Tuning the electronic and the crystalline structure of LaBi by pressure: From extreme magnetoresistance to superconductivity

Extreme magnetoresistance (XMR) in topological semimetals is a recent discovery which attracts attention due to its robust appearance in a growing number of materials. To search for a relation between XMR and superconductivity, we study the effect of pressure on LaBi. By increasing pressure, we observe the disappearance of XMR followed by the appearance of superconductivity at $P\approx 3.5$ GPa. We find a region of coexistence between superconductivity and XMR in LaBi in contrast to other superconducting XMR materials. The suppression of XMR is correlated with increasing zero-field resistance instead of decreasing in-field resistance. At higher pressures, $P\approx 11$ GPa, we find a structural transition from the face-centered cubic lattice to a primitive tetragonal lattice, in agreement with theoretical predictions. The relationship between extreme magnetoresistance, superconductivity, and structural transition in LaBi is discussed.

Figure 1

(a) Magnetoresistance as a function of pressure in LaBi. The extreme magnetoresistance (XMR) is suppressed by $P\approx 5$ GPa. (b) Unit-cell volume per atom as a function of pressure. Pressure reduces the cubic unit-cell volume smoothly across the region of XMR suppression. The discontinuous jump at $P\approx 11$ GPa is a structural transition from cubic to tetragonal marked by the vertical blue dotted line. (c) Temperature-pressure phase diagram of superconductivity in LaBi. The onset of superconductivity is marked by the vertical black dashed line. $T_c$ increases with increasing pressure until $P=6$ GPa, then decreases until $P=11$ GPa where it shows a sudden increase concurrent with the structural transition. The red circles show $T_c$ values from resistivity and the open magenta circles show the values from magnetization.

Figure 2

Normalized resistance $R/R\left(300\text{K}\right)$ at $H=0$ (blue) and $H=9$ T (red) as a function of temperature at (a) $P=0$, (b) $P=0.3$ GPa, (c) $P=1.6$ GPa, and (d) $P=2.4$ GPa. The normalized resistance at $H=9$ T in the plateau region is not systematically suppressed by increasing pressure and therefore does not explain the systematic suppression of XMR with pressure. A zoom into the normalized resistance $R/R\left(300\mathrm{K}\right)$ at $H=0$ is shown for $T<30$ K at (e) $P=0$, (f) $P=0.3$ GPa, (g) $P=1.6$ GPa, and (h) $P=2.4$ GPa. Solid black lines are power law fits to extract residual resistances. Broad and incomplete superconducting transitions appear at $P=1.6$ and 2.4 GPa, most likely due to pressure inhomogeneity.

Figure 3

(a) Magnetoresistance $\text{MR}=100\frac{R\left(H\right)-R\left(0\right)}{R\left(0\right)}$ at $T=2$ K plotted as a function of field from $H=0$ to 9 T at four representative pressure values. A systematic decrease of MR is observed with increasing pressure. (b) Normalized resistance at $H=0$ and $T=2$ K are extracted from the fits in Fig. 2 and plotted as a function of pressure (empty blue squares corresponding to the left $y$ axis). MR values at $H=9$ T and $T=2$ K are extracted from panel (a) and plotted as a function of pressure (red circles corresponding to the right $y$ axis). Both $y$ axes are logarithmic to show that the two quantities anticorrelate while they vary by orders of magnitude. (c) Normalized resistance at $H=9$ T and $T=2$ K are plotted as a function of pressure (empty black diamonds corresponding to the left $y$ axis). MR values at $H=9$ T and $T=2$ K are extracted from panel (a) and plotted as a function of pressure (red circles corresponding to the right $y$ axis). There is no clear correlation between the two quantities.

Figure 4

(a) Unit-cell volume per atom in LaBi as a function of pressure. The discontinuous drop at $P\approx 11$ GPa corresponds to a structural phase transition from face-centered cubic (fcc) to primitive tetragonal (PT) lattice as illustrated on the figure. Thick green lines are the results of theoretical calculations by Vaitheeswaran et al. [30]. Solid black lines show the Birch–Murnaghan equation of state [Eq. (1)] from which we extract the bulk moduli for both structures as reported in Table 1. Representative refinements are given in Appendix pp1. (b) Band structure of LaBi in the low-pressure fcc structure with two central hole pockets at $\mathrm{\Gamma }$ and one electron pocket at $X$. (c) Band structure of LaBi in the high-pressure PT structure with a small electron pocket at $X$, a larger hole pocket at $M$, and a gap with band inversion at $R$.

