Flux Line Lattice Melting and the Formation of a Coherent Quasiparticle Bloch State in the Ultraclean ${\mathrm{URu}}_2{\mathrm{Si}}_2$ Superconductor

We find that in the ultraclean heavy-fermion superconductor ${\mathrm{URu}}_2{\mathrm{Si}}_2$ ($T_{c0}=1.45\mathrm{K}$) a distinct flux line lattice melting transition with outstanding characters occurs well below the mean-field upper critical fields. We show that a very small number of carriers with heavy mass in this system results in exceptionally large thermal fluctuations even at sub-Kelvin temperatures, which are witnessed by a sizable region of the flux line liquid phase. The uniqueness is further highlighted by an enhancement of the quasiparticle mean free path below the melting transition, implying a possible formation of a quasiparticle Bloch state in the periodic flux line lattice.

Figure 1

Temperature dependence of the resistivity for (a) $\mathit{H}\parallel c$ and (b) $\mathit{H}\parallel a$. The very large magnetoresistance in the normal state stems from the compensation, i.e., essentially equal number of electrons and holes, $n_e=n_h$ [4]. The solid arrows indicate the melting transition $T_m$, which is defined as a peak of $d\rho /dT$ [inset of (b)]. The dashed arrows indicate the mean-field transition temperature $T_c$ determined by the cusp of the thermal conductivity [see Fig. 3]. The inset of (a) shows the resistivity in zero field. The inset of (b) shows $d\rho /dT$ vs $T$. The data are vertically shifted.

Figure 2

Exponent $\alpha$ in $E\propto J^{\alpha }$, as a function of temperature for $\mathit{H}\parallel a$ at 2 T and 4 T. The inset shows the $E\mathrm{\text{−}}J$ characteristics around $T_m$. The Ohmic resistivity $\alpha =1$ is observed at high temperatures, and $\alpha$ increases gradually with approaching $T_m$ and shows a sharp increase at $T_m$.

Figure 3

Temperature dependence of the thermal conductivity divided by temperature $\kappa /T$ (circles) in zero field (a) and in magnetic fields $\mathit{H}\parallel a$ (b)–(f). The resistivity data at corresponding fields are also shown (solid lines). The dashed arrows indicate the temperature at which $\kappa /T$ shows cusps, which correspond to the mean field $T_c(H)$. The solid arrows mark the melting temperature $T_m$ [inset of Fig. 1b]. Below $\sim T_m$, $\kappa /T$ becomes bigger than extrapolated values.

Figure 4

$H\mathrm{\text{−}}T$ phase diagram of ${\mathrm{URu}}_2{\mathrm{Si}}_2$ determined by the present study for (a) $\mathit{H}\parallel c$ and (b) $\mathit{H}\parallel a$. Open symbols represent the mean-field $H_{c2}$ lines. At low temperatures, this line becomes first order (open squares) [4]. The dashed lines are guides for the eyes. The solid squares represent the melting transition which is fitted by Eq. (1) (solid line). The FL liquid phase occupies a large portion in the $H\mathrm{\text{−}}T$ diagram for both field directions. The inset of (b) shows an expanded view of $H_m(T)$ near $T_{c0}$ for $\mathit{H}\parallel a$. The dash-dotted line is a fit to $H_m\propto (T_c-T{)}^{\beta }$ with $\beta =1.4$. This $\beta$-value is consistent with that in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ [7].