Magnetization of the metallic surface states in topological insulators

Tabert, C. J.; Ćarbotte, J. P.

doi:10.1088/0953-8984/27/1/015008

Cited by 12 publications

(22 citation statements)

References 45 publications

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“…A new expression for the amplitude of the magnetic oscillations is given which properly reduces to that of gapped graphene when the subdominant Schrödinger term is dropped and to that previously found in Ref. [51] when the Schrödinger mass is included but the gap is set to zero. ACKNOWLEDGMENT We thank E. J. Nicol for support of this work.…”

Section: Discussionmentioning

confidence: 80%

“…The last term in the above expression goes like E 0 ∝ B and will drop out in the limit B → 0 [51]. This leaves…”

Section: Appendixmentioning

confidence: 94%

“…For zero gap (solid black curve), the Hall conductivity at μ = 0 has ν = −1/2. This results from the finite value of the N = 0 level [51]. As is increased, the location of the N = 0 step moves lower in μ.…”

Section: Magnetization Of the Metallic Surface Statesmentioning

confidence: 96%

See 2 more Smart Citations

Particle-hole asymmetry in gapped topological insulator surface states

Tabert

Ćarbotte²

2015

Phys. Rev. B

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We consider the combined effect of a gap and the Zeeman interaction on the helical Dirac fermions that exist on the surface of a topological insulator. Magneto-optical properties, the magnetization, Hall effect, and the density of states are considered with emphasis on the particle-hole asymmetry, which arises when a subdominant Schrödinger piece is included along with the dominant Dirac part of the Hamiltonian. When appropriate, we compare our results with those of a single-valley gapped graphene system for which Zeeman splitting behaves differently. We provide a derivation of the phase offset in the magnetic oscillations brought about by the combined effect of the gap and Schrödinger term without requiring the semiclassical Onsager quantization condition. Our results agree with previous discussions based on semiclassical arguments.

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Section: Discussionmentioning

confidence: 80%

“…The last term in the above expression goes like E 0 ∝ B and will drop out in the limit B → 0 [51]. This leaves…”

Section: Appendixmentioning

confidence: 94%

See 1 more Smart Citation

Particle-hole asymmetry in gapped topological insulator surface states

Tabert

Ćarbotte²

2015

Phys. Rev. B

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“…For our purposes, this form is equivalent to Eqn. (7) 53 . Equation (25) has been worked out analytically for gapped graphene at T = 0 33 , and may be extended to silicene.…”

Section: A Zero Temperature Clean Limitmentioning

confidence: 99%

Magnetic properties of Dirac fermions in a buckled honeycomb lattice

2015

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We calculate the magnetic response of a buckled honeycomb lattice with intrinsic spin-orbit coupling (such as silicene) which supports valley-spin polarized energy bands when subjected to a perpendicular electric field Ez. By changing the magnitude of the external electric field, the size of the two band gaps involved can be tuned, and a transition from a topological insulator (TI) to a trivial band insulator (BI) is induced as one of the gaps becomes zero, and the system enters a valley-spin polarized metallic state (VSPM). In an external magnetic field (B), a distinct signature of the transition is seen in the derivative of the magnetization with respect to chemical potential (µ) which gives the quantization of the Hall plateaus through the Streda relation. When plotted as a function of the external electric field, the magnetization has an abrupt change in slope at its minimum which signals the VSPM state. The magnetic susceptibility (χ) shows jumps as a function of µ when a band gap is crossed which provides a measure of the gaps' variation as a function of external electric field. Alternatively, at fixed µ, the susceptibility displays an increasingly large diamagnetic response as the electric field approaches the critical value of the VSPM phase. In the VSPM state, magnetic oscillations exist for any value of chemical potential while for the TI, and BI state, µ must be larger than the minimum gap in the system. When µ is larger than both gaps, there are two fundamental cyclotron frequencies (which can also be tuned by Ez) involved in the de-Haas van-Alphen oscillations which are close in magnitude. This causes a prominent beating pattern to emerge.

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“…An unimportant constant has been dropped while arriving at the final expression in Eq. (20). Next we compare the free energies with various trial ground states for magnetic impurities.…”

Section: Variational Analysis Of a Coarse Grained Modelmentioning

confidence: 99%

Ferromagnetism and glassiness on the surface of topological insulators

Liu

Roy

2016

Phys. Rev. B

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We investigate the nature of the ordering among magnetic adatoms, randomly deposited on the surface of topological insulators. Restricting ourselves to dilute impurity and weak coupling (between itinerant fermion and magnetic impurities) limit, we show that for arbitrary amount of chemical doping away from the apex of the surface Dirac cone the magnetic impurities tend to arrange themselves in a spin-density-wave pattern, with the periodicity approximately $\pi/k_F$, where $k_F$ is the Fermi wave vector, when magnetic moment for impurity adatoms is isotropic. However, when magnetic moment possesses strong Ising or easy-axis anisotropy, pursuing both analytical and numerical approaches we show that the ground state is ferromagnetic for low to moderate chemical doping, despite the fragmentation of the system into multiple ferromagnetic islands. For high doping away from the Dirac point as well, the system appears to fragment into many ferromagnetic islands, but the magnetization in these islands is randomly distributed. Such magnetic ordering with net zero magnetization, is referred here as ferromagnetic spin glass, which is separated from the pure ferromagnet state by a first order phase transition. We generalize our analysis for cubic topological insulators (supporting three Dirac cones on a surface) and demonstrate that the nature of magnetic orderings and the transition between them remains qualitatively the same. We also discuss the possible relevance of our analysis to recent experiments.Comment: 14 pages, 10 figure

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Magnetization of the metallic surface states in topological insulators

Cited by 12 publications

References 45 publications

Particle-hole asymmetry in gapped topological insulator surface states

Particle-hole asymmetry in gapped topological insulator surface states

Magnetic properties of Dirac fermions in a buckled honeycomb lattice

Ferromagnetism and glassiness on the surface of topological insulators

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