Yamaji effect and quantum oscillation in Yang-Rice-Zhang model of underdoped cuprates

Abstract

Recent experiments have revealed signatures of small Fermi pockets in the pseudogap phase of cuprate superconductors, most notably the Yamaji effect observed in $\mathrm{HgBa}_2\mathrm{CuO}_{4+δ}$. The Yang-Rice-Zhang (YRZ) model provides a successful phenomenological description of the pseudogap state and naturally predicts such small pockets. In this work, we use a microscopic framework to calculate angle-dependent magnetoresistance and quantum oscillation within the YRZ model. Our calculations simultaneously reproduce the experimentally observed Yamaji oscillations and the Shubnikov-de Haas oscillation corresponding to a pocket area of about $p/8$, with $p$ the hole density. By further testing the effect of Green's-function zeros, we confirm that isolated zeros leave the oscillation period unchanged, whereas an extended zero segment suppresses and modifies the oscillation. Our findings demonstrate that the YRZ model captures essential features of the pseudogap regime and provides a general quantum approach that can be applied to more complex electronic structures.

Figures (7)

• Figure 1: (a) and (b) shows the Fermi pocket of YRZ model by (a) tight binding approximation in Eq. \ref{['eq:GF']} and (b) $k\cdot p$ approximation. The black line indicates the Luttinger surface of zeros and the red line represents the infinities of Green's function. In panel (b) within the blue area $G(\mathbf{k},0)>0$. (c) Spectral function $A(\mathbf{q},0)$ around one pocket in $k\cdot p$ expanded YRZ model. (d) Schematic of Fermi surface in a quasi-2D system. Left: yz cross section with the out-of-plane magnetic field $B_{\perp}$ tilted from c-axis by polar angle $\theta$. Right: xy cross section with caliper momentum $k_{\mathrm{cal}}$ along the in-plane magnetic field direction $B_{\parallel}$ marked by an arrow.
• Figure 2: Calculated interlayer resistivity $\rho_{zz}(\theta)/\rho_{zz}(0)$ as a function of the polar angle $\theta$. Panel (a) and (b) are results with azimuthal angle $\phi=0^\circ$ and $\phi=45^\circ$. The first Yamaji peak is marked with an arrow. The inset schemtically shows the caliper radius corresponding to $\phi$ in each case.
• Figure 3: (a) Calculated interlayer resistivity $\rho_{zz}$ as a function of the inverse magnetic field $B^{-1}$. (b) Absolute value of Fourier transformed interlayer resistivity
• Figure 4: Illustration of role of Green's function zeroes and poles to the quantum oscillation. Spectral function $A(\mathbf{k}, \omega = 0)$ (panels (a)–(c)) with red lines as pole positions, and quantum oscillation in density of states (panels (d)–(f)) in Green's function Eq.\ref{['eq:toy']}. Left panel: free electron case $V_0 = 0$, in which there are no zeroes. Middle panel: a small segment of zeroes with parameters $V_0 = 0.6,\; a = k_F =1/\sqrt{2},\; \mu = 0.5,\; \eta = 0.05$. Right panel: only half circle of poles with parameters as same as in the middle panel except $a = 0$.
• Figure 5: Calculated interlayer resistivity $\rho_{zz}(\theta)/\rho_{zz}(0)$ as a function of the polar angle $\theta$. The red curve represents results of quantum approcch, while the black curve represents results of semi-classical approach.