Evolution of the Fermi Surface of the Electron-Doped High-Temperature Superconductor ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$ Revealed by Shubnikov–de Haas Oscillations

We report on the direct probing of the Fermi surface in the bulk of the electron-doped superconductor ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$ at different doping levels by means of magnetoresistance quantum oscillations. Our data reveal a sharp qualitative change in the Fermi surface topology, due to translational symmetry breaking in the electronic system which occurs at a critical doping level significantly exceeding the optimal doping. This result implies that the ($\pi /a$, $\pi /a$) ordering, known to exist at low doping levels, survives up to the overdoped superconducting regime.

Figure 1

$c$-axis resistivity ${\rho }_c$ of NCCO plotted vs magnetic field applied perpendicular to the ${\mathrm{CuO}}_2$ planes at $T=4\mathrm{K}$ for different doping levels $x$. The upper inset shows schematically the currently accepted phase diagram of NCCO with the superconducting (SC), antiferromagnetic (AF), and pseudogap (PG) regions. The arrows mark the compositions studied in this work. The lower inset illustrates the geometry of the experiment.

Figure 2

(a) Oscillatory part of the interlayer resistivity of optimally doped NCCO as a function of a magnetic field ($\mathbf{B}\parallel c$ axis) at different $T$. The dotted lines are LK fits to the data using the values $F$, $m_c$, and $T_D$ obtained from plots in (b), (c), and (d), respectively. (b) Positions of the local maxima (solid circles) and minima (open circles) of ${\rho }_{\mathrm{osc}}$ on an inverse field scale. A linear fit (dotted line) yields $F=290\mathrm{T}$. (c) Temperature dependence of the oscillation amplitude at $B=55\mathrm{T}$. The dashed line is the LK temperature dependence with $m_c=0.6m_e$. (d) Dingle plot of the oscillation amplitude at $T=4.0\mathrm{K}$, yielding the Dingle temperature $T_D=15\mathrm{K}$.

Figure 3

Doping dependence of SdH oscillations in NCCO. (a) Slow oscillations in the optimally doped and slightly overdoped ($x=0.16$) samples at $T=4.0\mathrm{K}$. (b) Fast oscillations in the sample with $x=0.17$; $T=3.5\mathrm{K}$. Data from two different field pulses are shown. (c) Corresponding fast Fourier transform spectra of the oscillatory resistivity. For $x=0.17$, the spectrum corresponds to an average of the two data sets shown in (b).

Figure 4

(a) Single-component Fermi surface with a cross-sectional area equal to $\approx 41\%$ of the first Brillouin zone corresponding to $x=0.17$. The dashed line shows the large closed orbit, in the extended zone representation, responsible for the SdH oscillations. (b) Reconstructed Fermi surface comprising one electron and two hole pockets in the reduced Brillouin zone (dashed line). The hole pockets are responsible for the slow oscillations observed on the $x=0.15$ and 0.16 crystals.