Author(s):

Authors: Alexander Altland, Dmitry Bagrets, Alex Kamenev

We present an analytic theory of quantum criticality in quasi one-dimensional
topological Anderson insulators. We describe these systems in terms of two
parameters $(g,\chi)$ representing localization and topological properties,
respectively. Certain critical values of $\chi$ (half-integer for $\Bbb{Z}$
classes, or zero for $\Bbb{Z}_2$ classes) define phase boundaries between
distinct topological sectors. Upon increasing system size, the two parameters
exhibit flow similar to the celebrated two parameter flow of the integer
quantum Hall insulator. However, unlike the quantum Hall system, an exact
analytical description of the entire phase diagram can be given in terms of the
transfer-matrix solution of corresponding supersymmetric non-linear
sigma-models. In $\Bbb{Z}_2$ classes we uncover a hidden supersymmetry, present
at the quantum critical point.

link to article (opens in new tab)

 

Author(s):

Authors: Hiroki Isobe, Naoto Nagaosa

We theoretically study the electromagnetic interaction in Dirac systems with
$N$ nodes by using the renormalization group, which is relevant to the quantum
critical phenomena of topological phase transition ($N=1$) and Weyl semimetals
($N=4$ or $N=12$). Compared with the previous work for $N=1$ [H. Isobe and N.
Nagaosa, Phys. Rev. B 86, 165127 (2012); arXiv:1205.2427], we obtained the
analytic solution for the large $N$ limit, which differs qualitatively for the
scaling of the speed of light $c$ and that of electron $v$, i.e., $v$ does
notchange while $c$ is reduced to $v$. We also found a reasonably accurate
approximate analytic solution for generic $N$, which well interpolates between
$N=1$ and large $N$ limit, and it concludes that $c^2 v^N$ is almost
unrenormalized. The temperature dependence of the physical properties, the
dielectric constant, magnetic susceptibility, spectral function, DC
conductivity, and mass gap are discussed based on these results.

link to article (opens in new tab)

 

Author(s):

Authors: Wanjun Jiang, Pramey Upadhyaya, Wei Zhang, Guoqiang Yu, M. Benjamin Jungfleisch, Frank Y. Fradin, John E. Pearson, Yaroslav Tserkovnyak, Kang L. Wang, Olle Heinonen, Suzanne G. E. te Velthuis, Axel Hoffmann

Soap bubbles form when blowing air through a suspended thin film of soapy
water and this phenomenon entertains children and adults alike. The formation
of soap bubbles from thin films is accompanied by topological transitions, and
thus the natural question arises whether this concept is applicable to the
generation of other topological states. Here we show how a magnetic topological
structure, namely a skyrmion bubble, can be generated in a solid state system
in a similar manner. Beyond enabling the investigation of complex
surface-tension driven dynamics in a novel physical system, this observation
has also practical implications, since the topological charge of magnetic
skyrmions has been envisioned as an information carrier for new data processing
technologies. A main goal towards this end is the experimental creation and
manipulation of individual mobile skyrmions at room temperature. By utilizing
an inhomogeneous in-plane current in a system with broken inversion asymmetry,
we experimentally blow magnetic skyrmion bubbles through a geometrical
constriction. The presence of a spatially divergent spin-orbit torque gives
rise to instabilities of the magnetic domain structures that are reminiscent of
Rayleigh-Plateau instabilities in fluid flows. Experimentally we can determine
the electric current versus magnetic field phase diagram for skyrmion formation
and we reveal the efficient manipulation of these dynamically created
skyrmions, including depinning and motion. The demonstrated current-driven
transformation from stripe domains to magnetic skyrmion bubbles could provide
additional avenues for implementing skyrmion-based spintronics.

link to article (opens in new tab)

 

Author(s):

