Geometrical effects in orbital magnetic susceptibility

Gao, Yang; Yang, Shengyuan A.; Niu, Qian

doi:10.1103/physrevb.91.214405

Cited by 138 publications

(154 citation statements)

References 39 publications

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“…(38) are interband matrix elements of the magnetic dipole moment and of the position operator [13], where…”

Section: Curvatures Quantum Metrices Moments and Polarizationsmentioning

confidence: 99%

“…(33) has been given by Gao et al in Ref. [13]. In the semiclassical derivation of Gao et al the terms in the lines 5, 6, 7 and 8 in Eq.…”

Section: Curvatures Quantum Metrices Moments and Polarizationsmentioning

confidence: 99%

“…In the semiclassical derivation of Gao et al the terms in the lines 5, 6, 7 and 8 in Eq. (33) are explained by the k-space polarization energy and are related to the quadrupole moment of the velocity operator with respect to wave packets [13]. However, the semiclassical derivation yields a different prefactor for these polarization terms.…”

Section: Curvatures Quantum Metrices Moments and Polarizationsmentioning

confidence: 99%

“…Recently, geometrical contributions to OMS have been identified and shown to be generally significant and sometimes even dominant [13,14]. These contributions arise from the reciprocal-space Berry curvature and quantum metric, which describe geometrical properties of the electronic structure.…”

Section: Introductionmentioning

confidence: 99%

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Geometrical contributions to the exchange constants: Free electrons with spin-orbit interaction

2017

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Using thermal quantum field theory we derive an expression for the exchange constant that resembles Fukuyama's formula for the orbital magnetic susceptibility (OMS). Guided by this formal analogy between the exchange constant and OMS we identify a contribution to the exchange constant that arises from the geometrical properties of the band structure in mixed phase space. We compute the exchange constants for free electrons and show that the geometrical contribution is generally important. Our formalism allows us to study the exchange constants in the presence of spin-orbit interaction (SOI). Thereby, we find sizable differences between the exchange constants of helical and cycloidal spin spirals. Furthermore, we discuss how to calculate the exchange constants based on a gauge-field approach in the case of the Rashba model with an additional exchange splitting and show that the exchange constants obtained from this gauge-field approach are in perfect agreement with those obtained from the quantum field theoretical method.

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“…(38) are interband matrix elements of the magnetic dipole moment and of the position operator [13], where…”

Section: Curvatures Quantum Metrices Moments and Polarizationsmentioning

confidence: 99%

“…(33) has been given by Gao et al in Ref. [13]. In the semiclassical derivation of Gao et al the terms in the lines 5, 6, 7 and 8 in Eq.…”

Section: Curvatures Quantum Metrices Moments and Polarizationsmentioning

confidence: 99%

Section: Curvatures Quantum Metrices Moments and Polarizationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Geometrical contributions to the exchange constants: Free electrons with spin-orbit interaction

2017

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“…The quantum metric plays an important role in many-body systems and generally carries different information with respect to the Berry phase. The Bures metric has been connected to physical properties and observables of two-dimensional systems, such as density operators [25][26][27], quantum phase transitions [56][57][58], superfluid weight [59], orbital susceptibility [60,61]. Here, we focus on the geometric properties of gapped boundary of three-dimensional insulators in class AII, where a gap is induced by an external Zeeman field or by an ferromagnet on the surface [22].…”

Section: Bures Metric and Chern Numbermentioning

confidence: 99%

Momentum-space cigar geometry in topological phases

Palumbo

2018

Eur. Phys. J. Plus

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Abstract. In this paper, we stress the importance of momentum-space geometry in the understanding of two-dimensional topological phases of matter. We focus, for simplicity, on the gapped boundary of threedimensional topological insulators in class AII, which are described by a massive Dirac Hamiltonian and characterized by an half-integer Chern number. The gap is induced by introducing a magnetic perturbation, such as an external Zeeman field or a ferromagnet on the surface. The quantum Bures metric acquires a central role in our discussion and identifies a cigar geometry. We first derive the Chern number from the cigar geometry and we then show that the quantum metric can be seen as a solution of two-dimensional non-Abelian BF theory in momentum space. The gauge connection for this model is associated to the Maxwell algebra, which takes into account the Lorentz symmetries related to the Dirac theory and the momentum-space magnetic translations connected to the magnetic perturbation. The Witten black-hole metric is a solution of this gauge theory and coincides with the Bures metric. This allows us to calculate the corresponding momentum-space entanglement entropy that surprisingly carries information about the real-space conformal field theory describing the defect lines that can be created on the gapped boundary.

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Anomalous Response in the Orbital Magnetic Susceptibility of 2D Topological Systems

Faílde

Baldomir

2022

Physica Rapid Research Ltrs

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2D compounds with nonzero Berry curvature are ideal systems to study exotic and technologically favorable thermoelectric and magnetoelectric properties. Within this class of materials, the topological trivial and nontrivial regimes have to present very different behaviors, which are encoded for the orbital susceptibility and magnetization. To try to reveal them, it is found that it was necessary to introduce a k‐dependent mass term in the relativistic formalism of these materials. Thus, while a topologically trivial insulator is predicted to have a very limited response, in the nontrivial regime, a singular contribution to the orbital magnetic susceptibility, which is inversely proportional to the square of the quantum magnetic flux is unveiled. In this scenario, besides determining the measurement conditions a new route for enhancing the intrinsic orbital magnetism of topological materials widening the range of temperatures and magnetic fields without involving tiny bandgaps is found.

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Geometrical effects in orbital magnetic susceptibility

Cited by 138 publications

References 39 publications

Geometrical contributions to the exchange constants: Free electrons with spin-orbit interaction

Geometrical contributions to the exchange constants: Free electrons with spin-orbit interaction

Momentum-space cigar geometry in topological phases

Anomalous Response in the Orbital Magnetic Susceptibility of 2D Topological Systems

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