8,336 research outputs found
Dirac points merging and wandering in a model Chern insulator
We present a model for a Chern insulator on the square lattice with complex
first and second neighbor hoppings and a sublattice potential which displays an
unexpectedly rich physics. Similarly to the celebrated Haldane model, the
proposed Chern insulator has two topologically non-trivial phases with Chern
numbers . As a distinctive feature of the present model, phase
transitions are associated to Dirac points that can move, merge and split in
momentum space, at odds with Haldane's Chern insulator where Dirac points are
bound to the corners of the hexagonal Brillouin zone. Additionally, the
obtained phase diagram reveals a peculiar phase transition line between two
distinct topological phases, in contrast to the Haldane model where such
transition is reduced to a point with zero sublattice potential. The model is
amenable to be simulated in optical lattices, facilitating the study of phase
transitions between two distinct topological phases and the experimental
analysis of Dirac points merging and wandering
Hall conductivity as bulk signature of topological transitions in superconductors
Topological superconductors may undergo transitions between phases with
different topological numbers which, like the case of topological insulators,
are related to the presence of gapless (Majorana) edge states. In
topological insulators the charge Hall conductivity is quantized, being
proportional to the number of gapless states running at the edge. In a
superconductor, however, charge is not conserved and, therefore,
is not quantized, even in the case of a topological
superconductor. Here it is shown that while the evolves
continuously between different topological phases of a topological
superconductor, its derivatives display sharp features signaling the
topological transitions. We consider in detail the case of a triplet
superconductor with p-wave symmetry in the presence of Rashba spin-orbit (SO)
coupling and externally applied Zeeman spin splitting. Generalization to the
cases where the pairing vector is not aligned with that of the SO coupling is
given. We generalize also to the cases where the normal system is already
topologically non-trivial.Comment: 10 pages, 10 figure
Third-order topological insulator induced by disorder
We have found the first instance of a third-order topological Anderson
insulator (TOTAI). This disorder-induced topological phase is gapped and
characterized by a quantized octupole moment and topologically protected corner
states, as revealed by a detailed numerically exact analysis. We also find that
the disorder-induced transition into the TOTAI phase can be analytically
captured with remarkable accuracy using the self-consistent Born approximation.
For a larger disorder strength, the TOTAI undergoes a transition to a trivial
diffusive metal, that in turn becomes an Anderson insulator at even larger
disorder. Our findings show that disorder can induce third-order topological
phases in 3D, therefore extending the class of known higher-order topological
Anderson insulators
Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
We develop a renormalization group (RG) description of the localization
properties of onedimensional (1D) quasiperiodic lattice models. The RG flow is
induced by increasing the unit cell of subsequent commensurate approximants.
Phases of quasiperiodic systems are characterized by RG fixed points associated
with renormalized single-band models. We identify fixed-points that include
many previously reported exactly solvable quasiperiodic models. By classifying
relevant and irrelevant perturbations, we show that phase boundaries of more
generic models can be determined with exponential accuracy in the approximant's
unit cell size, and in some cases analytically. Our findings provide a unified
understanding of widely different classes of 1D quasiperiodic systems
Change of an insulator's topological properties by a Hubbard interaction
We introduce two dimensional fermionic band models with two orbitals per
lattice site, or one spinful orbital, and which have a non-zero topological
Chern number that can be changed by varying the ratio of hopping parameters. A
topologically non-trivial insulator is then realized if there is one fermion
per site. When interactions in the framework of the Hubbard model are
introduced, the effective hopping parameters are renormalized and the system's
topological number can change at a certain interaction strength, ,
smaller than that for the Mott transition. Two different situations may then
occur: either the anomalous Hall conductivity changes abruptly at
, as the system undergoes a transition from one topologically
non-trivial insulator to another, or the transition is through an anomalous
Hall metal, and changes smoothly between two different quantized
values as grows. Restoring time-reversal symmetry by adding spin to
spinless models, the half-filled system becomes a topological
insulator. The topological number then changes at a critical coupling
and the quantized spin Hall response changes abruptly.Comment: 5 pages, 3 figure
Incommensurability-Induced Enhancement of Superconductivity in One Dimensional Critical Systems
We show that incommensurability can enhance superconductivity in one
dimensional quasiperiodic systems with s-wave pairing. As a parent model, we
use a generalized Aubry-Andr\'e model that includes quasiperiodic modulations
both in the potential and in the hoppings. In the absence of interactions, the
model contains extended, critical and localized phases for incommensurate
modulations. Our results reveal that in a substantial region inside the parent
critical phase, there is a significant increase of the superconducting critical
temperature compared to the extended phase and the uniform limit without
quasiperiodic modulations. We also analyse the results for commensurate
modulations with period close to the selected incommensurate one. We find that
while in the commensurate case, the scaling of the critical temperature with
interaction strength follows the exponentially small weak-coupling BCS
prediction for a large enough system size, it scales algebraically in the
incommensurate case within the critical and localized parent phases. These
qualitatively distinct behaviors lead to a significant
incommensurability-induced enhancement of the critical temperature in the weak
and intermediate coupling regimes, accompanied by an increase in the
superconducting order parameter at zero temperature.Comment: 8 pages, 4 figure
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