Authors: Yi-Zhuang You, Cenke Xu

By definition, the physics of the $d-$dimensional (dim) boundary of a
$(d+1)-$dim symmetry protected topological (SPT) state cannot be realized as
itself on a $d-$dim lattice. If the symmetry of the system is unitary, then a
formal way to determine whether a $d-$dim theory must be a boundary or not, is
to couple this theory to a gauge field (or to “gauge” its symmetry), and check
if there is a gauge anomaly. In this paper we discuss the following question:
can the boundary of a SPT state be driven into a fully gapped topological order
which preserves all the symmetries? We argue that if the gauge anomaly of the
boundary is “perturbative”, then the boundary must remain gapless; while if the
boundary only has global gauge anomaly but no perturbative anomaly, then it is
possible to gap out the boundary by driving it into a topological state, when
$d \geq 2$. We will demonstrate this conclusion with two examples: (1) the $3d$
spin-1/2 chiral fermion with the well-known Witten’s global anomaly, which is
the boundary of a $4d$ topological superconductor with SU(2) or U(1)$\rtimes
Z_2$ symmetry; and (2) the $4d$ boundary of a $5d$ topological superconductor
with the same symmetry. We show that these boundary systems can be driven into
a fully gapped $\mathbb{Z}_{2N}$ topological order with topological degeneracy,
but this $\mathbb{Z}_{2N}$ topological order cannot be future driven into a
trivial confined phase that preserves all the symmetries due to some special
properties of its topological defects.

link to article (opens in new tab)

 

Author(s):

Authors: J. H. Pixley, Pallab Goswami, S. Das Sarma

We study the phase diagram of a three dimensional non-interacting Dirac
semimetal in the presence of both quenched axial and scalar potential disorder,
by calculating the average and the typical density of states as well as the
inverse participation ratio using numerically exact methods. We show that as a
function of the disorder strength a half-filled (i.e. undoped) Dirac semimetal
displays three distinct ground states, namely an incompressible semimetal, a
compressible diffusive metal, and a localized Anderson insulator, in stark
contrast to a conventional dirty metal that only supports the latter two
phases. We establish the existence of two distinct quantum critical points,
which respectively govern the semimetal-metal and the metal-insulator quantum
phase transitions. Away from half-filling the system behaves as an ordinary
diffusive metal that can undergo Anderson localization only, which is shown by
determining the mobility edge and the phase diagram in terms of energy and
disorder.

link to article (opens in new tab)

 

Author(s):

Authors: Tahereh Mazaheri, Gerardo Ortiz, Zohar Nussinov, Alexander Seidel

We introduce a “second-quantized” representation of the ring of symmetric
functions to further develop a purely second-quantized — or “lattice” –
approach to the study of zero modes of frustration free
Haldane-pseudo-potential-type Hamiltonians, which in particular stabilize
Laughlin ground states. We present three applications of this formalism. We
start demonstrating how to systematically construct all zero-modes of
Laughlin-type parent Hamiltonians in a framework that is free of
first-quantized polynomial wave functions, and show that they are in one-to-one
correspondence with dominance patterns. The starting point here is the
pseudo-potential Hamiltonian in “lattice form”, stripped of all information
about the analytic structure of Landau levels (dynamical momenta). Secondly, as
a by-product, we make contact with the bosonization method, and obtain an
alternative proof for the equivalence between bosonic and fermionic Fock
spaces. Finally, we explicitly derive the second-quantized version of Read’s
non-local (string) order parameter for the Laughlin state, extending an earlier
description by Stone. Commutation relations between the local quasi-hole
operator and the local electron operator are generalized to various geometries.

link to article (opens in new tab)

 

Author(s):

Authors: A. Pertsova, C.M. Canali, A.H. MacDonald

The response of thin films of Bi$_2$Se$_3$ to a strong perpendicular magnetic
field is investigated by performing magnetic bandstructure calculations for a
realistic multi-band tight-binding model. Several crucial features of Landau
quantization in a realistic three-dimensional topological insulator are
revealed. The $n=0$ Landau level is absent in ultra-thin films, in agreement
with experiment. In films with a crossover thickness of five quintuple layers,
there is a signature of the $n=0$ level, whose overall trend as a function of
magnetic field matches the established low-energy effective-model result.
Importantly, we find a field-dependent splitting and a strong spin-polarization
of the $n=0$ level which can be measured experimentally at reasonable field
strengths. Our calculations show mixing between the surface and bulk Landau
levels which causes the character of levels to evolve with magnetic field.

link to article (opens in new tab)

 

