We consider a low Tc metallic superconductor weakly coupled to the soft fluctuations associated with proximity to a nematic quantum critical point (NQCP). We show that: 1) a BCS-Eliashberg treatment remains valid outside of a parametrically narrow interval about the NQCP; 2) the symmetry of the superconducting state (d-wave, s-wave, p-wave) is typically determined by the non-critical interactions, but Tc is enhanced by the nematic fluctuations in all channels; 3) in 2D, this enhancement grows upon approach to criticality up to the point at which the weak coupling approach breaks-down, but in 3D the enhancement is much weaker.

The Ising nematic quantum critical point (QCP) associated with the zero temperature transition from a symmetric to a nematic metal is an exemplar of metallic quantum criticality. We have carried out a minus sign-free quantum Monte Carlo study of this QCP for a two dimensional lattice model with sizes up to 24 × 24 sites. For the parameters in this study, some (but not all) correlation functions exhibit scaling behavior over the accessible ranges of temperature, (imaginary) time, and distance, and the system remains non-superconducting down to the lowest accessible temperatures. The observed scaling behavior has remarkable similarities with recently measured properties of the Fe-based superconductors proximate to their putative nematic QCP. arXiv:1511.03282v2 [cond-mat.supr-con]

Using determinantal quantum Monte Carlo, we compute the properties of a lattice model with spin 1 2 itinerant electrons tuned through a quantum phase transition to an Ising nematic phase. The nematic fluctuations induce superconductivity with a broad dome in the superconducting Tc enclosing the nematic quantum critical point. For temperatures above Tc, we see strikingly nonFermi liquid behavior, including a "nodal-antinodal dichotomy" reminiscent of that seen in several transition metal oxides. In addition, the critical fluctuations have a strong effect on the lowfrequency optical conductivity, resulting in behavior consistent with "bad metal" phenomenology.superconductivity | non-Fermi liquid | quantum criticality U pon approach to a quantum critical point (QCP), the correlation length, ξ, associated with order parameter fluctuations diverges; consequently microscopic aspects of the physics are averaged out and certain properties of the system are universal. Asymptotically close to criticality, exact theoretical predictions concerning the scaling behavior of some measurable quantities are possible. However, in solids, it is rarely possible to convincingly access asymptopia; there are few experimentally documented cases in which a thermodynamic susceptibility grows as a function of decreasing temperature, T , in proportion to a single power law χ ∼ T −x over significantly more than one decade of magnitude. This is particularly true of metallic QCPs, where the metallic critical point may be preempted by the occurrence of a superconducting dome, a fluctuation-driven first-order transition, or some other catastrophe.However, there is a looser sense in which a QCP can serve as an organizing principle for understanding properties of solids over a range of parameters: In the "neighborhood" of a QCP, where χ is large (in natural units) and ξ is more than a few lattice constants, it is reasonable to conjecture that quantum critical fluctuations play a significant role in determining the properties of the material and that, at least on a qualitative level, those properties may be robust (i.e., not strongly dependent on microscopic details), even if they are not universal.With this in mind, we carried out extensive numerical "experiments" on a simple 2D lattice model of itinerant electrons coupled to an Ising-like "nematic" order parameter field, Eq. 1. By varying a parameter in the Hamiltonian, h, the system can be tuned through a quantum or thermal transition from a disordered (symmetric) phase to a nematic phase that spontaneously breaks the lattice symmetry from C4 to C2. Related models of nematic quantum criticality have been studied extensively (1-27), using various analytic methods, and can also be studied with minus-sign-free determinantal quantum Monte Carlo (DQMC) (28-30). Recent Monte Carlo studies have examined the scaling structure of nematic and related QCPs (31, 32) as well as the role of fluctuations in promoting superconductivity (33,34). Moreover, the model is particularly topical, as there is good evide...

Keywords quantum critical metal, superconductivity, non-Fermi liquid, Ising nematic order, spin density wave order, quantum Monte Carlo AbstractMetallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this article, we review the status of the understanding of metallic quantum criticality, and the recent progress made by QMC simulations. We focus on the cases of spin density wave and Ising nematic criticality. We describe the results obtained so far, and their implications for superconductivity, non-Fermi liquid behavior, and transport in the vicinity of metallic quantum critical points. Some of the outstanding puzzles and future directions are highlighted.

To establish the mechanism of unconventional superconductivity in Sr 2 RuO 4 , a prerequisite is direct information concerning the momentum-space structure of the energy gaps i (k), and in particular whether the pairing strength is stronger ("dominant") on the quasi-one-dimensional (α and β) or on the quasi-two-dimensional (γ ) Fermi surfaces. We present scanning tunneling microscopy measurements of the density of states spectra in the superconducting state of Sr 2 RuO 4 for 0.1T c < T < T c and analyze them along with published thermodynamic data using a simple phenomenological model. We show that our observation of a single superconducting gap scale with maximum value 2 ≈ 5T c along with a spectral shape indicative of line nodes is consistent, within a weak-coupling model, with magnetically mediated odd-parity superconductivity generated by dominant, near-nodal, Cooper pairing on the α and β bands. DOI: 10.1103/PhysRevB.88.134521 PACS number(s): 74.70. Pq, 74.55.+v, 74.20.Rp Strong experimental evidence has accumulated that the perovskite superconductor Sr 2 RuO 4 (T c = 1.5 K) (Refs. 1-3) has an unconventional, 4 odd parity 5-8 order parameter (OP) that breaks time reversal symmetry.9,10 A chiral p wave ("p + ip") state, the quasi-two-dimensional (2D) analog of the A phase of superfluid 3 He (Refs. 11 and 12), has long been a leading candidate for the order parameter symmetry of Sr 2 RuO 4 . Exotic phenomena, such as topologically protected Majorana edge modes, which are currently the subject of much speculation, [13][14][15][16] might then be possible in Sr 2 RuO 4 . Issues with this OP identification, however, include the apparent absence of the anticipated edge currents, [17][18][19][20] the absence of a splitting of the transition near T c by an in-plane magnetic field, 21 and the strong evidence [22][23][24][25][26][27][28][29][30] for lines of gap nodes, or near nodes, that are nongeneric in the presence of time-reversal symmetry breaking. We here follow the bulk of the literature and take a chiral p-wave order parameter as a working assumption. (This is discussed further in the Appendix.)Although, at a microscopic scale, Sr 2 RuO 4 is certainly "strongly correlated" (as evidenced, for instance, by the large mass renormalization) 1 the unconventional superconductivity condenses out of a well-characterized Fermi liquid 1,31,32 which itself "emerges" from an incoherent metallic regime at a much higher temperature, T FL ∼ 30 K. This observation suggests 33 that a satisfactory theory of the unconventional superconductivity in this material can be constructed from a weak-coupling perspective. Such a theory would be of great value as a reference point in the ongoing quest to understand unconventional superconductors more generally. Therefore it is important to identify measurements that can, in principle, distinguish between the predictions of different approaches to the superconductivity of Sr 2 RuO 4 . One way of doing this is to understand more precisely the structure of the superconducting order parame...