Low-temperature structural and transport anomalies in ${\mathrm{Cu}}_2\mathrm{Se}$

Through systematic examination of symmetrically nonequivalent configurations, first-principles calculations have identified a new ground state of ${\mathrm{Cu}}_2\mathrm{Se}$, which is constructed by repeating sextuple layers of Se-Cu-Cu-Cu-Cu-Se. The layered nature is in accord with electron and x-ray diffraction studies at and below room temperature and also is consistent with transport properties. Magnetoresistance measurements at liquid helium temperatures exhibit cusp-shaped field dependence at low fields and evolve into quasilinear field dependence at intermediate and high fields. These results reveal the existence of weak antilocalization effect, which has been analyzed using a modified Hikami, Larkin, and Nagaoka model, including a quantum interference term and a classical quadratic contribution. Fitting parameters suggest a quantum coherence length $L$ of 175 nm at 1.8 K. With increasing temperature, the classical parabolic behavior becomes more dominant, and $L$ decreases as a power law of $T^{-0.83}$.

Figure 1

(a) Projected (along the monoclinic $b$ axis) ab initio ground state structure of ${\mathrm{Cu}}_2\mathrm{Se}$ formed by repeating sextuple layers of Se-Cu-Cu-Cu-Cu-Se. (b) Simulated SAED pattern along the zone axis [011] of the monoclinic phase and the [101${\mathrm{]}}_{\mathrm{fcc}}$ with the diffractions from the fcc structure labeled as squares. (c) The experimental SAED pattern along the [011] zone axis of the monoclinic phase. (d) The calculated phonon band structure and density of states ($D_p$) indicate the proposed structure is dynamically stable. (e) The electronic band structure and density of states ($D_e$) calculated using HSE hybrid functional suggests that ${\mathrm{Cu}}_2\mathrm{Se}$ is a semiconductor with band gap $E_g$ = 1.03 eV.

Figure 2

Reduced total scattering XRD structure function, $F\left(Q\right)=Q\left[S\right(Q)-1]$, where $S$($Q$) is the total scattering structure function and $Q$ is the momentum transfer, in the 100–300 K range (main panel). Temperature evolution of the normalized intensity around (400) reflection in cubic notation, marked with an arrow in the upper left inset ($Q$ $\sim$ 4.3 Å${}^{-1}$). This region is sensitive to subtle structural changes and evidences the ${\alpha }^{\prime }$ to α superstructure transition at around 175 K, as denoted by a vertical dashed line (upper right inset). Red symbols denote the evolution with temperature of the intensity peaked at $Q$ $\sim$ 4.362 Å${}^{-1}$, while the blue symbols show the evolution of the intensity peaked at $Q$ $\sim$ 4.436 Å${}^{-1}$.

Figure 3

Low-temperature transport profile of stoichiometric ${\mathrm{Cu}}_2\mathrm{Se}$ as a function of temperature. (a) Electrical resistivity ρ and Hall coefficient $R_H$ show anomalies at 100–150 K, where ρ measurements overlap upon either warm-up or cooldown in the temperature. (b) Hall density $p$ and Hall mobility ${\mu }_H$.

Figure 4

(a) Magnetoresistance profile (as a function of magnetic field intensity) of ${\mathrm{Cu}}_2\mathrm{Se}$ at various temperatures (1.8–30 K) indicating evolution of weak antilocalization behavior as the temperature is lowered to 1.8 K. Theoretical fitting to differential magnetoconductance using a modified HLN model at selected temperatures (b) 1.8 K and (c) 9 K. The inset of (c) depicts the fitting parameters showing a power law behavior ($\sim T^{-0.83}$) of the quantum interference length.