Author(s):

Authors: Sthitadhi Roy, Krishanu Roychowdhury, Sourin Das

Inducing finite magnetization on the surface of 3-D topological insulator
(TI) has been a topic of recent interest. In this letter we argue that even the
pristine TI surfaces states are perfect analogs of ferromagnetic half metals
due to complete polarisation of an emergent momentum independent pseudo-spin
(SU(2)) degree of freedom (D.O.F) on the surface which in general is a
combination of spin (\sigma) and orbital parity (\tau) quantum numbers of
electrons belonging to a unit cell of TI crystals. To put this claim on firm
footing, we present analytic results which clearly show that the tunneling
conductance between two arbitrary TI surfaces of the same TI material is
dominated by this half metallic behaviour leading to physics reminiscent of a
spin-valve. These findings provide a completely new perspective on using TI-TI
junctions for device applications.

link to article (opens in new tab)

 

Author(s):

Authors: Christoph Kastl (1 and 2), Paul Seifert (1 and 2), Xiaoyue He (3), Kehui Wu (3), Yongqing Li (3), Alexander Holleitner (1 and 2) ((1) Walter Schottky Institut and Physik-Department, Technische Universität München, (2) Nanosystems Initiative Munich (NIM), (3) Institute of Physics, Chinese Academy of Sciences, Beijing)

We investigate the photocurrent properties of the topological insulator
(Bi$_{0.5}$Sb$_{0.5}$)$_2$Te$_3$ on SrTiO$_3$-substrates. We find reproducible,
submicron photocurrent patterns generated by long-range chemical potential
fluctuations, occurring predominantly at the topological insulator/substrate
interface. We fabricate nano-plowed constrictions which comprise single
potential fluctuations. Hereby, we can quantify the magnitude of the disorder
potential to be in the meV range. The results further suggest a dominating
photo-thermoelectric current generated in the surface states in such nanoscale
constrictions.

link to article (opens in new tab)

 

Author(s):

Authors: Jinsong Zhang, Xiao Feng, Yong Xu, Minghua Guo, Zuocheng Zhang, Yunbo Ou, Yang Feng, Kang Li, Haijun Zhang, Lili Wang, Xi Chen, Zhongxue Gan, Shou-Cheng Zhang, Ke He, Xucun Ma, Qi-Kun Xue, Yayu Wang

We report transport studies on (Bi,Sb)2Te3 topological insulator thin films
with tunable electronic band structure. We find a doping and temperature regime
in which the Hall coefficient is negative indicative of electron-type carriers,
whereas the Seebeck coefficient is positive indicative of hole-type carriers.
This sign anomaly is due to the distinct transport behaviors of the bulk and
surface states: the surface Dirac fermions dominate magnetoelectric transport
while the thermoelectric effect is mainly determined by the bulk states. These
findings may inspire new ideas for designing topological insulator-based high
efficiency thermoelectric devices.

link to article (opens in new tab)

 

Author(s):

We present an analytic theory of quantum criticality in quasi one-dimensional
topological Anderson insulators. We describe these systems in terms of two
parameters $(g,\chi)$ representing localization and topological properties,
respectively. Certain critical values of $\chi$ (half-integer for $\Bbb{Z}$
classes, or zero for $\Bbb{Z}_2$ classes) define phase boundaries between
distinct topological sectors. Upon increasing system size, the two parameters
exhibit flow similar to the celebrated two parameter flow of the integer
quantum Hall insulator. However, unlike the quantum Hall system, an exact
analytical description of the entire phase diagram can be given in terms of the
transfer-matrix solution of corresponding supersymmetric non-linear
sigma-models. In $\Bbb{Z}_2$ classes we uncover a hidden supersymmetry, present
at the quantum critical point.

link to article (opens in new tab)

 

Author(s):

