Dirac fermions have been studied intensively in condensed matter physics in recent years. Many theoretical predictions critically depend on the number of valleys where the Dirac fermions are realized. In this work, we report the discovery of a two dimensional system with a single valley Dirac cone. We study the transport properties of HgTe quantum wells grown at the critical thickness separating between the topologically trivial and the quantum spin Hall phases. At high magnetic fields, the quantized Hall plateaus demonstrate the presence of a single valley Dirac point in this system. In addition, we clearly observe the linear dispersion of the zero mode spin levels. Also the conductivity at the Dirac point and its temperature dependence can be understood from single valley Dirac fermion physics.
We develop a microscopic theory of the fine structure of Dirac states in $(0lh)$-grown HgTe/CdHgTe quantum wells (QWs), where $l$ and $h$ are the Miller indices. It is shown that bulk, interface, and structure inversion asymmetry causes the anticrossing of levels even at zero in-plane wave vector and lifts the Dirac state degeneracy. In the QWs of critical thickness, the two-fold degenerate Dirac cone gets split into non-degenerate Weyl cones. The splitting and the Weyl point positions dramatically depend on the QW crystallographic orientation. We calculate the splitting parameters related to …
We study transport properties of HgTe quantum wells with critical well thickness, where the band gap is closed, and the low energy spectrum is described by a single Dirac cone. In this work, we examined both macroscopic and micron-sized (mesocopic) samples. In micron-sized samples, we observe a magnetic field induced, quantized resistance ($\sim h/2e^{2}$) at Landau filling factor $ν=0$, corresponding to the formation of helical edge states centered at the charge neutrality point (CNP). In macroscopic samples, the resistance near zero Landau level (LL) reveals strong oscillations, which we att…
Topological insulators represent a new quantum state of matter which is characterized by edge or surface states and an insulating band gap in the bulk. In a two dimensional (2D) system based on the HgTe quantum well (QW) of critical width random deviations of the well width from its average value result in local crossovers from zero gap 2D Dirac fermion system to either the 2D topological insulator or the ordinary insulator, forming a complicated in-plane network of helical channels along the zero-gap lines. We have studied experimentally the transport properties of the critical width HgTe qua…
Preceded by the discovery of topological insulators, Dirac and Weyl semimetals have become a pivotal direction of research in contemporary condensed matter physics. While easily accessible from a theoretical viewpoint, these topological semimetals pose a serious challenge in terms of experimental synthesis and analysis to allow for their unambiguous identification. In this work, we report on detailed transport experiments on compressively strained HgTe. Due to the superior sample quality in comparison to other topological semimetallic materials, this enables us to resolve the interplay of topo…
Valence band in narrow HgTe quantum wells contains well-conductive Dirac-like light holes at the $Γ$ point and poorly conductive heavy hole subband located in the local valleys. Here we propose and employ two methods to measure the density of states for these heavy holes. The first method uses a gate-recharging technique to measure thermodynamical entropy per particle. As the Fermi level is tuned with gate voltage from light to heavy subband, the entropy increases dramatically, and the value of this increase gives an estimate for the density of states. The second method determines the density …
We theoretically study the thermoelectric transport properties of strained HgTe in the topological insulator phase. We developed a model for the system using a Dirac Hamiltonian including the effect of strain induced by the interface between HgTe and the CdTe substrate. The conductivity tensor was explored assuming the electrons are scattered by charge impurities, while the thermopower tensor was addressed using the Mott relation. Seebeck and Nernst responses exhibit remarkable enhancements in comparison with other two-dimensional Dirac materials, such as graphene, germanane, prosphorene and s…
We review low and high field magnetotransport in 80 nm-thick strained HgTe, a material that belongs to the class of strong three-dimensional topological insulators. Utilizing a top gate, the Fermi level can be tuned from the valence band via the Dirac surface states into the conduction band and allows studying Landau quantization in situations where different species of charge carriers contribute to magnetotransport. Landau fan charts, mapping the conductivity $ σ_{xx}(V_g, B) $ in the whole magnetic field - gate voltage range, can be divided into six areas, depending on the state of the parti…
The most interesting experimental results obtained in studies of 2D and 3D topological insulators (TIs) based on HgTe quantum wells and films are reviewed. In the case of 2D TIs, these include the observation of nonlocal ballistic and diffusion transport, the magnetic breakdown of 2D TIs, and an anomalous temperature dependence of edge-channel resistance. In 3D TIs, a record-setting high mobility of surface two-dimensional Dirac fermions (DFs) has been attained. This enabled determining all the main TI parameters (the bulk gap and the density of DFs on both of its surfaces) and provided inform…
It is well established that topological insulators sustain Dirac fermion surface states as a consequence of band inversion in the bulk. These states have a helical spin polarization and a linear dispersion with large Fermi velocity. In this article we report on a set of experimental observations indicating the existence of massive surface states. These states are confined at the interface and dominate equilibrium and transport properties at high energy and/or high electric field. By monitoring the AC admittance of HgTe topological insulator field-effect capacitors, we access the compressibilit…
Enhanced circular photogalvanic effect in HgTe quantum wells in the heavily inverted regime
由于HgTe基量子阱具有很强的自旋-轨道相互作用（SOI），因此表现出非常丰富的自旋相关性质。但由于窄禁带能带结构的强带间耦合，对它们的完整描述超出了简单的抛物线能带模型和传统的Rashba和Dresselhaus SOI项。本文基于密度矩阵的八带$\mathbf{k}\cdot\mathbf{p}$模型，建立了计算$_{0.3}$ Cd $_{0.7}$ Te/HgTe/$_{0.3}$ Cd $_{0.7}$ Te量子阱（HgTe QWs）中圆形光电流效应的理论方法.我们的方法考虑了HgTe量子阱的特殊能带结构和SOI，因此可以用来计算具有非抛物、类Dirac和反向色散的HgTe量子阱中的CPGE电流.本文还探讨了CPGE的微观成因以及结构反转不对称性（SIA）和体反转不对称性（BIA）的相互作用。此外，将该方法推广到线偏振光垂直入射碲化汞量子阱中的纯自旋电流的研究。我们的计算结果支持了以下发现：（i）在反相区，重反HgTe量子阱的能量色散会发生强烈的畸变，导致在一定能谱范围内CPGE的显著增强。(ii)SIA和BIA的相互作用可以导致CPGE电流各向异性地依赖于斜入射光的方位角。(iii)[110]线偏振光产生的PSC $j_{y'}^{x'}$（$x'\parallel[110]$和$y'\parallel[\bar{1}10]$）随HgTe量子阱由正相转变为反相而改变符号…
Bilayer Heisenberg ferromagnetic insulators hold degenerate terahertz Dirac magnon modes associated with two opposite valleys of the hexagonal Brillouin zone. We show that this energy degeneracy can be removed by breaking of the inversion symmetry (I), leading to a topological magnon valley current. We show furthermore that this current leads to valley Seebeck effect for magnons and is thereby detectable. We perform calculations in the specific example of bilayer CrBr3, where I can be broken by electrostatic doping.
