Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTopology of critical chiral phases: multiband insulators and superconductors
74
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Recent works have proved the existence of symmetry-protected edge states in certain one-dimensional topological band insulators and superconductors at the gap-closing points which define quantum phase transitions between two topologically nontrivial phases. We show how this picture generalizes to multiband critical models belonging to any of the chiral symmetry classes AIII, BDI, or CII of noninteracting fermions in one dimension.
rate research
Read More
Topological classification in our previous paper [K. Shiozaki and M. Sato, Phys. Rev. B ${bf 90}$, 165114 (2014)] is extended to nonsymmorphic crystalline insulators and superconductors. Using the twisted equivariant $K$-theory, we complete the classification of topological crystalline insulators and superconductors in the presence of additional order-two nonsymmorphic space group symmetries. The order-two nonsymmorphic space groups include half lattice translation with $Z_2$ flip, glide, two-fold screw, and their magnetic space groups. We find that the topological periodic table shows modulo-2 periodicity in the number of flipped coordinates under the order-two nonsymmorphic space group. It is pointed out that the nonsymmorphic space groups allow $mathbb{Z}_2$ topological phases even in the absence of time-reversal and/or particle-hole symmetries. Furthermore, the coexistence of the nonsymmorphic space group with the time-reversal and/or particle-hole symmetries provides novel $mathbb{Z}_4$ topological phases, which have not been realized in ordinary topological insulators and superconductors. We present model Hamiltonians of these new topological phases and the analytic expression of the $mathbb{Z}_2$ and $mathbb{Z}_4$ topological invariants. The half lattice translation with $Z_2$ spin flip and glide symmetry are compatible with the existence of the boundary, leading to topological surface gapless modes protected by such order-two nonsymmorphic symmetries. We also discuss unique features of these gapless surface modes.
Systems of free fermions are classified by symmetry, space dimensionality, and topological properties described by K-homology. Those systems belonging to different classes are inequivalent. In contrast, we show that by taking a many-body/Fock space viewpoint it becomes possible to establish equivalences of topological insulators and superconductors in terms of duality transformations. These mappings connect topologically inequivalent systems of fermions, jumping across entries in existent classification tables, because of the phenomenon of symmetry transmutation by which a symmetry and its dual partner have identical algebraic properties but very different physical interpretations. To constrain our study to established classification tables, we define and characterize mathematically Gaussian dualities as dualities mapping free fermions to free fermions (and interacting to interacting). By introducing a large, flexible class of Gaussian dualities we show that any insulator is dual to a superconductor, and that fermionic edge modes are dual to Majorana edge modes, that is, the Gaussian dualities of this paper preserve the bulk-boundary correspondence. Transmutation of relevant symmetries, particle number, translation, and time reversal is also investigated in detail. As illustrative examples, we show the duality equivalence of the dimerized Peierls chain and the Majorana chain of Kitaev, and a two-dimensional Kekule-type topological insulator, including graphene as a special instance in coupling space, dual to a p-wave superconductor. Since our analysis extends to interacting fermion systems we also briefly discuss some such applications.
We analyze the topological properties of a chiral ${p}+i{p}$ superconductor for a two-dimensional metal/semimetal with four Dirac points. Such a system has been proposed to realize second-order topological superconductivity and host corner Majorana modes. We show that with an additional $mathsf{C}_4$ rotational symmetry, the system is in an intrinsic higher-order topological superconductor phase, and with a lower and more natural $mathsf{C}_2$ symmetry, is in a boundary-obstructed topological superconductor phase. The boundary topological obstruction is protected by a bulk Wannier gap. However, we show that the well-known nested-Wilson loop is in general unquantized despite the particle-hole symmetry, and thus fails as a topological invariant. Instead, we show that the higher-order topology and boundary-obstructed topology can be characterized using an alternative defect classification approach, in which the corners of a finite sample is treated as a defect of a space-filling Hamiltonian. We establish Dirac+$({p}+i{p})$ as a sufficient condition for second-order topological superconductivity.
The dynamics of chaotic systems are, by definition, exponentially sensitive to initial conditions and may appear rather random. In this work, we explore relations between the chaotic dynamics of an observable and the dynamics of information (entropy) contained in this observable, focussing on a disordered metal coupled to a dissipative, e.g. phononic, bath. The chaotic dynamics is characterised by Lyapunov exponents $lambda$, the rates of growth of out-of-time order correlators (OTOCs), quantities of the form $langle[hat A(t),hat B(0)]^{2}rangleproptoexp(2lambda t)$, where $hat A$ and $hat B$ are the operators of, e.g., the total current of electrons in a metallic quantum dot. We demonstrate that the Lyapunov exponent $lambda$ matches the rate of decay of information stored in the observable $langle hat A(t)rangle$ after applying a small perturbation with a small classical uncertainty. This relation suggests a way to measure Lyapunov exponents in experiment. We compute both the Lyapunov exponent and the rate of decay of information microscopically in a disordered metal in the presence of a bosonic bath, which may, in particular, represent interactions in the system. For a sufficiently short range of the correlations in the bath, the exponent has the form $lambda=lambda_{0}-1/tau$, where $lambda_{0}$ is the (temperature-independent) Lyapunov exponent in the absence of the bath and $1/tau$ is the inelastic scattering rate. Our results demonstrate also the existence of a transition between chaotic and non-chaotic behaviour at $lambda_{0}=1/tau$, which may be triggered, e.g., by changing the temperature of the bath.
A method of determining the temperature of the nonradiative reservoir in a microcavity exciton-polariton system is developed. A general relation for the homogeneous polariton linewidth is theoretically derived and experimentally used in the method. In experiments with a GaAs microcavity under nonresonant pulsed excitation, the reservoir temperature dynamics is extracted from the polariton linewidth. Within the first nanosecond the reservoir temperature greatly exceeds the lattice temperature and determines the dynamics of the major processes in the system. It is shown that, for nonresonant pulsed excitation of GaAs microcavities, the polariton Bose-Einstein condensation is typically governed by polariton-phonon scattering, while interparticle scattering leads to condensate depopulation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
