Experimental observables near a nematic quantum critical point in the pnictide and cuprate superconductors

The high-temperature superconductor $\text{SmFeAs}\left({\text{O}}_{1-x}{\text{F}}_x\right)$ shows a clear nematic transition where the square lattice of Fe ions has a rectangular distortion. Similar nematic ordering has also been observed in the cuprate superconductors. We provide a detailed theory of experimental observables near such a nematic transition: we calculate the scaling of specific heat, local density of states, and NMR relaxation rate $1/T_{1}T$.

Figure 1

(Color online) The global phase diagram. The blue, red, and green curves are phase boundaries of SDW, nematic (structure distortion), and superconductivity, respectively.

Figure 2

The Feynman diagram used in this work; the dashed lines are the propagators of nematic order parameter $\varphi$. $a$—the self-energy correction to fermion $\Psi$; $b$—the self-energy correction to $\varphi$; $c$—the vertex correction to fermion bilinear ${\Psi }_i^{†}{T}_A{\Psi }_j$; $d$—the vertex correction to fermion bilinear ${\Psi }_i^t{T}_A{\Psi }_j$.

Figure 3

(Color online) Plot of local density of states with $v_{\Delta 0}/v_{f0}=1/5$, $v_{\Delta 0}/v_{f0}=1/10$, and $v_{\Delta 0}/v_{f0}=1/20$ from top to bottom. The horizontal axis is in scale of $\omega /T_c$. The curves are $y=x^{0.91}$ (red), $y=x^{0.935}$ (blue), $y=x^{0.955}$ (green), and $y=x$ (black).

Figure 4

(Color online) Plot of nodal fermion contribution to specific heat with $v_{\Delta 0}/v_{f0}=1/5$, $v_{\Delta 0}/v_{f0}=1/10$, and $v_{\Delta 0}/v_{f0}=1/20$ from top to bottom. The horizontal axis is in scale of $T/T_c$. The curves are $y=x^{1.86}$ (red), $y=x^{1.91}$ (blue), $y=x^{1.945}$ (green), and $y=x^2$ (black).

Figure 5

(Color online) Plot of $1/\left(T_{1}T\right)$ with $T$ from contribution of spin density at $\vec{q}=\left(0,0\right)$, with $v_{\Delta 0}/v_{f0}=1/5$, $v_{\Delta 0}/v_{f0}=1/10$, and $v_{\Delta 0}/v_{f0}=1/20$ from top to bottom. The horizontal axis is in scale of $T/T_c$. The curves are $y=x^{1.74}$ (red), $y=x^{1.83}$ (blue), $y=x^{1.89}$ (green), and $y=x^2$ (black).

Figure 6

(Color online) Plot of $1/\left(T_{1}T\right)$ with $T$ from contribution of spin density at $\vec{q}=\left(2Q,0\right)$ and $\vec{q}=\left(0,2Q\right)$, with $v_{\Delta 0}/v_{f0}=1/5$, $v_{\Delta 0}/v_{f0}=1/10$, and $v_{\Delta 0}/v_{f0}=1/20$ from top to bottom. The horizontal axis is in scale of $T/T_c$. The curves are $y=x^{1.88}$ (red), $y=x^{1.9}$ (blue), $y=x^{1.93}$ (green), and $y=x^2$ (black).

Figure 7

(Color online) Plot of $1/\left(T_{1}T\right)$ with $T$ from contribution of spin density at $\vec{q}=\left(2Q,2Q\right)$ and $\vec{q}=\left(2Q,-2Q\right)$, with $v_{\Delta 0}/v_{f0}=1/5$, $v_{\Delta 0}/v_{f0}=1/10$, and $v_{\Delta 0}/v_{f0}=1/20$ from the bottom to the top. The horizontal axis is in scale of $T/T_c$. The curves are $y=x^{2.08}$ (red), $y=x^{2.05}$ (blue), $y=x^{2.025}$ (green), and $y=x^2$ (black).