One-dimensional Coulomb problem in Dirac materials

Downing, C. A.; Portnoi, M. E.

doi:10.1103/physreva.90.052116

Cited by 59 publications

(49 citation statements)

References 66 publications

(73 reference statements)

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“…This suggests that a modulation of the magnetic field strength will allow one to observe successive confinement-deconfinement transitions of positive angular momentum states as they disappear into the continuum one-by-one with changing magnetic field strength. Such a phenomena of bound states diving into the continuum has the superficial appearance of being a magnetic version of the famous atomic collapse [48,49]. There the relativistic atom is modeled with a massive Dirac Hamiltonian in an external Coulomb field, and bound states merge from the gapped region into the continuum at critical charge strengths.…”

Section: Dirac Electron In a Regularized Magnetic Quantum Dotmentioning

confidence: 99%

Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields

Downing

Portnoi

2016

Phys. Rev. B

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We show how it is possible to trap two-dimensional massless Dirac fermions in spatially inhomogeneous magnetic fields, as long as the formed magnetic quantum dot (or ring) is of a slowly decaying nature. It is found that a modulation of the depth of the magnetic quantum dot leads to successive confinement-deconfinement transitions of vortexlike states with a certain angular momentum, until a regime is reached where only states with one sign of angular momentum are supported. We illustrate these characteristics with both exact solutions and a hitherto unknown quasi-exactly solvable model utilizing confluent Heun functions.

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Section: Dirac Electron In a Regularized Magnetic Quantum Dotmentioning

confidence: 99%

Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields

Downing

Portnoi

2016

Phys. Rev. B

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“…Interesting transport effects such as chiral (Klein) tunneling [3][4][5][6][7], vacuum polarization [8], atomic collapse [9,10], and the minimum conductivity at the Dirac point [11] have been widely discussed in the literature. The topic of elastic scattering in clean, low-temperature graphene, which can occur due to charged impurities, ripples, or strain fields, has been addressed by many authors [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Optimal traps in graphene

et al. 2015

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We transform the two-dimensional Dirac-Weyl equation, which governs the charge carriers in graphene, into a nonlinear first-order differential equation for scattering phase shift, using the so-called variable-phase method. This allows us to utilize the Levinson theorem, relating scattering phase shifts of a slow particle to its bound states, to find zero-energy bound states created electrostatically in realistic structures. These confined states are formed at critical potential strengths, which leads us to posit the use of "optimal traps" to combat the chiral tunneling found in graphene: this could be explored experimentally with an artificial network of point charges held above the graphene layer. We also discuss scattering on these states and find that the s states create a dominant peak in the scattering cross section as the energy tends towards the Dirac point energy, suggesting a dominant contribution to the resistivity.

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“…Constructions with different one-dimensional potentials, which overcome Klein paradox by considering states with finite momentum in the transverse direction (strip geometry) were proposed and analyzed in Refs. [18][19][20]. Similarly, the circular geometry leads to quasi-bound states [21][22][23][24][25][26], and may even lead to bound states if a confining potential enters as a mass term in the Dirac equation [27].…”

Section: Introductionmentioning

confidence: 99%

Excitonic physics in a Dirac quantum dot

Raca

Milovanović

2017

Phys. Rev. B

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We present a description of vacuum polarization in a circular Dirac quantum dot in two spatial dimensions assuming α -the relative strength of the Coulomb interaction small enough to render an approximation with a single electron (hole) lowest energy level relevant. Applying this approximation, we find that for αc ≈ 1.05 the lowest level is half-filled irrespective of the number of flavors that are present. The ground state can be represented as a superposition of particular (even number) excitonic states which constitute an excitonic cloud that evolves in a crossover manner. The ground state is degenerate with an intervalley excitonic state at αc ≈ 1.05, a critical strength, that in our approximation marks a point with single electron and exciton resonances.

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One-dimensional Coulomb problem in Dirac materials

Cited by 59 publications

References 66 publications

Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields

Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields

Optimal traps in graphene

Excitonic physics in a Dirac quantum dot

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