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Strained Hgte: a Textbook 3D Topological Insulator Cl´Ement Bouvier, Tristan Meunier, Philippe Ballet, Xavier Baudry, Roman Kramer, Laurent L´Evy

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Strained Hgte: a Textbook 3D Topological Insulator Cl´Ement Bouvier, Tristan Meunier, Philippe Ballet, Xavier Baudry, Roman Kramer, Laurent L´Evy View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by HAL-CEA Strained HgTe: a textbook 3D topological insulator Cl´ement Bouvier, Tristan Meunier, Philippe Ballet, Xavier Baudry, Roman Kramer, Laurent L´evy To cite this version: Cl´ement Bouvier, Tristan Meunier, Philippe Ballet, Xavier Baudry, Roman Kramer, et al.. Strained HgTe: a textbook 3D topological insulator. 2011. <hal-00650046> HAL Id: hal-00650046 https://hal.archives-ouvertes.fr/hal-00650046 Submitted on 9 Dec 2011 HAL is a multi-disciplinary open access L'archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destin´eeau d´ep^otet `ala diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publi´esou non, lished or not. The documents may come from ´emanant des ´etablissements d'enseignement et de teaching and research institutions in France or recherche fran¸caisou ´etrangers,des laboratoires abroad, or from public or private research centers. publics ou priv´es. HgTe-low-field Strained HgTe: a textbook 3D topological insulator Cl´ement Bouvier, Tristan Meunier, Roman Kramer, and Laurent P. L´evy Institut N´eel, C.N.R.S.- Universit´eJoseph Fourier, BP 166, 38042 Grenoble Cedex 9, France Xavier Baudry and Philippe Ballet CEA, LETI, MINATEC Campus, DOPT, 17 rue des martyrs 38054 Grenoble Cedex 9, France (Dated: December 9, 2011) Topological insulators can be seen as band-insulators with a conducting surface. The surface carriers are Dirac particles with an energy which increases linearly with momentum. This confers extraordinary transport properties characteristic of Dirac matter, a class of materials which elec- tronic properties are “graphene-like”. We show how HgTe, a material known to exhibit 2D spin-Hall effect in thin quantum wells,[1] can be turned into a textbook example of Dirac matter by opening a strain-gap by exploiting the lattice mismatch on CdTe-based substrates. The evidence for Dirac matter found in transport shows up as a divergent Hall angle at low field when the chemical potential coincides with the Dirac point and from the sign of the quantum correction to the conductivity. The material can be engineered at will and is clean (good mobility) and there is little bulk contributions to the conductivity inside the band-gap. PACS numbers: 85.25.Cp, 03.65.Vf, 74.50.+r, 74.78.Na Graphene research[2, 3] has stimulated a consider- holes bands is estimated to be of order 11 meV while able interest on Dirac matter, a novel class of materi- the indirect gap has been measured by thermal activa- als where one or more bands have a Dirac-like disper- tion transport to be ≈6 meV [supplementary material- sion in the vicinity of the Fermi level. Newly discovered a]. The Γ8 and Γ6 bands have a linear crossing[7] at materials show that Dirac matter can take a variety of the HgTe/Hg0.3Cd0.7Te interface (different symmetries) forms. For example, angle-resolved photo-emission ex- leading to 2D-“relativistic-like” surface bands which periments have measured bands with a linear spectrum band velocity c plays the role of the speed of light. below the Fermi level in topological insulators surface These surface states are one of the manifestations of states[4], in organic conductors[5] and of course graphene the non-trivial topology of HgTe[10]. The dispersion stacks[6] with an odd number of layers. Transport ex- of surface state in a strained material have been an- periments give smoking-gun evidences for Dirac fermions alyzed qualitatively from the surface local density of in graphene. For organic-conductors and topological- states[11] and in recent transport and magneto-optical insulators, other contributions make transport data more experiments[12, 13]. Nevertheless quantitative data is difficult to unravel. This letter presents textbook evi- not yet available for our stack structure: it is however dences of Dirac fermions in a strained Mercury Telluride relatively simple to infer the surface band and the Dirac stack, using the low field magneto-transport behavior of point positions by scanning the gate within the gap in a gated device. transport measurements. A 200 µm long by 50 µm wide six-probes gated device Mercury (HgTe) and Cadmium (CdTe) Telluride have has been made by etching the stack and contacting the the same zinc-blende structure.