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Nikolay N. Mikhailov

Bio: Nikolay N. Mikhailov is an academic researcher from Russian Academy of Sciences. The author has contributed to research in topics: Quantum well & Molecular beam epitaxy. The author has an hindex of 23, co-authored 250 publications receiving 2099 citations. Previous affiliations of Nikolay N. Mikhailov include Tomsk State University & Novosibirsk State University.


Papers
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TL;DR: In this paper, a zinc-blende crystal, HgCdTe, at the point of the semiconductor-to-semimetal topological transition was studied.
Abstract: Solid-state physics and quantum electrodynamics, with its ultrarelativistic (massless) particles, meet in the electronic properties of one-dimensional carbon nanotubes, two-dimensional graphene or topological-insulator surfaces. However, clear experimental evidence for electronic states with a conical dispersion relation in all three dimensions, conceivable for certain bulk materials, is still missing. Here, we study a zinc-blende crystal, HgCdTe, at the point of the semiconductor-to-semimetal topological transition. For this compound, we observe three-dimensional massless electrons, as certified from the dynamical conductivity increasing linearly with the photon frequency, with a velocity of about 106 m s−1. Applying a magnetic field B results in a -dependence of dipole-active inter-Landau-level resonances and spin splitting of Landau levels also following a -dependence—well-established signatures of ultrarelativistic particles but until now not observed experimentally in any solid-state electronic system. Graphene and topological-insulator surfaces are well known for their two-dimensional conic electronic dispersion relation. Now three-dimensional hyperconic dispersion is shown for electrons in a HgCdTe crystal—once again bridging solid-state physics and quantum electrodynamics.

187 citations

Journal ArticleDOI
TL;DR: In this paper, a far-infrared magnetospectroscopy study of a set of HgTe/Cd quantum wells with different thicknesses from below to above the critical value was performed.
Abstract: Recently, a new class of materials, so-called topological insulators, has emerged. These are systems characterized by the inversion of the electronic band structure and also by a certain strength of the spin-orbit interaction. HgTe/Cd${}_{x}$Hg${}_{1\ensuremath{-}x}$Te quantum wells represent a prominent example. They can change to the topological insulator phase from the conventional insulator phase when the thickness of the quantum well is increased over the critical thickness ${d}_{c}$ = 6.3 nm. Here, we report on a far-infrared magnetospectroscopy study of a set of HgTe/Cd${}_{x}$Hg${}_{1\ensuremath{-}x}$Te quantum wells with different thicknesses from below to above the critical value ${d}_{c}$. In quantizing magnetic fields up to 16 T, both intraband and interband transitions have been clearly observed. In the widest quantum well with inverted band structure, we confirm the avoided crossing of the zero-mode Landau levels observed earlier in similar structures. In both noninverted quantum wells close to the critical thickness, we report unambiguously on the square root dependence of the transition energy on the magnetic field, as expected in the single-particle model of massless Dirac fermions. The obtained results are compared with the allowed transition energies between Landau levels in the valence and conduction bands calculated using the 8 \ifmmode\times\else\texttimes\fi{} 8 Kane model.

93 citations

Journal ArticleDOI
TL;DR: 2D, 1D, 2D and even 3D massless particles can be observed in topological phase transitions driven by intrinsic (quantum well thickness, Cd content) and external (magnetic field, temperature or pressure) physical parameters.
Abstract: Kane fermions are predicted to be tunable with external parameters such as temperature. Here, Teppe et al. show a band structure evolution of bulk HgCdTe as temperature is tuned across topological phase transition, demonstrating that Kane fermions change sign in rest-mass and remain constant in velocity.

77 citations

Journal ArticleDOI
TL;DR: A two-dimensional electron-hole system consisting of light highmobility electrons with a density of Ns = (4−7) × 1010 cm−2 and a mobility of μn = ( 4−6) × 105 cm2/V s and heavier low-mobility holes with density of Ps = (0.7−1.6)-1.
Abstract: A two-dimensional electron-hole system consisting of light high-mobility electrons with a density of Ns = (4–7) × 1010 cm−2 and a mobility of μn = (4–6) × 105 cm2/V s and heavier low-mobility holes with a density of Ps = (0.7–1.6) × 1011 cm−2 and a mobility of μp = (3–7) × 104 cm2/V s has been discovered in a quantum well based on mercury telluride with the (013) surface orientation. The system exhibits a number of specific magnetotransport properties in both the classical magnetotransport (positive magnetoresistance and alternating Hall effect) and the quantum Hall effect regime. These properties are associated with the coexistence of two-dimensional electrons and holes.

73 citations

Proceedings ArticleDOI
TL;DR: In this article, a new generation of ultra high vacuum set, ultra-fast ellipsometer of high accuracy and automatic system for reproducibility of MCT Hs's growth on substrates up to 4" in diameter.
Abstract: View of basic and specific physical and chemical features of growth and defect formation in mercury cadmium telluride (MCT) heterostructures (HS's) on GaAs substrates by molecular beam epitaxy (MBE) was made. On the basis of this knowledge a new generation of ultra high vacuum set, ultra-fast ellipsometer of high accuracy and automatic system for control of technological processes was produced for reproducibility of MCT Hs's growth on substrates up to 4" in diameter. The development of industrially oriented technolgoy of MCT HS's growth by MBE on GaAs substrates 2" in diameter and without intentional doping is presented. The electrical characteristics of n-type and p-type of MCT HS's and uniformity of MCT composition over the surface area are excellent. The residual donor and acceptor centres are supposed as hypothetically tellurium atoms in metallic sublattice ("antisite" tellurium) and double-ionised mercury vacancies. The technology of fabricating focal plane arrays is developed. The high quality characteristics of infrared detectors conductance and diode mode are measured. Calculations of detector parameters predicted the improvement in serial resistance and detectivity of infrared diode detectors based on MCT heterostructures with graded composition throughout the thickness.

