Features of the energy gap above $T_c$ in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ as seen by break-junction tunneling

We report tunneling measurements of the energy gap above $T_c$ using as-grown ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ single crystals with $T_c=86\mathrm{}–89\mathrm{K},$ which are in slightly overdoped regions. The measurements were done with break junction for the temperatures mainly above 77 K at which the gap magnitudes of $4\Delta \approx 100\mathrm{meV}$ are obtained. We find clear evidence for the gap above $T_c.$ For the most significant data, the gap magnitude decreases with increasing the temperature up to $T_c,$ but it turns to increase to reach ≈130 meV at ≈120–130 K. The gap feature begins to reduce above this temperature and eventually disappears at the well-defined temperature of $T^{*}\approx 170–190\mathrm{K}.$ The observation of the above characteristics is believed to be a consequence of the clean interface of the break junction, which enables us to probe delicate electronic structures in bulk ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }.$