Quantum Oscillation Signatures of Pressure-induced Topological Phase Transition in BiTeI

Abstract We report the pressure-induced topological quantum phase transition of BiTeI single crystals using Shubnikov-de Haas oscillations of bulk Fermi surfaces. The sizes of the inner and the outer FSs of the Rashba-split bands exhibit opposite pressure dependence up to P = 3.35 GPa, indicating pressure-tunable Rashba effect. Above a critical pressure P ~ 2 GPa, the Shubnikov-de Haas frequency for the inner Fermi surface increases unusually with pressure, and the Shubnikov-de Haas oscillations for the outer Fermi surface shows an abrupt phase shift. In comparison with band structure calculations, we find that these unusual behaviors originate from the Fermi surface shape change due to pressure-induced band inversion. These results clearly demonstrate that the topological quantum phase transition is intimately tied to the shape of bulk Fermi surfaces enclosing the time-reversal invariant momenta with band inversion. Introduction Topological quantum phase transition (TQPT) is a zero temperature transition between distinct topological phases. Unlike conventional phases of matter classified by symmetry breaking1, topological phases are defined by topological invariants reflecting a “twist” of bulk electronic wave functions in the presence of an energy gap2. When the TQPT occurs by tuning an external parameter like pressure3 or chemical composition4,5, there should be band-gap closing at some points in the Brillouin zone (BZ). At the TQPT, therefore, low energy excitations are described by various types of Dirac dispersions6,7, offering a fertile ground to test quantum critical phenomena of unconventional relativistic fermions8,9,10,11. In this respect, the pressure-induced TQPT is of particular interest. Applying pressure provides a continuous and reversible means to tune electronic structures, which has been widely employed to access closely to the quantum critical point12,13,14. Under pressure, however, the surface-sensitive probes like angle-resolved photoemission spectroscopy cannot be used for detecting the topological surface states as a direct evidence of the TQPT4,5. Hence experimental identification of the pressure-induced TQPT has remained a challenge so far. A noncentrosymmetric BiTeI is one of the most interesting candidate systems harboring the pressure-induced TQPT3,15,16,17. For the systems with broken inversion symmetry18,19, low energy excitations at the TQPT are predicted to be a semi-Dirac type, having quadratic dispersion in one direction and linear in the others6,7. Such intriguing electronic structures have indeed been proposed in a noncentrosymmetric BiTeI at high pressures by recent band structure calculations3. Experimental verification, however, remains highly controversial15,16,17. For example, recent optical spectroscopy studies on BiTeI have drawn contradictory conclusions, i.e. presence15 or absence16 of the TQPT at high pressures. Recent studies on pressure-dependent quantum oscillations were also not sufficient to identify the pressure-induced TQPT20,21, because of the small pressure range, that doesn’t cover the critical pressure20 or because of coarse-tuning of pressure that missed the critical pressure21. In this paper, we provide experimental evidence of the pressure-induced TQPT in BiTeI by monitoring the Rashba-split bulk FS using magnetic quantum oscillations. From systematic change in Shubnikov de-Haas (SdH) oscillations with pressure up to P = 3.35 GPa, we found that the SdH frequency for the inner FS starts to increase unusually with pressure at the critical pressure of Pc ~ 2 GPa. At the same pressure, the SdH oscillations for the outer FS show an abrupt phase shift. Comparison with band structure calculations reveals that these unusual behaviors arise from the FS shape change due to pressure-induced band inversion across the TQPT. These findings confirm the TQPT in BiTeI at high pressures, and demonstrate that quantum oscillations can provide an effective probe for detecting the pressure-induced TQPT in other candidate systems22,23,24. Results The temperature dependence of the in-plane resistivity (ρxx) at zero magnetic field exhibits a systematic decrease in the whole temperature range with increasing pressure. The absolute value of ρxx at T = 5 K begins to saturate above P ~ 2 GPa as shown in the inset of Fig. 1(a). This pressure coincides with the one showing the maximum of the spectral weight of free carriers in a recent optical spectroscopy measurement15. The in-plane resistivity ρxx under magnetic fields along the c-axis also exhibits systematic changes with pressure as shown in Fig. 1(b). Clear SdH oscillations with two distinct frequencies are observed. The well-separated oscillations are due to large difference in size between the inner Fermi surface (IFS) and the outer Fermi surface (OFS) of the Rashba bands25,26. Figure 1 (a) Temperature dependence of the in-plane resistivity (ρxx) at various pressures from ambient pressure to P = 2.92 GPa. (b) The magnetoresistance for H//c taken at different pressures from P = 0.77 GPa to P = 3.35 GPa. Full size image Figure 2(a,b) show the background-subtracted SdH oscillations as a function of inverse magnetic fields for both IFS and OFS. They are well reproduced by fitting to the Lifshits-Kosevich formula with a single frequency as plotted together in Fig. 2. The resistive peak corresponding to the Landau level n = 2 for the IFS shifts to higher magnetic fields, while the peak at n = 20 for the OFS shifts to lower magnetic fields. Accordingly, the size of the IFS increases, while the OFS shrinks with pressure. This is also confirmed by the fast fourier transform (FFT) as shown in Fig. 2(c,d). From the Onsager relation F = (Φ0/2π2)SF, where Φ0 is the flux quantum and SF the Fermi surface size27, we found that the size of the IFS (SFIFS) increases by 330% up to P ~ 3 GPa. For the same pressure range, the size of the OFS (SFOFS) decreases only by 12%. Figure 2: Shubnikov-de Haas oscillations as a function of inverse magnetic field taken at different pressures for (a) the inner Fermi surface and (b) the outer Fermi surface. The background subtracted data were shifted in the y-axis for clarity. The fitted curves using the Lifshits-Kosevich formula are presented with grey lines in both (a,b). The fast fourier transform of the SdH oscillations from the (c) inner and (d) outer Fermi surfaces. The schematic energy dispersion of Rashba split bands (α, the band index) at the A point of BZ and the corresponding Fermi surfaces are shown in the inset. Full size image The opposite pressure dependence of SFIFS and SFOFS is understood from the change of electronic structures upon pressure. As illustrated in Fig. 3(a), the Rashba-split bands from the Bi 6p and the Te 5p bands form the conduction and valence bands, respectively. With increasing pressure, the overlap of Bi pz (Te pz) states in the neighboring atoms increases. As a result the bandwidth of the conduction (...truncated)