Figure 1

(Color online) This plot shows the averaged DOS vs $1/B$ in the vortex-mixed state with $\left(\pi ,\pi \right)$ SF-DDW order. From this figure and below, if not mentioned otherwise, $B$ is in units of $\left(\frac{{\Phi }_0}{2\pi a^2}\right)$. If we view $H_{c2}$ as the field strength where vortices are overlapping, it corresponds to $1/B=25$ in the plot. Different lines in the plot show states with different pairing fields. The maximum pairing gap in the antinodal direction would have size $\sim 4\Delta$. We can see that as the gap increases, the frequency decreases. The inset is a plot of the Fermi surface in the normal state. There are four hole pockets with 2.5% area each of the original BZ. This corresponds to $p=0.1$ from half filling. In this plot, ${\Delta }_{\text{sf}}=0.25t$.Reuse & Permissions

Figure 2

(Color online) Fourier transforms of plots shown in Figs. 1, 3, 4. We take $a=4\text{Å}$ and the frequency is then in units of tesla. The color used is the same as in the averaged DOS vs $1/B$ plots. The normal-state frequency is shown by the green line. (a) SF-DDW. (b) SDW, $p=0.125$. The peak at the right is the second harmonic. (c) Electron pocket centered at origin. (d) Two-pocket SDW; the peak at $\sim 380\text{T}$ is from the electron pockets and the one at $\sim 750\text{T}$ is from the hole pockets.Reuse & Permissions

Figure 3

(Color online) An electron pocket is centered at the origin. The pocket has an area of 14% of the original BZ. In this plot, $t^{\prime }=-0.14t$. The maximum gap $\sim 1.5\Delta$.Reuse & Permissions

Figure 4

(Color online) Four hole pockets and two electron pockets are present. In this plot, $A_h=2.9\%$ and $A_e=1.44\%$ of the original BZ and $p=0.086$. In the normal state, from Onsager’s relation we can determine that the peaks with period 11 are from electron pockets. The amplitude is heavily suppressed in the mixed state. In this plot, $V_s=0.2t$.Reuse & Permissions

Figure 5

(Color online) 1/8 stripe state with $t^{\prime }=-0.4t$, $V_{s0}=0.4$, and $V_{c0}=0.1$. The upper inset shows the hybridization of the primary band as we turn on $V_s$ (with $V_c=0$), and the lower inset shows the developed Fermi surface. The fast oscillations localized around $1/B\sim 20$ is a breakdown effect. At lower fields, the fast oscillation (period 6) is from the electron pockets and the very slow oscillation (only 1 period seen in the range) is from the hole pockets. As we turn on superconductivity, the oscillation from the electron pockets is diminished.Reuse & Permissions