Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point

Abstract

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...

The unreasonable effectiveness of Eliashberg theory for pairing of non-Fermi liquids

“…The problem of a metal near a nematic quantum critical point is free of the sign problem, thanks to the presence of two spin flavors. This problem has been studied extensively [40,41,42] using the determinant quantum Monte Carlo technique. In particular, it has been found that the quantum critical point is covered by a broad superconducting 'dome'.…”

Orthogonal metal in the Hubbard model with liberated slave spins

“…and involves a quadratic fit near τ = β/2 [61] (here, statistical errors were propagated but we did not quantify the impact of the fit range). We also extracted σ dc from the real part of the optical conductivity σ (ω) via…”

“…The accuracy of the estimators (38) and (39) depends on the spectral shape of σ (ω) and the temperature, see Refs. [14,60,61]. For example, σ (1) dc gives reliable results if σ (ω) has no low-energy contribution sharper than ∆ω ≈ 8T [14].…”

Collective modes near a Pomeranchuk instability in two dimensions

“…(13), as it should. We see thatδ is positive but smaller than δ in (15). This implies that the poles are located above the branch cuts.…”

“…In this paper we focus on dynamical aspects of a Pomeranchuk instability. We consider primarily the 2D case, because examples of Pomeranchuk transitions have been discussed mostly for 2D systems [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] . We consider an isotropic FL but do not specifically assume Galilean invariance, i.e., the single-particle dispersion in our model is not necessarily quadratic in |k|.…”