We theoretically study the electromagnetic interaction in Dirac systems with
$N$ nodes by using the renormalization group, which is relevant to the quantum
critical phenomena of topological phase transition ($N=1$) and Weyl semimetals
($N=4$ or $N=12$). Compared with the previous work for $N=1$ [H. Isobe and N.
Nagaosa, Phys. Rev. B 86, 165127 (2012); arXiv:1205.2427], we obtained the
analytic solution for the large $N$ limit, which differs qualitatively for the
scaling of the speed of light $c$ and that of electron $v$, i.e., $v$ does
notchange while $c$ is reduced to $v$. We also found a reasonably accurate
approximate analytic solution for generic $N$, which well interpolates between
$N=1$ and large $N$ limit, and it concludes that $c^2 v^N$ is almost
unrenormalized. The temperature dependence of the physical properties, the
dielectric constant, magnetic susceptibility, spectral function, DC
conductivity, and mass gap are discussed based on these results.

link to article (opens in new tab)

 

Author(s):

Soap bubbles form when blowing air through a suspended thin film of soapy
water and this phenomenon entertains children and adults alike. The formation
of soap bubbles from thin films is accompanied by topological transitions, and
thus the natural question arises whether this concept is applicable to the
generation of other topological states. Here we show how a magnetic topological
structure, namely a skyrmion bubble, can be generated in a solid state system
in a similar manner. Beyond enabling the investigation of complex
surface-tension driven dynamics in a novel physical system, this observation
has also practical implications, since the topological charge of magnetic
skyrmions has been envisioned as an information carrier for new data processing
technologies. A main goal towards this end is the experimental creation and
manipulation of individual mobile skyrmions at room temperature. By utilizing
an inhomogeneous in-plane current in a system with broken inversion asymmetry,
we experimentally blow magnetic skyrmion bubbles through a geometrical
constriction. The presence of a spatially divergent spin-orbit torque gives
rise to instabilities of the magnetic domain structures that are reminiscent of
Rayleigh-Plateau instabilities in fluid flows. Experimentally we can determine
the electric current versus magnetic field phase diagram for skyrmion formation
and we reveal the efficient manipulation of these dynamically created
skyrmions, including depinning and motion. The demonstrated current-driven
transformation from stripe domains to magnetic skyrmion bubbles could provide
additional avenues for implementing skyrmion-based spintronics.

link to article (opens in new tab)

 

Author(s):

By definition, the physics of the $d-$dimensional (dim) boundary of a
$(d+1)-$dim symmetry protected topological (SPT) state cannot be realized as
itself on a $d-$dim lattice. If the symmetry of the system is unitary, then a
formal way to determine whether a $d-$dim theory must be a boundary or not, is
to couple this theory to a gauge field (or to “gauge” its symmetry), and check
if there is a gauge anomaly. In this paper we discuss the following question:
can the boundary of a SPT state be driven into a fully gapped topological order
which preserves all the symmetries? We argue that if the gauge anomaly of the
boundary is “perturbative”, then the boundary must remain gapless; while if the
boundary only has global gauge anomaly but no perturbative anomaly, then it is
possible to gap out the boundary by driving it into a topological state, when
$d \geq 2$. We will demonstrate this conclusion with two examples: (1) the $3d$
spin-1/2 chiral fermion with the well-known Witten’s global anomaly, which is
the boundary of a $4d$ topological superconductor with SU(2) or U(1)$\rtimes
Z_2$ symmetry; and (2) the $4d$ boundary of a $5d$ topological superconductor
with the same symmetry. We show that these boundary systems can be driven into
a fully gapped $\mathbb{Z}_{2N}$ topological order with topological degeneracy,
but this $\mathbb{Z}_{2N}$ topological order cannot be future driven into a
trivial confined phase that preserves all the symmetries due to some special
properties of its topological defects.

link to article (opens in new tab)

 

Author(s):

We study the phase diagram of a three dimensional non-interacting Dirac
semimetal in the presence of both quenched axial and scalar potential disorder,
by calculating the average and the typical density of states as well as the
inverse participation ratio using numerically exact methods. We show that as a
function of the disorder strength a half-filled (i.e. undoped) Dirac semimetal
displays three distinct ground states, namely an incompressible semimetal, a
compressible diffusive metal, and a localized Anderson insulator, in stark
contrast to a conventional dirty metal that only supports the latter two
phases. We establish the existence of two distinct quantum critical points,
which respectively govern the semimetal-metal and the metal-insulator quantum
phase transitions. Away from half-filling the system behaves as an ordinary
diffusive metal that can undergo Anderson localization only, which is shown by
determining the mobility edge and the phase diagram in terms of energy and
disorder.

