ARPES study is the direct evidence for the topological insulating state. However, some of the trivial insulators can be transformed into non-trivial topological insulators by alloying, applying hydrostatic pressure or by applying strain in the quantum wells. Since ARPES can't be implemented at high pressure, high pressure XRD, high pressure Raman, high pressure electrical resistivity studies etc can be used to detect the changes during electronic topological transition (ETT) and topological quantum phase transition (TPQT). These signatures are only indirect evidences for either ETT or TPQT. In BiTeI, the TPQT signature is guessed by observing the behavior of P Vs FWHM of E2g phonon mode. Are there more evidences to distinguish between ETT and TPQT from high pressure XRD, Raman and electrical resistivity studies?.
In principle both type of transitions affect the 3D electronic structure.
An electronic topological transition (ETT) involves a drastic change in the topology of the Fermi surface (in metals or degenerate semiconductors) or in the VBM-CBM density of states (in non degenerate semiconductors). Changes induced by topological quantum phase transitions (TQPT) are more subtle, as they involve the topology of the wavefunction and their main effect (the emergence of a 2D Dirac electron system) affects only the material surface.
It seems doubtful that a TQPT can be detected through essentially bulk techniques like Raman effect or XRD. I would say that changes detected through these techniques are more likely to be a consequence of an ETT.
As regards transport measurements, they can certainly be used to detect an ETT because it affects all transport parameters. On the opposite in a TQPT, given that the transition from a trivial to a topological insulator state involves some type of bandgap closing, and then a very large 3D electron density, the contribution of the 2D Dirac electrons to charge transport will, most probably, be masked by the enormous contribution of 3D bulk electrons. This will happen both in standard DC transport or in free-carrier FTIR spectroscopy. To the best of my knowledge, the only transport technique that has been able to separate both contributions is Shubnikov-de-Haas effect in the extreme quantum regime, using magnetic fields up to 50T [Analytis et al., Nature Physics 6, 690 (2010)]
Dear sir,
Recently, extensive studies have been carried out on BiTeI (Eg=~0.38 eV, S.G: P3m1) in the view point of pressure induced topological insulating state. Please find the link.
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.155701
In the above article, the authors observed dual signatures of TPQT using both XRD studies and infrared spectrosopy under high pressure. At around 2-2.9 GPa, they noticed a minimum in their P Vs c/a ratio and also from the IR studies they observed maximum in the free-carrier spectral weight at the same pressure which reflect the closing and reopening of the semiconducting band gap. This observation was further supported by HPXRD studies along with first principle calculations. But the controversy over critical pressure was solved by SDH oscillations study under high pressure.Using SDH oscillations and transport measurements, the critical pressure for the quantum phase transition was observed near Pc = 3.5 GPa
[ PRB 90 161107(R) (2014)].
Similarly, the phonon mode anomaly in P Vs FWHM of Sb2Se3 is possibly due to TPQT, however more experimental evidences are required to prove this debate. The phonon life time is affected during TPQT, which will be reflected in P Vs FWHM.
So, what I am trying to say is that TPQT signatures can be probed using XRD, Raman and transport studies.
Dear Dr. Yesudhas, Thank you for sending the references on BiTeI.
Concerning the effects observed in the pressure dependence of the a/c ratio and the Raman peak width for BiTeI, virtually identical effects have also been observed for Bi2Se3 [PRB 84, 184110 (2011)] and Bi2Te3[PRB 83, 113106 (2011) and PRB 84, 104112 (2011)]. Those effects were attributed to an ETT occurring at around 3 GPa. Both semiconductors are topological insulators (TI) at ambient pressure and remain so up to 6-7 GPa. Then, at least for Bi2Se3 and Bi2Te3, those changes can hardly be attributed to a TQPT.
The case of BiTeI seems to be quite different because the band inversion associated to the TQPT involves a bandgap closing and a strong change in the band structure, that could also be interpreted as an ETT. It seems that in BiTeI both electronic transitions are closely correlated.
It seems also relevant to notice that Shubnikov-de-Haas results in [PRB 90 161107(R) (2014)] are used to investigate the Fermi surface of bulk 3D electrons in BiTeI. No mention to the surface 2D Dirac electron system (that should exist in the TI phase) seems to be done in the paper. Given the large 3D electron concentration in the bulk (larger that 10^19 cm^-3) the response of the 2D Dirac electrons is masked.
Dear Alfredo Segura sir,
In TPQT the band invertion is associated with a change in the sign of the product of the parities. That means the product of parities of the bulk primitive unit cell should be neagative, then only we can say that the system is undergoing TPQT. On the other hand, if the product of parities is positive, then the system is in the trivial insulating state. Is there any parity analysis is reported in ETT?
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