HgTe quantum wells with a thickness of ${\sim}$7 nm may have a graphene-like band structure and have been recently proposed to be potential candidates for quantum Hall effect (QHE) resistance standards under the condition of operation in the fields above certain critical field $B_c$, above which the topological phase (with parasitic edge conduction) disappears. We present experimental studies of the magnetoresistance of different of HgTe quantum wells as a function temperature and magnetic field, determining the critical magnetic field $B_c$. We demonstrate that for QWs of specific width $B_c$…
Graphene on hexagonal boron nitride (hBN) can exhibit a topological phase via mutual crystallographic alignment. Recent measurements of nonlocal resistance ($R_{nl}$) near the secondary Dirac point (SDP) in ballistic graphene/hBN superlattices have been interpreted as arising due to the quantum valley Hall state. We report hBN/graphene/hBN superlattices in which $R_{nl}$ at SDP is negligible, but below 60 K approaches the value of $h/2e^{2}$ in zero magnetic field at the primary Dirac point with a characteristic decay length of 2 $μ$m. Furthermore, nonlocal transport transmission probabilities…
We study massive Dirac fermion tunneling through time periodic potential in a silicene-based N-TP-N junction, where Ns are normal silicene regions and TP is the time periodic potential barrier. The fermions would absorb or emit photons due to the presence of the Floquet sidebands created in the TP. The nearly perfect spin-valley-sideband filtering is predicted. Applying only the exchange field leads to just only the electron absorbing a single photon almost purely allowed to tunnel through the junction for the large electric field. Reversing direction of electric field can select spin of the a…
The magnetotransport properties of massless Dirac fermions in a gapless HgTe quantum well are investigated. In samples with narrow channels, a large negative magnetoresistance with a Lorentzian profile is observed, which is interpreted as a manifestation of electron viscosity due to electron-electron interaction. Comparison of experiment with theory yields the shear stress relaxation time of the Dirac fermions caused by electron-electron scattering.
Angular momentum conversion between mechanical rotation and the valley degree of freedom in 2D Dirac materials is investigated theoretically. Coupling between the valley and vorticity of dynamic lattice distortions is derived by applying the k.p method to 2D Dirac materials with an inertial effect. Lattice strain effects are also incorporated. Valley transfer and valley-dependent carrier localization are predicted using the dynamic lattice distortions. The transport properties are found to be controllable, allowing the system to be insulating and to generate pulsed charge current. Our formalis…
We consider a lateral hetero-junction where the left and right leads are made of monolayer graphene and the middle region is made of a gapped tilted Dirac material (borophene or quinoid graphene) illuminated with off-resonant circularly polarized radiation. The tilt parameter $v_t$ makes the band gap indirect and smaller in magnitude as compared to Dirac materials without tilt. Exposure to radiation makes the band gaps of the central region valley-dependent which show their signatures as valley polarized charge and thermal currents, thereby causing a valley Seebeck effect. We study the variati…
Modifying the hexagonal lattices of graphene enables the repositioning and merging of the Dirac cones which proves to be a key element in the use of these materials for alternative electronic applications such as valleytronics. Here we study the nonequilibrium transport of carriers within a system containing two Dirac cones in both standard graphene and semi-Dirac graphene. In the latter, the lattice modifications cause the relativistic and parabolic dispersion bands to coexist, furnishing the Fermi surface with a rich pseudospin texture and a versatile Dirac cones separation. We construct a k…
We study the momentum alignment of photoexcited carriers and the optical control of valley population in gapless and gapped two-dimensional Dirac materials. The trigonal warping effect leads to the spatial separation of charge carriers belonging to different valleys upon linearly polarized high-frequency photoexcitation. Valley separation in gapped materials can be detected by measuring the degree of circular polarization of band-edge photoluminescence at different sides of the sample or light spot (optical valley Hall effect). We demonstrate that the celebrated Rashba effect, caused by substr…