link to article (opens in new tab)

 

Author(s):

We introduce a “second-quantized” representation of the ring of symmetric
functions to further develop a purely second-quantized — or “lattice” –
approach to the study of zero modes of frustration free
Haldane-pseudo-potential-type Hamiltonians, which in particular stabilize
Laughlin ground states. We present three applications of this formalism. We
start demonstrating how to systematically construct all zero-modes of
Laughlin-type parent Hamiltonians in a framework that is free of
first-quantized polynomial wave functions, and show that they are in one-to-one
correspondence with dominance patterns. The starting point here is the
pseudo-potential Hamiltonian in “lattice form”, stripped of all information
about the analytic structure of Landau levels (dynamical momenta). Secondly, as
a by-product, we make contact with the bosonization method, and obtain an
alternative proof for the equivalence between bosonic and fermionic Fock
spaces. Finally, we explicitly derive the second-quantized version of Read’s
non-local (string) order parameter for the Laughlin state, extending an earlier
description by Stone. Commutation relations between the local quasi-hole
operator and the local electron operator are generalized to various geometries.

link to article (opens in new tab)

 

Author(s):

The response of thin films of Bi$_2$Se$_3$ to a strong perpendicular magnetic
field is investigated by performing magnetic bandstructure calculations for a
realistic multi-band tight-binding model. Several crucial features of Landau
quantization in a realistic three-dimensional topological insulator are
revealed. The $n=0$ Landau level is absent in ultra-thin films, in agreement
with experiment. In films with a crossover thickness of five quintuple layers,
there is a signature of the $n=0$ level, whose overall trend as a function of
magnetic field matches the established low-energy effective-model result.
Importantly, we find a field-dependent splitting and a strong spin-polarization
of the $n=0$ level which can be measured experimentally at reasonable field
strengths. Our calculations show mixing between the surface and bulk Landau
levels which causes the character of levels to evolve with magnetic field.

link to article (opens in new tab)

 

Author(s):

Inducing finite magnetization on the surface of 3-D topological insulator
(TI) has been a topic of recent interest. In this letter we argue that even the
pristine TI surfaces states are perfect analogs of ferromagnetic half metals
due to complete polarisation of an emergent momentum independent pseudo-spin
(SU(2)) degree of freedom (D.O.F) on the surface which in general is a
combination of spin (\sigma) and orbital parity (\tau) quantum numbers of
electrons belonging to a unit cell of TI crystals. To put this claim on firm
footing, we present analytic results which clearly show that the tunneling
conductance between two arbitrary TI surfaces of the same TI material is
dominated by this half metallic behaviour leading to physics reminiscent of a
spin-valve. These findings provide a completely new perspective on using TI-TI
junctions for device applications.

link to article (opens in new tab)

 

Author(s):

We investigate the photocurrent properties of the topological insulator
(Bi$_{0.5}$Sb$_{0.5}$)$_2$Te$_3$ on SrTiO$_3$-substrates. We find reproducible,
submicron photocurrent patterns generated by long-range chemical potential
fluctuations, occurring predominantly at the topological insulator/substrate
interface. We fabricate nano-plowed constrictions which comprise single
potential fluctuations. Hereby, we can quantify the magnitude of the disorder
potential to be in the meV range. The results further suggest a dominating
photo-thermoelectric current generated in the surface states in such nanoscale
constrictions.

link to article (opens in new tab)

 

Author(s):

We report transport studies on (Bi,Sb)2Te3 topological insulator thin films
with tunable electronic band structure. We find a doping and temperature regime
in which the Hall coefficient is negative indicative of electron-type carriers,
whereas the Seebeck coefficient is positive indicative of hole-type carriers.
This sign anomaly is due to the distinct transport behaviors of the bulk and
surface states: the surface Dirac fermions dominate magnetoelectric transport
while the thermoelectric effect is mainly determined by the bulk states. These
findings may inspire new ideas for designing topological insulator-based high
efficiency thermoelectric devices.

link to article (opens in new tab)

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