Landau levels in graphene layers with topological defects

Bueno, M.J.; Furtado, C.; Carvalho, Alexandre M. de M.

doi:10.1140/epjb/e2011-20726-4

Cited by 73 publications

(56 citation statements)

References 28 publications

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“…We can observe that the topological effects of the spiral dislocation modify the spectrum of energy of the two-dimensional harmonic oscillator, by yielding a new contribution given by the second term of the right-hand side of Eq. (8). In contrast to the results obtained in Ref.…”

Section: Tioncontrasting

confidence: 75%

“…The common point between these areas of physics is the description of these defects made by the Volterra process [1,2,4,5]. Up to now, a great deal of study has explored quantum system in the presence of disclinations [6][7][8][9][10] and screw dislocations [5,[11][12][13][14][15][16] in the context of condensed matter physics. In particular, torsion effects related to the presence of topological defects are in the interests of studies of semiconductors [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Harmonic oscillator in an elastic medium with a spiral dislocation

Maia

Bakke

2018

Physica B: Condensed Matter

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We investigate the behaviour of a two-dimensional harmonic oscillator in an elastic medium that possesses a spiral dislocation (an edge dislocation). We show that the Schrödinger equation for harmonic oscillator in the presence of a spiral dislocation can be solved analytically. Further, we discuss the effects of this topological defect on the confinement to a hard-wall confining potential.In both cases, we analyse if the effects of the topology of the spiral dislocation gives rise to an Aharonov-Bohm-type effect for bound states.PACS numbers:

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Section: Tioncontrasting

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Harmonic oscillator in an elastic medium with a spiral dislocation

Maia

Bakke

2018

Physica B: Condensed Matter

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“…1A). The radial equation for ϕðrÞ may be solved using arguments similar to those used for finding simple harmonic oscillator wavefunctions (20), and in general has two types of solutions (17). The "type I" energy eigenstate wavefunctions, expressed in terms of associated Laguerre polynomials, L, are…”

Section: Significancementioning

confidence: 99%

“…Much literature exists, however, for effects of disclinations in graphene (14)(15)(16)(17)(18)(19). The point of singular curvature is equivalent to the apex of a cone in real space, with a deficit angle α, and a corresponding singularity in the Gaussian curvature field, KðxÞ, localized at the apex:…”

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confidence: 99%

Fractional charge and inter-Landau–level states at points of singular curvature

Biswas

Son

2016

Proc. Natl. Acad. Sci. U.S.A.

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The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. Here we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau-level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. An important technological implication of these results is that these inter-Landau-level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.quantum Hall | geometry | gravitational response | singularity | quantum computation Q uantum Hall (QH) states (1) were among the first known examples of topologically nontrivial quantum states, a rapidly expanding category that now includes other exotica, such as Chern and topological insulators (2, 3), topological superconductors (2, 3), and spin liquids (4). The distinguishing feature of QH states is that they possess quantized values of Hall conductance, which are rational multiples of the conductance quantum, e 2 =h, a fundamental physical constant. This characteristic property results from the interplay between the degeneracy of QH states and their topological response to phase twists across their boundaries (5, 6).An additional topological feature of QH states, less wellknown and appreciated several years after the first, is that they possess a universal coupling to the intrinsic geometry of the 2D real-space manifold where the electrons reside (7). This coupling causes a real-space curvature field, KðxÞ, to induce an excess carrier number density,KðxÞ.[1]Here, and subsequently, we set the magnetic length ℓ = ffiffiffiffiffiffiffiffiffiffi Z=eB p to unity; ν, the filling fraction, is equal to 1 for an isolated filled Landau level (LL). The value of the so-called "gravitational" coupling constant, κ, is a characteristic of the QH state, and is robust to small perturbations to the Hamiltonian (7). LLs with indices n = 0,1, . . ., are characterized by corresponding distinct values (7, 8) of the coupling constant, κ n = n + 1=2, allowing us to distinguish between continuum LLs on the basis of a local measurement. Nonintuitive and interesting new behaviors resulting from this gravitational coupling are being increasingly appreciated: It has rece...

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“…This is probably due to the analogies and possible technological applications [31] found in condensed matter physics (e.g. disclination in crystals).…”

Section: Introductionmentioning

confidence: 98%

Relativistic Landau levels in the rotating cosmic string spacetime

et al. 2016

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In the spacetime induced by a rotating cosmic string we compute the energy levels of a massive spinless particle coupled covariantly to a homogeneous magnetic field parallel to the string. Afterwards, we consider the addition of a scalar potential with a Coulomb-type and a linear confining term and completely solve the Klein-Gordon equations for each configuration. Finally, assuming rigid-wall boundary conditions, we find the Landau levels when the linear defect is itself magnetized. Remarkably, our analysis reveals that the Landau quantization occurs even in the absence of gauge fields provided the string is endowed with spin.

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Landau levels in graphene layers with topological defects

Cited by 73 publications

References 28 publications

Harmonic oscillator in an elastic medium with a spiral dislocation

Harmonic oscillator in an elastic medium with a spiral dislocation

Fractional charge and inter-Landau–level states at points of singular curvature

Relativistic Landau levels in the rotating cosmic string spacetime

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