Temperature induced first order electronic topological transition in $\beta$-Ag$_2$Se

$\beta$-Ag$_2$Se is a promising material for room temperature thermoelectric applications and magneto-resistive sensors. However, no attention was paid earlier to the hysteresis in the temperature dependence of resistivity ($\rho$($T$)). Here, we show that a broad hysteresis above 35 K is observed not only in $\rho$($T$), but also in other electronic properties such as Hall coefficient ($R_H$($T$)), Seebeck coefficient, thermal conductivity and ultraviolet photoelectron spectra (UPS). We also show that the hysteresis is not associated with a structural transition. The $\rho$($T$) and $R_H$($T$) show that $\beta$-Ag$_2$Se is semiconducting above 300 K, but metallicity is retained below 300 K. While electronic states are absent in the energy range from the Fermi level ($E_F$) to 0.4 eV below the $E_F$ at 300 K, a distinct Fermi edge is observed in the UPS at 15 K suggesting that the $\beta$-Ag$_2$Se undergoes an electronic topological transition from a high temperature semiconducting state to a low temperature metallic state. Our study reveals that a constant and moderately high thermoelectric figure of merit ($ZT$) in the range 300-395 K is observed due to the broad semiconductor to metal transition in $\beta$-Ag$_2$Se.