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Insights into the fundamental properties of graphene's Dirac-Weyl fermions have emerged from studies of electron tunnelling transistors in which an atomically thin layer of hexagonal boron nitride (hBN) is sandwiched between two layers of high purity graphene. Here, we show that when a single defect is present within the hBN tunnel barrier, it can inject electrons into the graphene layers and its sharply defined energy level acts as a high resolution spectroscopic probe of electron-electron interactions in graphene. We report a magnetic field dependent suppression of the tunnel current flowing through a single defect below temperatures of $\sim$ 2 K. This is attributed to the formation of a magnetically-induced Coulomb gap in the spectral density of electrons tunnelling into graphene due to electron-electron interactions.

Let $m$ be a positive integer and let $\Omega$ be a finite set. The $m$-closure of $G\leq\operatorname{Sym}(\Omega)$ is the largest permutation group on $\Omega$ having the same orbits as $G$ in its induced action on the Cartesian product $\Omega^m$. The $1$-closure and $2$-closure of a solvable permutation group need not be solvable. We prove that the $m$-closure of a solvable permutation group is always solvable for $m\geq3$.

Hexagonal boron nitride (hBN) is a large band gap layered crystal, frequently incorporated in van der Waals (vdW) heterostructures as an insulating or tunnel barrier. Localised states with energies within its band gap can emit visible light, relevant to applications in nanophotonics and quantum information processing. However, they also give rise to conducting channels, which can induce electrical breakdown when a large voltage is applied. Here we use gated tunnel transistors to study resonant electron tunnelling through the localised states in few atomic-layer hBN barriers sandwiched between two monolayer graphene electrodes. The measurements are used to determine the energy, linewidth, tunnelling transmission probability, and depth within the barrier of more than 50 distinct localised states. A three-step process of electron percolation through two spatially separated localised states is also investigated., Comment: Supplementary information can be found at https://doi.org/10.1038/s42005-018-0097-1

We observe a series of sharp resonant features in the differential conductance of graphene-hexagonal boron nitride-graphene tunnel transistors over a wide range of bias voltages between $\sim$10 and 200 mV. We attribute them to electron tunneling assisted by the emission of phonons of well-defined energy. The bias voltages at which they occur are insensitive to the applied gate voltage and hence independent of the carrier densities in the graphene electrodes, so plasmonic effects can be ruled out. The phonon energies corresponding to the resonances are compared with the lattice dispersion curves of graphene-boron nitride heterostructures and are close to peaks in the single phonon density of states.

A new class of multilayered functional materials has recently emerged in which the component atomic layers are held together by weak van der Waals forces that preserve the structural integrity and physical properties of each layer. An exemplar of such a structure is a transistor device in which relativistic Dirac Fermions can resonantly tunnel through a boron nitride barrier, a few atomic layers thick, sandwiched between two graphene electrodes. An applied magnetic field quantises graphene's gapless conduction and valence band states into discrete Landau levels, allowing us to resolve individual inter-Landau level transitions and thereby demonstrate that the energy, momentum and chiral properties of the electrons are conserved in the tunnelling process. We also demonstrate that the change in the semiclassical cyclotron trajectories, following a tunnelling event, is a form of Klein tunnelling for inter-layer transitions., Comment: in Nature Physics (2015)

A subgroup $H$ of a group $G$ is called {\it pronormal}, if for every $g\in G$ subgroups $H$ and $H^g$ are conjugate in $\langle H, H^g\rangle$. It is proven that if a finite group $G$ possesses a $\pi$-Hall subgroup for a set of primes $\pi$, the every its normal subgroup (in particular, $G$ itself) possesses a $\pi$-Hall subgroup that is pronormal in~$G$.

In the note we prove that all composition factors of a finite group possessing a Carter subgroup of odd order either are abelain, or are isomorphic to $L_2(3^{2n+1})$.

Recent developments in the technology of van der Waals heterostructures made from two-dimensional atomic crystals have already led to the observation of new physical phenomena, such as the metal-insulator transition and Coulomb drag, and to the realisation of functional devices, such as tunnel diodes, tunnel transistors and photovoltaic sensors. An unprecedented degree of control of the electronic properties is available not only by means of the selection of materials in the stack but also through the additional fine-tuning achievable by adjusting the built-in strain and relative orientation of the component layers. Here we demonstrate how careful alignment of the crystallographic orientation of two graphene electrodes, separated by a layer of hexagonal boron nitride (hBN) in a transistor device, can achieve resonant tunnelling with conservation of electron energy, momentum and, potentially, chirality. We show how the resonance peak and negative differential conductance in the device characteristics induces a tuneable radio-frequency oscillatory current which has potential for future high frequency technology., Comment: For Supplementary Information see http://www.nature.com/nnano/journal/vaop/ncurrent/extref/nnano.2014.187-s1.pdf

