Vortex state of a<b><i>d</i></b>-wave superconductor at low temperatures

I review two classes of strong coupling problems in condensed matter physics, and describe insights gained by application of the AdS/CFT correspondence. The first class concerns non-zero temperature dynamics and transport in the vicinity of quantum critical points described by relativistic field theories. I describe how relativistic structures arise in models of physical interest, present results for their quantum critical crossover functions and magneto-thermoelectric hydrodynamics. The second class concerns symmetry breaking transitions of twodimensional systems in the presence of gapless electronic excitations at isolated points or along lines (i.e. Fermi surfaces) in the Brillouin zone. I describe the scaling structure of a recent theory of the Ising-nematic transition in metals, and discuss its possible connection to theories of Fermi surfaces obtained from simple AdS duals.

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“…We can now expand E BCS in Eq. ( 35) for small φ (with ∆ x 2 −y 2 finite) and find a series with the structure [47,48]…”

Section: Time-reversal Symmetry Breakingmentioning

confidence: 99%

“…The Ising nematic theory began with a 2+1 dimensional Hamiltonian S c + S φ + S cφ in Eqs. (41,47,48), and ended up with a S 1 /Z 2 set of 2+1 dimensional field theories. In AdS/CFT, there is the emergent radial direction representing energy scale.…”

Section: Ads/cft Correspondencementioning

confidence: 99%

Condensed Matter and AdS/CFT

Sachdev

2011

Lecture Notes in Physics

132

157

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“…For example, while the authors of papers [23,24,25] believe that such a role for a magnetic field in that phase is plausible, the analysis of the authors of Ref. [26] indicates that the magnetic field can actually supress id xy and is gaps in a d-wave state.…”

mentioning

confidence: 99%

Thermal conductivity and competing orders in d-wave superconductors

Gusynin

Miransky

2003

The European Physical Journal B - Condensed Matter

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Abstract. We derive the expression for the thermal conductivity κ in the low-temperature limit T → 0 in d-wave superconductors, taking into account the presence of competing orders such as spin-density wave, is-pairing, etc. . The expression is used for analyzing recent experimental data in La2−x Srx CuO4. Our analysis strongly suggests that competing orders can be responsible for anomalies in behavior of thermal conductivity observed in those experiments. The existence of four nodal points in d-wave superconductors provides rich and, sometimes, controllable dynamics of quasiparticle excitations at zero temperature. In particular, the expressions for electrical, thermal, and spin conductivity simplify considerably in the universallimit ω → 0, T → 0 [1,2]. It is noticeable that the role of the thermal conductivity κ is special: while vertex and/or Fermi-liquid corrections modify the bare, "universal", values of both electric and spin conductivities, the universal value of the thermal conductivity is not influenced by them [2]. It is: PACSwhere v F is a Fermi velocity, v ∆ is a gap velocity, and k B is the Boltzmann constant (we use units withh = c = 1). The basis for such a remarkably simple expression is that there is a finite density of states N (0) of gapless quasiparticles down to zero energy [2,3]:where Γ 0 ≡ Γ (ω → 0), with Γ (ω) an impurity scattering rate, and p 0 = √ πv F v ∆ /a is an ultraviolet momentum cutoff (a is a lattice constant) [2]. Note that expression (1) itself is valid in the so-called "dirty" limit, T ≪ Γ 0 . Therefore, although this expression does not contain Γ 0 explicitly, a nonzero Γ 0 is crucial both for Eqs. (1) and (2). But what will happen if those quasiparticles become gapped? One may think that in that case both N (0) and κ 0 are zero. However, as will be shown in this paper, they both are finite even in that case, if the impurity scattering rate is non-zero. In fact, it will be shown that they are:andwhere m a quasiparticle gap. The noticeable point is that, for all values of the gap up to m ≃ Γ 0 , the suppression of both thermal conductivity and quasiparticle density is mild:and N (0)/N m (0) are of order one. However, the suppression in thermal conductivity rapidly becomes strong as m crosses this threshold. The second noticeable point is that, as we will discuss below, the gap m plays here a universal role and may represent different competing orders in d-wave superconductors, such as as spin density wave, charge density wave, is-pairing, etc. . Although their dynamics are different, expressions (3) and (4) for κ (m) 0 and N m are the same. This happens because, first, all those gaps m correspond to different types of "masses" in the Dirac equation describing nodal quasiparticle excitations, and, secondly, unlike electric and spin conductivities, the thermal conductivity k is blind with respect to quantum numbers distinguishing those masses.The expression k (m) 0 corresponds to the dirty limit when T ≪ Γ 0 . In d-wave superconductors, Γ 0 can be as

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“…The analytical expansion of the BCS solution near the infinity point has been obtained perturbatively by Li, Hirschfeld and Wölfle (LHW theory) [10]. In Ginsburg-Landau regime near T c they found…”

Section: Quasiclassical Approachmentioning

confidence: 94%

“…To obtain the quasiclassical Green functions we solve the quasiclassical Eilenberger equations for the pairing potential ∆(θ, r) =∆(r) cos (2θ) exp (iϕ) [8,9], where θ is the angle between the k vector and the a axis (or x axis) and exp (iϕ) = (x + iy)/r. It should be noted here that the spatial variation of the supercurrent and the d-wave order parameter induce small subdominant s and d xy components in the pairing order parameter [10]. We are not considering these effects because they can be included in a straightforward way in our calculations.…”

Section: Quasiclassical Approachmentioning

confidence: 99%