Figure 5

(a) $T_c$ and $H_{c2}$ of LaBi as a function of pressure. Superconductivity onsets at $P\approx 3.5$ GPa, then $T_c$ shows enhancement at the structural transition at $P\approx 11$ GPa. The onset of superconductivity is shown by a black dashed line and the onset of structural transition is shown by a dotted blue line. (b) $R_{10\mathrm{K}}/R_{300\mathrm{K}}$ plotted as a function of pressure in LaBi. At the structural transition ($P=11$ GPa), $R_{10\mathrm{K}}/R_{300\mathrm{K}}$ reverses direction from decreasing to increasing. (c) The zero-temperature limit of the Hall coefficient $R_H$ as a function of pressure showing a sign change as XMR disappears and superconductivity appears. $R_H\to 0$ after the structural transition. (d) The ratio $H_{c2}/T_c$ plotted as a function of pressure shows a sudden twofold drop across the structural transition.

Figure 6

(a) Normalized electrical resistance at $H=0$ T, from $T=2$ to 300 K, at several pressures below 11 GPa before the structural transition. (b) Normalized electrical resistance at $H=0$ T, from $T=2$ to 300 K, at several pressures above 11 GPa after the structural transition. (c) Hall coefficient as a function of temperature for several representative pressures. Note the sign change in $R_H(T=0)$ with increasing pressure. (d) Normalized resistivity curves in the region of superconducting transition from which the phase diagrams in Figs. 1 and 5 are constructed. The arrow on the 10.6 GPa curve shows that we define $T_c$ using $R=0$ criterion.

Figure 7

(a) Normalized electrical resistance at $P=5.6$ GPa plotted as a function of temperature in several magnetic fields as indicated on the figure. (b) Normalized electrical resistance at $P=17.9$ GPa plotted as a function of temperature in several magnetic fields. (c) $H_{c2}=11.5$ T is extracted by fitting Eq. (2) to the $H-T$ data at $P=5.6$. (d) $H_{c2}=6.1$ T is extracted by fitting Eq. (2) to the $H-T$ data at $P=17.9$.

Figure 8

$T_c$ plotted as a function of pressure in LaBi (red), La (green) and Bi (blue). Data points for La come from Ref. [39]. and [40]. Data points for Bi come from Ref. [41]. and [42]. Superconductivity in La starts from $P=0$ and shows a dome-like structure with $T_c$ that is 4 to 6 K higher than LaBi at all pressures. Therefore, superconductivity from La impurity is not likely. Superconductivity in Bi starts from $P=2.5$ GPa with $T_c=4$ K and shows a profile close to that of LaBi.

Figure 9

Representative refinement of the x-ray diffraction patterns collected at (a) $P=7$ GPa and (b) $P=21$ GPa. Empty circles show the XRD data plotted as intensity versus $2\mathrm{\Theta }$. Black lines are the best fit to the data. Blue lines show the difference between the data and the fits. Cu (pressure gauge) and Ne (pressure transmitting medium) peaks are indexed individually.

Figure 10

(a) Band structure of LaBi at $P=0$ in the fcc structure. The large circles represent the $p$ orbitals of Bi and the small circles represent the $d$ orbitals of La. The $y$ axis is energy relative to $E_F$ with the $E_F$ given on top of each panel. The corresponding Fermi surface is rendered next to the plot. (b) Band structure of LaBi at $P=3.0$ GPa. Notice that the electron pocket shrinks in size and its shape changes from cylindrical to round. The corresponding Fermi surface is rendered next to the plot. (c) Band structure of LaBi at $P=8.8$ GPa. The electron pocket continues to shrink and become more spherical. Notice that the Fermi energy $E_F$ increases with increasing pressure and makes the material less compensated. The corresponding Fermi surface is rendered next to the plot. (d) Band structure of LaBi at $P=16.6$ GPa in the PT structure after the structural transition. This calculation is without spin-orbit coupling to show the mixing between the bands at $R$. (e) After including SOC, the bands hybridize and a gap opens at $R$ with a clear band inversion. (f) Band structure of LaBi at $P=32.9$ GPa in the PT structure. Pressure does not change the band structure that much in this phase.

Figure 11

Superconducting transition from magnetic susceptibility at $P=4.5$, 5, 6, and 7.8 GPa evidence for the bulk transition in LaBi under pressure. Full circles show data points and solid lines show $d\chi /dT$. $T_c$ is defined as the peak in the derivative curves. The error in $T_c$ is estimated from the FWHM in the peak. Magnetization was measured at $H=25$ Oe.