Fermi surface reconstruction by a charge density wave with finite correlation length

Even a small amplitude charge-density wave (CDW) can reconstruct a Fermi surface, giving rise to new quantum oscillation frequencies. Here, we investigate quantum oscillations when the CDW has a finite correlation length $\xi$—a case relevant to the hole-doped cuprates. By considering the Berry phase induced by a spatially varying CDW phase, we derive an effective Dingle factor that depends exponentially on the ratio of the cyclotron orbit radius, $R_c$, to $\xi$. In the context of $\mathrm{YBa}{}_2\mathrm{Cu}{}_3\mathrm{O}{}_y$ (YBCO), we conclude that the values of $\xi$ reported to date for bidirectional CDW order are, prima facie, too short to account for the observed Fermi surface reconstruction; on the other hand, the values of $\xi$ for the unidirectional CDW are just long enough.

Figure 1

Reconstruction by a $Q=(1/3)(2\pi /a)$ CDW in the model Hamiltonian. Top: $k$-space cyclotron orbit, visualized in terms of scattering across the unreconstructed Fermi surface. For clarity, each scattering process is folded back into the first Brillouin zone. Bottom: Corresponding real-space orbit.

Figure 2

Effective scattering near real space scattering point.

Figure 3

Proposed reconstruction by bidirectional order in the cuprates.

Figure 4

Proposed reconstruction by unidirectional order in YBCO, with nematic distortion of the underlying Fermi surface.

Figure 5

Numerically computed QOs in the density of states for several values of $\xi$. Parameter values indicated in the main text.

Figure 6

Comparison of QOs for disordering via DCs and smoothly varying phase, for $\xi =400$ (top) and $\xi =100$ (bottom).

Figure 7

Position-resolved density of states with a single DC at $x=0$, whose phase slips by $+2\pi /3$ (top) or $-2\pi /3$ (bottom) as $x$ increases. Red dashed lines mark $\pm R_c$.

Figure 8

Raw (top) and background-removed (bottom) data for $y=6.59$. We extract $B_D$ from the 4 K data, where the second harmonic is suppressed by temperature. We divide out the factor $R_T=\frac{2{\pi }^2{k}_{B}T}{\hslash {\omega }_c}/sinh\left(\frac{2{\pi }^2{k}_{B}T}{\hslash {\omega }_c}\right)$, where the cyclotron frequency ${\omega }_c=eB/m^{★}$ is known from previous measurements [26]. The data is then scaled by $e^{+B_D/B}$, with $B_D$ chosen so that the amplitude is field-independent.