Massive and massless Dirac fermions in Pb1−xSnxTe topological crystalline insulator probed by magneto-optical absorption

Assaf, Badih A.; Phuphachong, Thanyanan; Volobuev, Valentine V.; Inhofer, A.; Bauer, G.; Springholz, G.; Vaulchier, L. A. de; Guldner, Y.

doi:10.1038/srep20323

Cited by 53 publications

(56 citation statements)

References 44 publications

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“…The fourfold bulk valley degeneracy combined with the mirror symmetric character of the rock-salt crystal structure of Pb 1-x Sn x Se and Pb 1-x Sn x Te yields a TCI state that hosts fourfold degenerate TSS. 5,15,24,[44][45][46][47][48][49] Despite this subtlety, the band structure and Landau levels of IV-VI semiconductors is ideal to study under the proposed scope, due to their relative simplicity 23,50 compared to other materials such as II-VI and V-VI systems that have highly asymmetric conduction and valence bands. It can actually be shown that a description similar to that of BHZ can be applied to describe the band structure of Pb 1-x Sn x Se and Pb 1-x Sn x Te.…”

Section: Resultsmentioning

confidence: 99%

“…This anisotropy in v D is small for Pb 1-x Sn x Se but rather large for Pb 1-x Sn x Te (Supplement (S3)). 23 The interband transitions in Figs. 3a, b can be well described using a massive Dirac-like Landau-level spectrum given in Eq.…”

Section: Resultsmentioning

confidence: 99%

“…Epilayers having a thickness >0.5 µm are proven to be fully relaxed by studying reciprocal space maps showing the (513) Bragg reflection. 23 From the peak positions, the lattice constant a 0 and Sn concentration of the ternary material can be directly obtained from Vegard's law (Fig. 2b).…”

Section: Resultsmentioning

confidence: 99%

“…Among all, in the Z 2 topological insulator (TI) class, the band inversion occurs at an odd number of time-reversal symmetric points 13,14 in the first Brillouin zone (BZ), whereas in topological crystalline insulators (TCI) it occurs at an even number of crystalline mirror symmetric points. 5,[15][16][17][18] Both the TI 8,[19][20][21][22] and TCI [15][16][17][23][24][25][26][27] states have been thoroughly studied experimentally. Moreover, the topological phase transition (Fig.…”

Section: Introductionmentioning

confidence: 99%

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Magnetooptical determination of a topological index

et al. 2017

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When a Dirac fermion system acquires an energy-gap, it is said to have either trivial (positive energy-gap) or non-trivial (negative energy-gap) topology, depending on the parity ordering of its conduction and valence bands. The non-trivial regime is identified by the presence of topological surface or edge-states dispersing in the energy gap of the bulk and is attributed a non-zero topological index. In this work, we show that such topological indices can be determined experimentally via an accurate measurement of the effective velocity of bulk massive Dirac fermions. We demonstrate this approach analytically starting from the Bernevig-HughesZhang Hamiltonian to show how the topological index depends on this velocity. We then experimentally extract the topological index in Pb 1-x Sn x Se and Pb 1-x Sn x Te using infrared magnetooptical Landau level spectroscopy. This approach is argued to be universal to all material classes that can be described by a Bernevig-Hughes-Zhang-like model and that host a topological phase transition.npj Quantum Materials (2017) 2:26 ; doi:10.1038/s41535-017-0028-5 INTRODUCTIONThe concept of band topology in condensed matter systems has revolutionized our understanding of quantum phases of matter.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Magnetooptical determination of a topological index

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“…We have shown that the LL in IV-IV TCIs can be well described by a massive Dirac spectrum that includes spin-splitting [24] [29] [30] [31], resulting from a 6-band k.p Hamiltonian. [30] If the contributions from the far-bands are neglected a 2-band k.p Hamiltonian results, the solution of which is an ideal massive Dirac model [32].…”

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confidence: 99%

Negative Longitudinal Magnetoresistance from the Anomalous N=0 Landau Level in Topological Materials