57 citations


Cited by
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TL;DR: Topological superconductors are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors and are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry.
Abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

11,092 citations

Journal ArticleDOI
TL;DR: Weyl and Dirac semimetals as discussed by the authors are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry, and they have generated much recent interest.
Abstract: Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

3,407 citations

Journal ArticleDOI
TL;DR: In this paper, the authors discuss the underpinnings of the topological band theory and its materials applications, and propose a framework for predicting new classes of topological materials.
Abstract: First-principles band theory, properly augmented by topological considerations, has provided a remarkably successful framework for predicting new classes of topological materials. This Colloquium discusses the underpinnings of the topological band theory and its materials applications.

1,179 citations

Journal ArticleDOI
05 Aug 2016-Science
TL;DR: The guiding principle of the classification is to find irreducible representations of the little group of lattice symmetries at high-symmetry points in the Brillouin zone for each of the 230 space groups (SGs), the dimension of which corresponds to the number of bands that meet at the high-Symmetry point.
Abstract: INTRODUCTION Condensed-matter systems have recently become a fertile ground for the discovery of fermionic particles and phenomena predicted in high-energy physics; examples include Majorana fermions, as well as Dirac and Weyl semimetals. However, fermions in condensed-matter systems are not constrained by Poincare symmetry. Instead, they must only respect the crystal symmetry of one of the 230 space groups. Hence, there is the potential to find and classify free fermionic excitations in solid-state systems that have no high-energy counterparts. RATIONALE The guiding principle of our classification is to find irreducible representations of the little group of lattice symmetries at high-symmetry points in the Brillouin zone (BZ) for each of the 230 space groups (SGs), the dimension of which corresponds to the number of bands that meet at the high-symmetry point. Because we are interested in systems with spin-orbit coupling, we considered only the double-valued representations, where a 2π rotation gives a minus sign. Furthermore, we considered systems with time-reversal symmetry that squares to –1. For each unconventional representation, we computed the low-energy k · p Hamiltonian near the band crossings by writing down all terms allowed by the crystal symmetry. This allows us to further differentiate the band crossings by the degeneracy along lines and planes that emanate from the high-symmetry point, and also to compute topological invariants. For point degeneracies, we computed the monopole charge of the band-crossing; for line nodes, we computed the Berry phase of loops encircling the nodes. RESULTS We found that three space groups exhibit symmetry-protected three-band crossings. In two cases, this results in a threefold degenerate point node, whereas the third case results in a line node away from the high-symmetry point. These crossings are required to have a nonzero Chern number and hence display surface Fermi arcs. However, upon applying a magnetic field, they have an unusual Landau level structure, which distinguishes them from single and double Weyl points. Under the action of spatial symmetries, these fermions transform as spin-1 particles, as a consequence of the interplay between nonsymmorphic space group symmetries and spin. Additionally, we found that six space groups can host sixfold degeneracies. Two of these consist of two threefold degeneracies with opposite chirality, forced to be degenerate by the combination of time reversal and inversion symmetry, and can be described as “sixfold Dirac points.” The other four are distinct. Furthermore, seven space groups can host eightfold degeneracies. In two cases, the eightfold degeneracies are required; all bands come in groups of eight that cross at a particular point in the BZ. These two cases also exhibit fourfold degenerate line nodes, from which other semimetals can be derived: By adding strain or a magnetic field, these line nodes split into Weyl, Dirac, or line node semimetals. For all the three-, six- and eight-band crossings, nonsymmorphic symmetries play a crucial role in protecting the band crossing. Last, we found that seven space groups may host fourfold degenerate “spin-3/2” fermions at high symmetry points. Like their spin-1 counterparts, these quasiparticles host Fermi surfaces with nonzero Chern number. Unlike the other cases we considered, however, these fermions can be stabilized by both symmorphic and nonsymmorphic symmetries. Three space groups that host these excitations also host unconventional fermions at other points in the BZ. We propose nearly 40 candidate materials that realize each type of fermion near the Fermi level, as verified with ab initio calculations. Seventeen of these have been previously synthesized in single-crystal form, whereas others have been reported in powder form. CONCLUSION We have analyzed all types of fermions that can occur in spin-orbit coupled crystals with time-reversal symmetry and explored their topological properties. We found that there are several distinct types of such unconventional excitations, which are differentiated by their degeneracies at and along high-symmetry points, lines, and surfaces. We found natural generalizations of Weyl points: three- and four-band crossings described by a simple k · S Hamiltonian, where S i is the set of spin generators in either the spin-1 or spin-3/2 representations. These points carry a Chern number and, consequently, can exhibit Fermi arc surface states. We also found excitations with six- and eightfold degeneracies. These higher-band crossings create a tunable platform to realize topological semimetals by applying an external magnetic field or strain to the fourfold degenerate line nodes. Last, we propose realizations for each species of fermion in known materials, many of which are known to exist in single-crystal form.

1,054 citations