We report transport studies on a three dimensional, 70 nm thick HgTe layer, which is strained by epitaxial growth on a CdTe substrate. The strain induces a band gap in the otherwise semimetallic HgTe, which thus becomes a three dimensional topological insulator. Contributions from residual bulk carriers to the transport properties of the gapped HgTe layer are negligible at mK temperatures. As a result, the sample exhibits a quantized Hall effect that results from the 2D single cone Dirac-like topological surface states. PACS numbers:The discovery of two (2D) and three dimensional (3D) topological insulators (TI)1-10 has generated strong activity in the condensed matter physics community 11,12 . Current research on 3D TIs is mostly focused on Bi 2 Te 3 , Bi 2 Se 3 and Sb 2 Te 3 compounds 8-10 due to their simple Dirac-like surface states, which have been observed by angle resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy 11 . However, these compounds show strong defect doping and low carrier mobility, and the observation of surface charge transport is obscured by the bulk conductivity. Many of the predicted novel properties of a 3D TI, such as the quantized magneto-electric effect 13,14 and the surface Majorana fermions 15 , can only be observed when bulk carriers are negligible compared to the surface states. Experimentally reaching the intrinsic TI regime, where bulk carriers are absent, is now the central focus of the field.The two dimensional TI state was first predicted and observed in 2D HgTe quantum wells (QW) 1,3 , and non-local transport measurements demonstrate edge state transport without any contributions from 2D bulk carriers.16 3D HgTe is a semi-metal which is charge-neutral when the Fermi energy is at the touching point between the light-hole and heavy-hole Γ 8 bands at the Brillouin zone center. A unique property of the band structure of HgTe is the energetic inversion of the Γ 6 and Γ 8 band ordering, which is the origin of the quantum spin Hall effect in 2D HgTe/CdTe QWs 3 . Due to the band inversion, 3D HgTe is also expected to have Dirac-like surface states 17,18 , but since the material is semi-metallic, this state is always coupled to metallic bulk states. With applied strain, a gap opens up between the light-hole and heavy-hole bands, so that strained 3D HgTe is expected to be a 3D TI 4,19 . In this paper we demonstrate experimentally that a gap opens up in in-plane strained 3D HgTe bulk layers grown by molecular beam epitaxy (MBE), and we reach the much sought after intrinsic TI regime in a material with negligible bulk carriers. In this regime, the Hall effect of the 3D HgTe bulk layer is quantized, due to the contributions from the surface states only. Theoretical considerations are in agreement with the experimental results and confirm the transport through 2D surface states with Dirac type dispersion.HgTe bulk samples have been grown by MBE on CdTe subtrates, which have a lattice constant that is 0.3 % larger than that of bulk HgTe (0.646 nm). At this mismat...

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