et al. 2017

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Negative longitudinal magnetoresistance (NLMR) is shown to occur in topological materials in the extreme quantum limit, when a magnetic field is applied parallel to the excitation current. We perform pulsed and DC field measurements on Pb1-xSnxSe epilayers where the topological state can be chemically tuned. The NLMR is observed in the topological state, but is suppressed and becomes positive when the system becomes trivial. In a topological material, the lowest N=0 conduction Landau level disperses down in energy as a function of increasing magnetic field, while the N=0 valence Landau level disperses upwards. This anomalous behavior is shown to be responsible for the observed NLMR. Our work provides an explanation of the outstanding question of NLMR in topological insulators and establishes this effect as a possible hallmark of bulk conduction in topological matter. [13]. This stems from the helical Dirac nature of surface-states in 3D TIs or, that of edge-states in 2D TIs. In fact, a huge amount of literature (for reviews [14] [15] [16] [17]) took interest in this question and investigated electronic transport of 2D Dirac electrons in 3D-TIs. The majority of these studies were, however, impeded by the significant and dominant bulk transport that occurs in TIs. On the other hand, little attention has been given to signatures of non-trivial band topology in 3D electron transport in a TI.Naively speaking, one can think of the bulk energy bands of a TI as being identical to those of conventional semiconductors and, thus, unlikely to generate non-conventional physical phenomena. However, one should not forget that the basis of a topological insulator lies in the inverted orbital character of these bulk energy bands. [23] shown, that the energy of the lowest (N=0) conduction (valence) Landau level in topological insulators decreases (increases) as a function of increasing magnetic field, opposite to what usually happens in a topologically trivial system ( Fig.1(a,b)). This behavior is anomalous and leads to a field-induced closure of the energy gap in a TI [21] (Fig.1(b)), whereas in a trivial material, the energy gap usually opens with increasing magnetic field ( Fig.1(a)). This anomaly is a hallmark of the inverted band structure of topological materials. Its implications on magnetotransport have not yet been considered. In the present work, we study the MR in topological insulators in the extreme quantum limit -the regime where only the lowest Landau level (LL) is occupied. We measure magnetotransport in pulsed magnetic field up to 61T in high mobility Pb1-xSnxSe epitaxial layers. We show that, when all Lorentz components contributing to the MR are suppressed by applying the magnetic field in-plane and parallel to the excitation current, a negative longitudinal MR (NLMR) emerges near the onset of the quantum limit. This NLMR is only observed in the topological regime of Pb1-xSnxSe (x>0.16) and is absent in trivial samples (x<0.16). We theoretically argue that this NLMR is a result of the anomalous beh...

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Giant Rashba Splitting in Pb_1–_xSn_xTe (111) Topological Crystalline Insulator Films Controlled by Bi Doping in the Bulk

et al. 2016

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to external perturbations. [10,15,16] Therefore, the trivial to nontrivial topological phase transition can be controlled by many different means, such as by varying temperature, [1,6] pressure, [2] hybridization in ultrathin film geometries, [17][18][19] magnetic interactions, [20] or by breaking of mirror symmetries by strain, [16,[21][22][23] electrostatic fields, [18] or ferroelectric (FE) lattice distortions. [24,25] This provides ample degrees of freedom for topology control not available in conventional Z 2 TIs. For this reason, TCIs offer an ideal template for observation of exotic phenomena such as partially flat band helical snake states and interfacial superconductivity, [16] large-Chern-number quantum anomalous Hall effect, [26] as well as for realization of novel topology-based devices such as topological photodetectors, [23] spin transistors, [18] and spin torque devices. [27] For most of such applications, thin film structures with precisely controlled composition and Fermi level are required. Up to now, most work has been performed on highly p-type bulk crystals exploiting the natural (001) cleavage plane of the IV-VI compounds, [3,4,6] whereas for other surface orientations and practical devices epitaxial TCI film structures are required. [18,[28][29][30][31][32] The (111) orientation is particularly interesting due to the polar nature of its surface [12] as well as the ease of lifting the fourfold valley degeneracy at the L-points of the Brillouin zone (BZ) [33] by opening a gap at particular Dirac points by strain [16] and quantum confinement [17][18][19] to induce a transition from a TCI to a normal Z 2 -TI material. [25]

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Massive and massless Dirac fermions in Pb1−xSnxTe topological crystalline insulator probed by magneto-optical absorption

Cited by 53 publications

References 44 publications

Magnetooptical determination of a topological index

Magnetooptical determination of a topological index

Negative Longitudinal Magnetoresistance from the Anomalous N=0 Landau Level in Topological Materials

Giant Rashba Splitting in Pb_1–_xSn_xTe (111) Topological Crystalline Insulator Films Controlled by Bi Doping in the Bulk

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Massive and massless Dirac fermions in Pb1−xSnxTe topological crystalline insulator probed by magneto-optical absorption

Cited by 53 publications

References 44 publications

Magnetooptical determination of a topological index

Magnetooptical determination of a topological index

Negative Longitudinal Magnetoresistance from the Anomalous N=0 Landau Level in Topological Materials

Giant Rashba Splitting in Pb1–xSnxTe (111) Topological Crystalline Insulator Films Controlled by Bi Doping in the Bulk

Contact Info

Product

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About

Giant Rashba Splitting in Pb_1–_xSn_xTe (111) Topological Crystalline Insulator Films Controlled by Bi Doping in the Bulk