[7] However compared to top surface. The accessible range of gate voltages allows CdTe, HgTe has a band inversion at the Γ point: the scanning part of the heavy-hole band (below V ≈ 0.8 V) Γ bands which have a P character lie 0.3 eV above g0 8 and the gap region (V between 1 and 6 V). An overview the Γ band (S character). When growing epitaxially g 6 of the sample resistivity is shown in Fig.1. The resistiv- HgTe on top of CdTe, the HgTe lattice constant ex- ity is lowest (→ 1.2 kΩ at 6V) in the gap area where pands to match the CdTe lattice, which applies a lat- the surface conduction dominates the transport. In the eral strain to HgTe. As long as the HgTe thickness does “hole region” (below 1 V), there is a co-existence between not exceed a critical value above which dislocations ap- surface and bulk hole conduction. The mobility of heavy pear, the strain is homogenous through the material.[7] holes is low (large mass and short mean free path) lead- A number of papers[10] have pointed out that such ing to a higher resistivity (≈ 4 kΩ) below 1 V in spite of strain opens a gap between the Γ light and heavy 8 the higher carrier density. hole bands, turning HgTe into a topological insulator.[8] The value of this gap can be engineered to some ex- The hole and electron character of the conduction can tend in the epitaxial growth. In this work, a sym- be read-off directly from the Hall conductivity plot shown metric Hg0.3Cd0.7Te/HgTe/Hg0.3Cd0.7Te stack (shown in Fig.3-top panel, where the slope at B=0 is negative in the inset of Fig. 1) was epitaxially grown on a CdTe at negative gate voltages and positive above Vg0. Note [211] face. The direct gap between light and heavy also that the Hall slope gets larger as Vg0 is approached 2 5 k gate SS a-CdTe gate insulator 4 200nm Hg Cd Te .7 .3 30nm HgTe ) HgTe ε 100nm Ω Hg Cd Te CdTe .7 .3 HH (k 3 30nm Γ8 CdTe xx ρ SS LH Γ8 2 T=1.5 K k 0.3 1 T=1.5K -2 -1 0 1 2 3 4 5 6 0.2 Vg )/B FIG. 1: Inset: the 100nm thick HgTe slab is sandwiched be- Hall 0.1 θ tween two 30nm thick Hg0.3Cd0.7Te barriers. A 200 nm thick amorphous CdTe layer on top serves as a gate insulator. Gate- tan( ≈ voltage dependence of the resistivity. Vg0 1V separates 0.0 the electron and hole transport regimes: Above Vg0 trans- Dirac part. µ port is dominated by the surfaces while a coexistence with D low-mobility heavy holes increases the resistivity below Vg0 -0.1 -2 0 2 4 6 8 V g (V) from below or from above. These observations suggest FIG. 2: Bottom: plot of the Hall angle slope as a function an analysis of the magneto-transport using a two-fluid of the gate voltage. An asymmetric cutt-off divergence is model: a surface contribution with a Dirac-like character observed on each side of Vg0 consistent the expected mag- and a bulk contribution. netoconductance of Dirac particles. Vg0 is interpreted as the The Lorentz force affects the motion of a relativistic location of the Dirac point (µD) in gate voltage. The observed charged particle with energy ǫ(k) = ~c|k| and momen- asymmetry is attributed to a difference in diffusion coefficients on the electron (Vg > Vg0) and the hole side where the bulk tum ~k in a similar fashion as for a massive charged car- heavy hole band starts to be populated. Top: putting to- dk ec ˆ rier: the semiclassical equation of motion dt = − ~ k ×B gether the analysis of the magneto-transport and activation describes a cyclotron motion with angular frequency data, the inferred positions of the heavy (HH) and light (LH) 2 Ω = eBc which diverges at the Dirac point ǫ(k) → 0. In hole bands with respect to the surface states (SS) connecting c ǫ(k) them. The position of the Dirac point (Vg0 = 0.8V) can also the presence of the electric field Exˆ induced by the bias be verified by extrapolating the observed n = 0 quantum Hall voltage and of particle collisions (specified by the scat- state to zero magnetic field[14].) tering time τ), the average particle velocity v = ckˆ drifts at an angle ΘHall with respect to the electric field ticles because of their low mobilities. By contrast, the σxy vy 2eD B electron side of the Dirac dispersion lies inside the strain- tanΘHall = = =Ωcτ = B = , (1) σxx vx µ B∗ induced Γ8 light-heavy holes gap. The observation of this divergent Hall angle, very similar to graphene[15], where the particle energy has been replaced by the chemi- is a strong evidence for Dirac particles at the HgTe sur- cal potential µ, D = c2τ/2 is the Dirac particles diffusion faces. A bulk hole conductivity σ0(Vg ) appears below coefficient, and the characteristic field B∗ = µ/(2eD) is V , which is nearly field independent at low (¡1 T) field proportional to the chemical potential.
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