states but meanwhile shorten the lifetime of fermions, which tend to promote and suppress superconductivity, respectively. To determine which of the two competing effects wins, we study the interplay of Cooper pairing interaction and disorder scattering by means of renormalization group method. We consider three types of disorders, including random mass, random gauge potential, and random chemical potential, and show that the first two suppress superconductivity. In particular, the critical BCS coupling |uc| is increased to certain larger value if the system contains only random mass or random gauge potential, which makes the onset of superconductivity more difficult. In the case of random chemical potential, the effective disorder parameter flows to the strong coupling regime, where the perturbation expansion breaks down and cannot provide a clear answer concerning the fate of superconductivity. When different types of disorder coexist in one system, their strength parameters all flow to strong couplings. In the strong coupling regime, the perturbative renormalization group method becomes invalid, and one needs to employ other methods to treat the disorder effects. We perform a simple gap equation analysis of the impact of random chemical potential on superconductivity by using the AbrikosovGorkov diagrammatic approach, and also briefly discuss the possible generalization of this approach.

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“…To this end, we will compute the superfluid density after taking into account the ordering competition among nematic (C 2 SDW), C 4 SDW and SC orders. The T -dependence of superfluid density ρ s (T ) is computed based on the l-dependence of parameter α A ≡ α A (l) [66,67], which is extracted from the coupled flow equa- tion (8) In this work, we consider only the competition between distinct order parameters and neglect the contribution of the normal component, i.e. ρ n (T ) ≪ ρ A s (T ), which is possible for the T ≪ T c , focusing on how superfluid density is modified by ordering competition.…”

Section: B Suppression Of Superconductivity Due To Ordering Competitionmentioning

confidence: 99%

Order parameter fluctuation and ordering competition in Ba1−xKxFe2As2

et al. 2017

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The competition among superconductivity, stripe-type magnetic order, and a new type of C4 symmetric magnetic order in Ba1−xKxFe2As2 is theoretically studied, focusing on its impact on the global phase diagram. By carrying out a renormalization group analysis of an effective field theory, we obtain the energy-scale dependent flows of all the model parameters, and then apply the results to understand the observed phase diagram. On the basis of the renormalization group analysis, we show that the critical line of nematic order has a negative slope in the superconducting dome and superconductivity is suppressed near the magnetic quantum critical point, which are both consistent with recent experiments. Moreover, we find that, although the observed C4 symmetric magnetic state could be a charge-spin density wave or a spin-vortex crystal at high temperatures, charge-spin density wave is the only stable C4 magnetic state in the low-temperature regime. Therefore, ordering competition provides a method to distinguish these two candidate C4 magnetic states.

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Renormalization group theory of nematic ordering ind-wave superconductors

Cited by 112 publications

References 15 publications

Quantum phase transitions of metals in two spatial dimensions. I. Ising-nematic order

Quantum phase transitions of metals in two spatial dimensions. I. Ising-nematic order

Superconductivity in two-dimensional disordered Dirac semimetals

Order parameter fluctuation and ordering competition in Ba1−xKxFe2As2

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