We report the recent progress in understanding of symmetries which can be implemented in the scalar sector of electroweak symmetry breaking models with several Higgs doublets. In particular we present the list of finite reparametrization symmetry groups which can appear in the three-Higgs-doublet models., Comment: 4 pages, talk given at the conference "Rencontres du Vietnam: Beyond The Standard Model of Particle Physics", Quy Nhon, Vietnam July 15-21, 2012

Symmetries play a crucial role in electroweak symmetry breaking models with non-minimal Higgs content. Within each class of these models, it is desirable to know which symmetry groups can be implemented via the scalar sector. In N-Higgs-doublet models, this classification problem was solved only for N=2 doublets. Very recently, we suggested a method to classify all realizable finite symmetry groups of Higgs-family transformations in the three-Higgs-doublet model (3HDM). Here, we present this classification in all detail together with an introduction to the theory of solvable groups, which play the key role in our derivation. We also consider generalized-CP symmetries, and discuss the interplay between Higgs-family symmetries and CP-conservation. In particular, we prove that presence of the Z_4 symmetry guarantees the explicit CP-conservation of the potential. This work completes classification of finite reparametrization symmetry groups in 3HDM., Comment: 41 pages, 3 figure; v2: additional explanations on group-theoretical issues, matches the published version

N-Higgs-doublet models (NHDM) are among the most popular examples of electroweak symmetry breaking mechanisms beyond the Standard Model. Discrete symmetries imposed on the NHDM scalar potential play a pivotal role in shaping the phenomenology of the model, and various symmetry groups have been studied so far. However, in spite of all efforts, the classification of finite Higgs-family symmetry groups realizable in NHDM for any N>2 is still missing. Here, we solve this problem for the three-Higgs-doublet model by making use of Burnside's theorem and other results from pure finite group theory which are rarely exploited in physics. Our method and results can be also used beyond high-energy physics, for example, in study of possible symmetries in three-band superconductors., Comment: 5 pages; v2: expanded introduction, some minor corrections, matches the published version

The classification of finite simple strongly real groups is complete. It is easy to see that strong reality for every nonabelian finite simple group is equivalent to the fact that each element can be written as a product of two involutions. We thus obtain a solution to Problem 14.82 from the Kourovka notebook from the classification of finite simple strongly real groups.

A finite group $G$ is said to satisfy $C_\pi$ for a set of primes $\pi$, if $G$ possesses exactly one class of conjugate $\pi$-Hall subgroups. In the paper we obtain a criterion for a finite group $G$ to satisfy $C_\pi$ in terms of a normal series of the group., Comment: Appear in Siberian Mathematical Journal, vol. 51 (2010), No3.

In this paper we find the number of conjugate $\pi$-Hall subgroups in all finite almost simple groups. We also complete the classification of $\pi$-Hall subgroups in finite simple groups and correct some mistakes from our previous paper., Comment: article in press in "Journal of algebra"

We show that the resonant tunnel current through a single energy level of an individual quantum dot within an ensemble of dots is strongly sensitive to photoexcited holes that become bound in the close vicinity of the dot. The presence of these holes lowers the electrostatic energy of the quantum dot state and switches the current carrying channel from fully open to fully closed with a high on/off ratio (> 50). The device can be reset by means of a bias voltage pulse. These properties are of interest for charge sensitive photon counting devices., Comment: 5 pages, 4 figures

In this paper we continue our investgation of the prime graph of a finite simple group started in http://arxiv.org/abs/math/0506294 (the printed version appeared in [1]). We describe all cocliques of maximal size for all finite simple groups and also we correct mistakes and misprints from our previous paper. The list of correction is given in Appendix of the present paper., Comment: published version with corrections

In the paper we consider the following conjecture: if a finite group $G$ possesses a solvable $\pi$-Hall subgroup $H$, then there exist elements $x,y,z,t\in G$ such that the identity $H\cap H^x\cap H^y\cap H^z\cap H^t=O_\pi(G)$ holds. The minimal counter example is shown to be an almost simple group of Lie type.

In the paper we prove that the Hall property $C_\pi$ is inherited by normal subgroups which index is a $\pi'$-number.

