Ground state of a spin-½ charged particle in a two-dimensional magnetic field

Aharonov, Yakir; Casher, A.

doi:10.1103/physreva.19.2461

Cited by 415 publications

(446 citation statements)

References 2 publications

Supporting

Mentioning

428

Contrasting

Unclassified

Order By: Relevance

“…It is well known that Pauli operator h has infinite dimensional kernel. More precisely (cf [1]) we have Ker h − = {0} and Ker h + = {u ∈ L 2 (R 2 ) | u(x) = f (x)e −Ψ(x) , ∂f = 0}, dim Ker h + = ∞.…”

Section: Introductionmentioning

confidence: 99%

Spectral Asymptotics of Pauli Operators and Orthogonal Polynomials in Complex Domains

Filonov

Pushnitski

2006

Commun. Math. Phys.

View full text Add to dashboard Cite

We consider the spectrum of a two-dimensional Pauli operator with a compactly supported electric potential and a variable magnetic field with a positive mean value. The rate of accumulation of eigenvalues to zero is described in terms of the logarithmic capacity of the support of the electric potential. A connection between these eigenvalues and orthogonal polynomials in complex domains is established.

show abstract

Section: Introductionmentioning

confidence: 99%

Spectral Asymptotics of Pauli Operators and Orthogonal Polynomials in Complex Domains

Filonov

Pushnitski

2006

Commun. Math. Phys.

View full text Add to dashboard Cite

show abstract

“…The strategy of our treatment of zero modes differs from the one in [AC79] and other previous papers including [Ogu93]. Usually, when studying zero modes, one shows first that they, after having been multiplied by some known factor, are holomorphic function in the whole space; then one easily counts the number of such functions.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…Zero modes were discovered in [AC79] in dimension n = 2. Unlike the purely electric interaction, a compactly supported magnetic field can generate zero modes, as soon as the total flux of the field is sufficiently large.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Zero Modes for the Magnetic Pauli Operator in Even-Dimensional Euclidean Space

Persson

2008

Lett Math Phys

View full text Add to dashboard Cite

Abstract. We study the ground state of the Pauli Hamiltonian with a magnetic field in R 2d . We consider the case where a scalar potential W is present and the magnetic field B is given by B = 2i ∂∂ W . The main result is that there are no zero modes if the magnetic field decays faster than quadratically at infinity. If the magnetic field decays quadratically then zero modes may appear, and we give a lower bound for the number of them. The results in this paper partly correct a mistake in a paper from 1993. Introduction and main resultThe Pauli operator P in R n describes a charged spin-1 2 particle in a magnetic field. Along with the Dirac operator, it lies in the base of numerous models in quantum physics. The problem about zero modes, the bound states with zero energy, is one of many questions to be asked about the spectral properties of these operators.Zero modes were discovered in [AC79] in dimension n = 2. Unlike the purely electric interaction, a compactly supported magnetic field can generate zero modes, as soon as the total flux of the field is sufficiently large. Quantitatively, this is expressed by the famous Aharonov-Casher formula. The two-dimensional case is by now quite well studied; the AC formula is extended to rather singular magnetic field, moreover, if the total flux is infinite (and the field has constant sign), there are infinitely many zero modes.On the other hand, in the three-dimensional case the presence of zero modes is a rather exceptional feature, and the conditions for them to appear are not yet found, see the discussion in [MR03] and references therein.Even less clear is the situation in the higher dimensions. In [Shi91], for even n some sufficient conditions for the infiniteness of the number of zero modes were found, requiring, in particular, that the field decays rather slowly (more slowly than r −2 ) at infinity. On the other hand, in [Ogu93], again for even n, the case where a finite number of zero modes should appear was considered. Under the assumption of a rather regular behavior of the scalar potential of the magnetic field at infinity the number of zero modes was calculated. In particular, for a field with compact support or decaying faster than quadratically at infinity the formula in [Ogu93] implies the absence of zero modes, thus making a difference with the two-dimensional situation.2000 Mathematics Subject Classification. 81Q05 (Primary); 35Q40, 81Q10 (Secondary).

show abstract

“…Now, if one is interested to investigate further consequences due to the altered topology in graphene, without taking into account the modulation of the hopping strengths, one may ask whether fractional charge might also be induced even when no modulation (distortion) of the hopping strength in the graphene honeycomb lattice is present, that is, by considering only a pseudomagnetic field (associated to the axial-vector gauge field), which would describe a local single disclination. Naturally, we have found a positive answer to this question, since the results we present here rely upon the theorem associating the number of fermion zero-modes to the magnetic flux [7] and on the proof carried out in Ref. [16] that the index of Dirac Hamiltonian in 2 + 1 space-time dimensions is proportional to the magnetic flux.…”

Section: Fermion Zero Modes On Vortexlike (Pseudo)magnetic Fieldsmentioning

confidence: 96%

“…The induced charge may be fractional and proportional to the magnetic flux on the plane [6]. In the case of a vortex magnetic field, one has a finite magnetic flux and the number of fermion zero modes is proportional to the magnetic flux [7].…”

Section: Introductionmentioning

confidence: 99%

Fractional fermion charges induced by axial-vector and vector gauge potentials and parity anomaly in planar graphenelike structures

Obispo

Hott

2014

Phys. Rev. B

View full text Add to dashboard Cite

We show that fermion charge fractionalization can take place in a recently proposed chiral gauge model for graphene even in the absence of Kekulé distortion in the graphene honeycomb lattice. In this model, electrons couple in a chiral way to a pseudomagnetic field with a vortex profile in such a way that it can be used to describe the influences of topological defects, such as disclinations, on the electronic states. We also extend the model by adding the coupling of fermions to an external magnetic field and show that the fermion charge can be fractionalized by means of only gauge potentials. It is shown that the chiral fermion charge can also have fractional value. We also relate the fractionalization of the fermion charge to the parity anomaly in an extended quantum electrodynamics, which involves vector and axial-vector gauge fields.

show abstract

Ground state of a spin-½ charged particle in a two-dimensional magnetic field

Cited by 415 publications

References 2 publications

Spectral Asymptotics of Pauli Operators and Orthogonal Polynomials in Complex Domains

Spectral Asymptotics of Pauli Operators and Orthogonal Polynomials in Complex Domains

Zero Modes for the Magnetic Pauli Operator in Even-Dimensional Euclidean Space

Fractional fermion charges induced by axial-vector and vector gauge potentials and parity anomaly in planar graphenelike structures

Contact Info

Product

Resources

About