Evidence of a Lifshitz transition in the high-pressure behavior of the intermetallic compound AuIn 2 B. K. Godwal, S. Meenakshi, P. Modak, R. S. Rao, S. K. Sikka, and V. Vijayakumar High Pressure Physics Division, Bhabha Atomic Research Center, Mumbai 400 085, India E. Bussetto and A. Lausi Sincrotrone Trieste, ss14, Science Park, 34012 Basovizza-Trieste, Italy Received 14 February 2002; published 4 April 2002 Accurate equation of state of AuIn 2 was obtained by x-ray diffraction measurements with ELETTRA synchrotron source to pressures over 20 GPa. Below 5 GPa, the P -V data when transformed to universal equation of state UEOS, shows a deviation from linearity, confirming an electronic transition, consistent with the anomaly observed earlier in fusion and electrical data. The present high-resolution data also reaffirm a structural phase transition beyond 9 GPa. Full potential electronic band-structure calculations reveal a Lifshitz transition at the observed anomaly in the UEOS. Its transition pressure was found to be sensitive to the exchange-correlation terms. DOI: 10.1103/PhysRevB.65.140101 PACS numbers: 62.50.+p, 61.66.Fn, 64.70.Kb, 82.40.Fp Predictions of phase transitions at high pressures and their confirmations using diamond anvil cell measurements have led to significant improvements in density-functional theo- ries for exchange-correlation potentials beyond the local- density approximation LDA. 1 The emphasis so far has been to generate simultaneously pressures of several megabars and temperatures of several thousands of degrees Kelvin to obtain physical conditions in the laboratory that mimic those existing in the mantle and core of the earth, in order to en- able studies on its constituent materials. 2 However, the mod- erate pressure region continues to remain exciting with the observations of certain phenomena and associated controver- sies in the data. 3,4 One of the most dramatic manifestations of subtle electronic structure changes brought about by pres- sure has been the exhibition of anomalies in the thermody- namic properties of materials. Some of these anomalies oc- cur due to the proximity of an energy band extremum Van Hove singularity to the Fermi level ( E F ), and its passage through E F as the pressure is varied, known as Lifshitz tran- sitions or electronic topological transition ETT. 5,6 There had been difficulties till the recent past in correlating them with experimental data due to the lack of controlled high- pressure experiments and precision in the pressure volume ( P -V ) measurements. 7 The availability of synchrotron sources and incorporation of an imaging plate area detector in the angle dispersive x-ray diffraction ADXRD technique have made it possible. 2 In the present work, we demonstrate an interesting interplay between state-of-the-art results of first-principles calculations and experimental data yielding evidence of a Lifshitz transition for an intermetallic, AuIn 2 . The significance of present investigations is in providing a method to identify an ETT. The traditional methods used for its detection in transport properties and superconducting transition temperature ( T c ) measurements are indirect, like when no other significant change is known to occur, the ob- served anomaly is attributed to an ETT. In the present work, we identify its presence experimentally from the equation of state measurements, which can be calculated from theory with more ease compared to T c and thermoelectric power TEP. This has been possible with the availability of intense synchrotron source that enables accurate measurements of diffraction data at small intervals of pressures. The com- pound AuIn 2 crystallizing in the calcium flourite (CaF 2 ) structure, 8 exhibits anomalies in various physical properties, such as variation with pressure of fusion temperature, TEP, and electronic and structural behaviors. Hence it serves as an excellent prototype to demonstrate the interesting interplay between theory and experiment for high-pressure investiga- tion. Also, as several oxides of geophysical interest occur in CaF 2 structure, phase transformation studies under compres- sion on intermetallic compounds in this structure are useful in providing information concerning the high-pressure metal- lic phases of these oxides. Whereas most of the current elec- tronic structure calculations related to geophysical materials are being carried out at 0 K, the finite temperature effects have been included in the present work. It is possible to extend these to higher temperatures, a case in which the tem- perature corrections, such as the entropy effects would be more significant. These temperature effects are important since most of the phenomena of geophysical interest exist at high temperatures. For example, another structure was ob- served in iron in the pressure range 44 –100 GPa between 2100 and 2300 K, whereas the related electronic structure calculations were carried out at 0 K. 2,4 Also, most of the studies related to geophysical materials focus on structural transitions only, and the electronic transitions, like ETT, are usually not investigated. The present work highlights the fact that such transitions could also be equally important leading to anomalies in physical properties, and can be relevant to geophysical modeling. Further the applicability of the present method to detect ETT is not limited to AuIn 2 but is quite general. With the availability of very high pressure to which variety of materials can be subjected, it will be pos- sible to detect ETT in them. Storm et al. 9 studied the fusion behavior of the interme- tallic compound AuIn 2 up to a pressure of 5 GPa, and found RAPID COMMUNICATIONS PHYSICAL REVIEW B, VOLUME 65, 140101R 0163-1829/2002/6514/1401014/$20.00 ©2002 The American Physical Society 65 140101-1