We investigate the effect of an applied magnetic field on resonant tunneling of electrons through the bound states of self-assembled InAs quantum dots (QDs) embedded within an (AlGa)As tunnel barrier. At low temperatures (no more than 2 K), a magnetic field B applied either parallel or perpendicular to the direction of current flow causes a significant enhancement of the tunnel current. For the latter field configuration, we observe a strong angular anisotropy of the enhanced current when B is rotated in the plane of the quantum dot layer. We attribute this behavior to the effect of the lowered symmetry of the QD eigenfunctions on the electron-electron interaction., Comment: Revtex4, 6 pages, 6 figures

Graphene, a one-atom thick zero gap semiconductor [1, 2], has been attracting an increasing interest due to its remarkable physical properties ranging from an electron spectrum resembling relativistic dynamics [3-12] to ballistic transport under ambient conditions [1-4]. The latter makes graphene a promising material for future electronics and the recently demonstrated possibility of chemical doping without significant change in mobility has improved graphene's prospects further [13]. However, to find optimal dopants and, more generally, to progress towards graphene-based electronics requires understanding the physical mechanism behind the chemical doping, which has been lacking so far. Here, we present the first joint experimental and theoretical investigation of adsorbates on graphene. We elucidate a general relation between the doping strength and whether or not adsorbates have a magnetic moment: The paramagnetic single NO2 molecule is found to be a strong acceptor, whereas its diamagnetic dimer N2O4 causes only weak doping. This effect is related to the peculiar density of states of graphene, which provides an ideal situation for model studies of doping effects in semiconductors. Furthermore, we explain recent results on its "chemical sensor" properties, in particular, the possibility to detect a single NO2 molecule [13]., Comment: 5 pages, 4 figures

We use magnetotunneling spectroscopy to observe the spin splitting of the ground state of an X-valley-related Si-donor impurity in an AlAs barrier. We determine the absolute magnitude of the effective Zeeman spin splitting factors of the impurity ground state to be g$_{I}$= 2.2 $\pm $ 0.1. We also investigate the spatial form of the electron wave function of the donor ground state, which is anisotropic in the growth plane.

Tunnel spectroscopy is used to probe the electronic structure in GaAs quantum well of resonant tunnel junction over wide range of energies and magnetic fields normal to layers. Spin degenerated high Landau levels ($N=2\div7$) are found to be drastically renormalised near energies when the longitudinal optical-phonon ($\hbar\omega_{LO}$) and cyclotron energy ($\hbar\omega_{C}$) are satisfied condition $\hbar\omega_{LO}=m\hbar\omega_{C}$, where $m=1,2,3$. This renormalisation is attributed to formation of resonant magnetopolarons, i.e. mixing of high index Landau levels by strong interaction of electrons at Landau level states with LO-phonons., Comment: 4 pages, 3 eps figures, revtex4

Magnetic field suppression of the tunneling between disordered 2D electron systems in GaAs around zero bias voltage has been studied. Magnetic field B normal to the layers induces a dip in the tunneling density of states (TDOS) centered precisely at the Fermi level, i.e. soft tunneling gap. The soft gap has a linear form with finite TDOS diminishing with B at the Fermi level. Driven by magnetic field the transition soft-hard gap has been observed, i.e. the TDOS vanishes in the finite energy window around Fermi level at B>13 T., Comment: Revtex4, 6 pages, 5 Postscript figures, to be submitted to Physical Review B

We use magnetotunnelling spectroscopy as a non-invasive probe to produce two-dimensional spatial images of the probability density of an electron confined in a self-assembled semiconductor quantum dot. The images reveal clearly the elliptical symmetry of the ground state and the characteristic lobes of the higher energy states., Comment: 5 pages, 5 figures, revtex

Nonlinear electron transport in normally pinched-off quantum wires was studied. The wires were fabricated from AlGaAs/GaAs heterostructures with high-mobility two-dimensional electron gas by electron beam lithography and following wet etching. At certain critical source-drain voltage the samples exhibited a step rise of the conductance. The differential conductance of the open wires was noticeably lower than e^2/h as far as only part of the source-drain voltage dropped between source contact and saddle-point of the potential relief along the wire. The latter limited the electron flow injected to the wire. At high enough source-drain voltages the decrease of the differential conductance due to the real space transfer of electrons from the wire in GaAs to the doped AlGaAs layer was found. In this regime the sign of differential magnetoconductance was changed with reversing the direction of the current in the wire or the magnetic field, whet the magnetic field lies in the heterostructure plane and is directed perpendicular to the current. The dependence of the differential conductance on the magnetic field and its direction indicated that the real space transfer events were mainly mediated by the interface scattering., Comment: LaTeX 2e (epl.cls) 6 pages, 3 figures