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Electron-phonon correlations on spin texture of gapped helical Dirac Fermions
The metallic surface states of a topological insulator support helical Dirac
fermions protected by topology with their spin locked perpendicular to their
momentum. They can acquire mass through magnetic doping or through
hybridization of states on opposite faces of a thin sample. In this case there
can be a component of electron spin oriented perpendicular to the surface
plane. The electron-phonon interaction renormalizes the dynamics of the charge
carriers through their spectral density. It also modifies the gap channel and a
second spectral function enters which, not only determines the out of plane
spin component, but also comes into in-plane properties. While the out of plane
spin component is decreased below the Fermi momentum (), the in plane
component increases. There are also correlation tails extending well beyond
. The angular resolved photo-emission line shapes aquire Holstein side
bands. The effective gap in the density of states is reduced and the optical
conductivity aquires distinct measurable phonon structure even for modest value
of the electron-phonon coupling.Comment: 9pages, 9 figure
Conductivity of Dirac fermions with phonon induced topological crossover
We study the Hall conductivity in single layer gapped Dirac fermion materials
including coupling to a phonon field, which not only modifies the
quasi-particle dynamics through the usual self-energy term but also
renormalizes directly the gap. Consequently the Berry curvature is modified. As
the temperature is increased the sign of the renormalized gap can change and
the material can cross over from a band insulator to a topological insulator at
higher temperature (T). The effective Chern numbers defined for valley and spin
Hall conductivity show a rich phase diagram with increasing temperature. While
the spin and valley DC Hall conductivity is no longer quantized at elevated
temperature a change in sign with increasing T is a clear indication of a
topological crossover. The chirality of the circularly polarized light which is
dominantly absorbed by a particular valley can change with temperature as a
result of a topological crossover.Comment: 6 pages, 5 figures, to appear in Phys. Rev.
Longitudinal and spin/valley Hall optical conductivity in single layer
A monolayer of has a non-centrosymmetric crystal structure, with
spin polarized bands. It is a two valley semiconductor with direct gap falling
in the visible range of the electromagnetic spectrum. Its optical properties
are of particular interest in relation to valleytronics and possible device
applications. We study the longitudinal and the transverse Hall dynamical
conductivity which is decomposed into charge, spin and valley contributions.
Circular polarized light associated with each of the two valleys separately is
considered and results are filtered according to spin polarization. Temperature
can greatly change the spin admixture seen in the frequency window where they
are not closely in balance.Comment: 8 pages, 5 figures, accepted by Phys. Rev.
Phonon structure in dispersion curves and density of states of massive Dirac Fermions
Dirac fermions exist in many solid state systems including graphene, silicene
and other two dimensional membranes such as are found in group VI
dichalcogenides, as well as on the surface of some insulators where such states
are protected by topology. Coupling of those fermions to phonons introduces new
structures in their dispersion curves and, in the case of massive Dirac
fermions, can shift and modify the gap. We show how these changes present in
angular-resolved photoemission spectroscopy of the dressed charge carrier
dispersion curves and scanning tunneling microscopy measurements of their
density of states. In particular we focus on the region around the band gap. In
this region the charge carrier spectral density no longer consists of a
dominant quasiparticle peak and a smaller incoherent phonon related background.
The quasiparticle picture has broken down and this leads to important
modification in both dispersion curves and density of states.Comment: 12 pages, 6 figures, to appear in PR
Hexagonal warping on spin texture, Hall conductivity and circular dichroism of Topological Insulator
The topological protected electronic states on the surface of a topological
insulator can progressively change their Fermi cross-section from circular to a
snowflake shape as the chemical potential is increased above the Dirac point
because of an hexagonal warping term in the Hamiltonian. Another effect of
warping is to change the spin texture which exists when a finite gap is
included by magnetic doping, although the in-plane spin component remains
locked perpendicular to momentum. It also changes the orbital magnetic moment,
the matrix element for optical absorption and the circular dichroism. We find
that the Fermi surface average of z-component of spin is closely related to the
value of the Berry phase. This holds even when the Hamiltonian includes a
subdominant non-relativistic quadratic in momentum term (which provides
particle-hole asymmetry) in addition to the dominant relativistic Dirac term.
There is also a qualitative correlation between and the dichroism. For the case when the chemical potential
falls inside the gap between valence and conduction band, the Hall conductivity
remains quantized and unaffected in value by the hexagonal warping term.Comment: 10 figures, accepted in PR
Hexagonal warping on optical conductivity of surface states in Topological Insulator Bi_{2}Te_{3}
ARPES studies of the protected surface states in the Topological Insulator have revealed the existence of an important hexagonal warping
term in its electronic band structure. This term distorts the shape of the
Dirac cone from a circle at low energies to a snowflake shape at higher
energies. We show that this implies important modifications of the interband
optical transitions which no longer provide a constant universal background as
seen in graphene. Rather the conductivity shows a quasilinear increase with a
slightly concave upward bending as energy is increased. Its slope increases
with increasing magnitude of the hexagonal distortion as does the magnitude of
the jump at the interband onset. The energy dependence of the density of states
is also modified and deviates downward from linear with increasing energy.Comment: 6 pages, 4 figures, accepted to Phys. Rev.
Magneto-optical conductivity in a topological insulator
Adding a small subdominant quadratic in momentum term to a dominant linear
Dirac dispersion curve affects conduction and valence band differently and
leads to an hourglass-like structure for energy as a function of momentum. This
applies to the protected surface states in topological insulators. The energies
of the conduction and valence band Landau levels are also different and this
leads to the splitting of optical absorption lines produced by the magnetic
field, which acquire a two peak structure. It also changes the peaks in the
imaginary part of the Hall conductivity into two distinct contributions of
opposite signs. The real part of the circularly polarized optical conductivity
however retains its single peak structure but the peaks in right and left
handedness case are shifted in energy with respect to each other in contrast to
the pure Dirac case. The magnitude of the semiclassical cyclotron frequency is
significantly modified by the presence of a mass term as is its variation with
value of the chemical potential . Its optical spectral weight is found to
decrease with increasing rather than increase as it does in the pure
Dirac limit.Comment: 11 pages, 8 figures, to appear in PR
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Atomic electron tomography in three and four dimensions
Atomic electron tomography (AET) has become a powerful tool for atomic-scale structural characterization in three and four dimensions. It provides the ability to correlate structures and properties of materials at the single-atom level. With recent advances in data acquisition methods, iterative three-dimensional (3D) reconstruction algorithms, and post-processing methods, AET can now determine 3D atomic coordinates and chemical species with sub-Angstrom precision, and reveal their atomic-scale time evolution during dynamical processes. Here, we review the recent experimental and algorithmic developments of AET and highlight several groundbreaking experiments, which include pinpointing the 3D atom positions and chemical order/disorder in technologically relevant materials and capturing how atoms rearrange during early nucleation at four-dimensional atomic resolution
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