Structure of Amorphous Aluminum Oxide

Lee, Sung Keun; Lee, Sung Bo; Park, Sun Young; Yi, Yoo Soo; Ahn, Chi Won

doi:10.1103/physrevlett.103.095501

Cited by 187 publications

(186 citation statements)

References 27 publications

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“…The effective surface Hamiltonian of the 3D topological insulators with spherical boundary condition has also been discussed in Ref. [54,55]. The surface Hamiltonian in the eigen-basis of j and j z can be written as…”

Section: The Z2 Helical Surface Statesmentioning

confidence: 99%

Two- and three-dimensional topological insulators with isotropic and parity-breaking Landau levels

Zhou

2012

Phys. Rev. B

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We investigate topological insulating states in both two and three dimensions with the harmonic potential and strong spin-orbit couplings breaking the inversion symmetry. Landau-level like quantization appear with the full 2D and 3D rotational symmetry and time-reversal symmetry. Inside each band, states are labeled by their angular momenta over which energy dispersions are strongly suppressed by spin-orbit coupling to nearly flat. The radial quantization generates energy gaps between neighboring bands at the order of the harmonic frequency. Helical edge or surface states appear on open boundaries characterized by the Z2 index. These Hamiltonians can be viewed from the dimensional reduction of the high dimensional quantum Hall states in 3D and 4D flat spaces. These states can be realized with ultra-cold fermions inside harmonic traps with the synthetic gauge fields.

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Section: The Z2 Helical Surface Statesmentioning

confidence: 99%

Two- and three-dimensional topological insulators with isotropic and parity-breaking Landau levels

Zhou

2012

Phys. Rev. B

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“…19 The surface states of topological insulators in strong magnetic fields have been investigated in Ref. 20.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional surface charge transport in topological insulators

et al. 2010

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We construct a theory of charge transport by the surface states of topological insulators in three dimensions. The focus is on the experimentally relevant case when the Fermi energy εF and transport scattering time τ satisfy εF τ / 1, but εF lies below the bottom of the conduction band. Our theory is based on the spin density matrix and takes the quantum Liouville equation as its starting point. The scattering term is determined to linear order in the impurity density ni and explicitly accounts for the absence of backscattering, while screening is included in the random phase approximation. The main contribution to the conductivity is ∝ n −1 i and has different carrier density dependencies for different forms of scattering, while an additional contribution is independent of ni. The dominant scattering angles can be inferred by studying the ratio of the transport time to the Bloch lifetime as a function of the Wigner-Seitz radius rs. The current generates a spin polarization that could provide a smoking-gun signature of surface state transport. We also discuss the effect on the surface states of adding metallic contacts.

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“…1 . In the Landau gauge, the eigenenergy is a function of the azimuthal quantum number m which serves as a "guiding center" coordinate.…”

mentioning

confidence: 99%

“…Thus, for the singly connected topology, the portion of the surface approximately tangential to the external magnetic field harbors the chiral quantum Hall edge states together with the conducting non-chiral surface states, which disperse as Dirac particles. Since the latter do not localize 1,15 , the two terminal conductance is not quantized even when the Fermi energy lies between Landau levels. It was proposed 1 that the way to measure the quantized Hall effect is to set up a potential difference between the electrode placed in the caps of the sphere and to measure the circulating current on the outer surface.…”

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confidence: 99%

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Quantum Hall effect in a singly and doubly connected three-dimensional topological insulator

Vafek

2011

Phys. Rev. B

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The surface states of topological insulators, which behave as charged massless Dirac fermions, are studied in the presence of a quantizing uniform magnetic field. Using the method of D.H. Lee 1 , analytical formula satisfied by the energy spectrum is found for a singly and doubly connected geometry. This is in turn used to argue that the way to measure the quantized Hall conductivity is to perform the Laughlin's flux ramping experiment and measure the charge transferred from the inner to the outer surface, analogous to the experiment in Ref. 2 . Unlike the Hall bar setup used currently, this has the advantage of being free of the contamination from the delocalized continuum of the surface edge states. In the presence of the Zeeman coupling, and/or interaction driven Quantum Hall ferromagnetism, which translate into the Dirac mass term, the quantized charge Hall conductivity σxy = ne 2 /h, with n = 0, ±1, ±3, ±5 . . .. Backgating of one of the surfaces leads to additional Landau level splitting and in this case n can be any integer.Theoretical prediction of the existence of an odd number of Dirac cones in the dispersion of the surface states of topological insulators 3,4 and subsequent experimental observation of such unusual surface states 5-8 has propelled this research field into an active area of condensed matter physics (for reviews see Refs. [9][10][11] ). Particularly interesting is the problem of the topological insulator surface Dirac Fermions in magnetic field. Because the Dirac Fermions carry definite charge, the magnetic field couples to the orbital motion. If this motion is constrained to be perpendicular to the applied field, the Landau level quantization results. However, as discussed by D.H. Lee 1 , since the Dirac Fermions move on the surface of a 3-dimensional material, in the absence of magnetic monopoles, i.e for ∇ · B = 0, it is impossible for the magnetic field to be everywhere along the normal of an oriented surface. Instead, in a typical experimental setting, the three dimensional material is placed in a uniform external magnetic field, and only portions of the surface, say the top and the bottom ones, experience Landau quantization. The Dirac Fermions on the surfaces tangential to the external magnetic field continue moving as plane-waves.In addition, the spin-orbit coupling, which causes the appearance of the Dirac particles in the first place, makes the Zeeman coupling different from that in graphene, where Dirac particles also appear but where the spinorbit coupling is negligible. Thus, instead of simply spin splitting the electronic energy levels, the Zeeman term in topological insulators acts as a Dirac mass. As illustrated in Fig.II, this causes the splitting of the zeroth Landau level, but the higher Landau levels are not split unless their guiding center approaches the edge. Rather, at positive energies they move up and at negative energies they move down. Of course, because of the Dirac structure, the energy scale associated with Zeeman splitting ∼ 1K × H[T ] is much smaller 1 th...

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Structure of Amorphous Aluminum Oxide

Cited by 187 publications

References 27 publications

Two- and three-dimensional topological insulators with isotropic and parity-breaking Landau levels

Two- and three-dimensional topological insulators with isotropic and parity-breaking Landau levels

Two-dimensional surface charge transport in topological insulators

Quantum Hall effect in a singly and doubly connected three-dimensional topological insulator

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