Fig. 3: Pressure and magnetic field tuning of CeRu4Sn6.
From: Emergent topological semimetal from quantum criticality
a, Spontaneous Hall resistivity \({\rho }_{xy}^{{\rm{spont}}}\) as a function of temperature for different pressures p, showing the suppression of the onset temperature TH with increasing p. The 1-bar curve was measured after recontacting the sample (Supplementary Discussion 2), once with the same setup as the measurements under pressure (open symbols) and once using low-temperature transformers for higher resolution (full symbols). Above 15 kbar, the background subtraction via αRxx introduces a sizable error due to the steep increase in Rxx(T) at the lowest temperatures (Supplementary Discussion 4; strongly affected parts of the curves are shown with open symbols). \({\sigma }_{xy}^{{\rm{spont}}}(T)\) is less sensitive to the Rxx background and is almost fully suppressed at 18.2 kbar (Supplementary Discussion 2). b, Electronic specific heat coefficient Cel/T versus T, scaled to the low-temperature ambient pressure data from Fig. 1d (black diamonds), for different pressures obtained via a.c. calorimetry (Supplementary Discussion 3 provides details on the measurement technique and the determination of the phonon contribution). The solid lines are phenomenological fits describing a crossover between the NFL behaviour and a contribution from linearly dispersing Weyl bands (Supplementary Discussion 3). Note that this ‘anomaly’ cannot be attributed to a nuclear Schottky contribution (Supplementary Discussion 3). c, Pressure-dependent Weyl velocity vWeyl normalized to its maximum value \({\nu}_{{\rm{Weyl}}}^{{\rm{max}}}\). It was calculated from the Weyl contribution obtained from the fits in b (Supplementary Discussion 3). The increase in vWeyl and the overall suppression of Cel with pressure indicate that pressure tunes the system away from the QCP. The error bars represent the largest standard error obtained from the fits of the different isobars. The grey line is a guide for the eyes. d,e, As expected for the finite-field extension of the spontaneous Hall effect, the magnetic-field-dependent Hall resistivity ρxy(B) can be split into an even-in-field component \({\rho }_{xy}^{{\rm{even}}}\) (d) and an odd-in-field component \({\rho }_{xy}^{{\rm{odd}}}\) (e) (Supplementary Discussion 2). \({\rho }_{xy}^{{\rm{even}}}\) is suppressed with increasing T and B. f, The even-in-field Hall component \({\rho }_{xy}^{{\rm{even}}}(B)\) persists even up to the highest pressure of 24 kbar reached in these experiments, where the detection of the zero-field spontaneous Hall effect was no longer possible due to the rapid increase in ρxx(T) in the relevant temperature range. Also here, the onset field \({B}_{{\rm{H}}}^{{\rm{even}}}\) is suppressed with increasing p, in agreement with the suppression of TH presented in a.
