Thermal conductivity and competing orders in d-wave superconductors

Abstract

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

Heat transport inBi2+xSr2−xCuO6+δ: Departure from the Wiedemann-Franz law i

“…5d), thermal conductivity decreases with the application of magnetic field as it does in underdoped LSCO. 6,16 In the latter case, the field-induced decrease in thermal conductivity was interpreted as a field-induced thermal metalinsulator transition presumably as a consequence of a competing order with superconductivity such as spindensity-wave 39 . The existence of such competing order has been theoretically predicted in the phase diagram of cuprates when disorder plays a prominent role 40 .…”

Renormalization of thermal conductivity of disordered d-wave superconductors by impurity-induced local moments

“…Localization effects were discussed in this context in Ref. [6], and effects of bulk subdominant competing orders have been shown to suppress κ 0 /T but do not immediately eliminate it, despite the removal of the d-wave nodes [7]. Here, we inves-tigate the effects on κ(T ) by local impurity-induced moments relevant e.g.…”

Breakdown of Universal Transport in Correlatedd-Wave Superconductors

“…Localization effects were discussed in this context in Ref. [9], and effects of bulk subdominant competing orders have been shown to suppress κ 0 /T but do not immediately eliminate it, despite the removal of the d-wave nodes [10]. Here, we investigate the effects on κ(T ) by local impurity-induced moments relevant e.g.…”