Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userUniversalities of thermodynamic signatures in topological phases
87
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Topological insulators (superconductors) are materials that host symmetry-protected metallic edge states in an insulating (superconducting) bulk. Although they are well understood, a thermodynamic description of these materials remained elusive, firstly because the edges yield a non-extensive contribution to the thermodynamic potential, and secondly because topological field theories involve non-local order parameters, and cannot be captured by the Ginzburg-Landau formalism. Recently, this challenge has been overcome: by using Hill thermodynamics to describe the Bernevig-Hughes-Zhang model in two dimensions, it was shown that at the topological phase change the thermodynamic potential does not scale extensively due to boundary effects. Here, we extend this approach to different topological models in various dimensions (the Kitaev chain and Su-Schrieffer-Heeger model in one dimension, the Kane-Mele model in two dimensions and the Bernevig-Hughes-Zhang model in three dimensions) at zero temperature. Surprisingly, all models exhibit the same universal behavior in the order of the topological-phase transition, depending on the dimension. Moreover, we derive the topological phase diagram at finite temperature using this thermodynamic description, and show that it displays a good agreement with the one calculated from the Uhlmann phase. Our work reveals unexpected universalities and opens the path to a thermodynamic description of systems with a non-local order parameter.
rate research
Read More
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 present a physical construction of degenerate groundstates of the Moore-Read Pfaffian states, which exhibits non-Abelian statistics, on general Riemann surface with genus g. The construction is given by a generalization of the recent argument [M.O. and T. Senthil, Phys. Rev. Lett. 96, 060601 (2006)] which relates fraction- alization and topological order. The nontrivial groundstate degeneracy obtained by Read and Green [Phys. Rev. B 61, 10267 (2000)] based on differential geometry is reproduced exactly. Some restrictions on the statistics, due to the fractional charge of the quasiparticle are also discussed. Furthermore, the groundstate degeneracy of the p+ip superconductor in two dimensions, which is closely related to the Pfaffian states, is discussed with a similar construction.
We study a double-nanowire setup proximity coupled to an $s$-wave superconductor and search for the bulk signatures of the topological phase transition that can be observed experimentally, for example, with an STM tip. Three bulk quantities, namely, the charge, the spin polarization, and the pairing amplitude of intrawire superconductivity are studied in this work. The spin polarization and the pairing amplitude flip sign as the system undergoes a phase transition from the trivial to the topological phase. In order to identify promising ways to observe bulk signatures of the phase transition in transport experiments, we compute the spin current flowing between a local spin-polarized probe, such as an STM tip, and the double-nanowire system in the Keldysh formalism. We find that the spin current contains information about the sign flip of the bulk spin polarization and can be used to determine the topological phase transition point.
A fundamental dichotomous classification for all physical systems is according to whether they are spinless or spinful. This is especially crucial for the study of symmetry-protected topological phases, as the two classes have distinct symmetry algebra. As a prominent example, the spacetime inversion symmetry $PT$ satisfies $(PT)^2=pm 1$ for spinless/spinful systems, and each class features unique topological phases. Here, we reveal a possibility to switch the two fundamental classes via $mathbb{Z}_2$ projective representations. For $PT$ symmetry, this occurs when $P$ inverses the gauge transformation needed to recover the original $mathbb{Z}_2$ gauge connections under $P$. As a result, we can achieve topological phases originally unique for spinful systems in a spinless system, and vice versa. We explicitly demonstrate the claimed mechanism with several concrete models, such as Kramers degenerate bands and Kramers Majorana boundary modes in spinless systems, and real topological phases in spinful systems. Possible experimental realization of these models is discussed. Our work breaks a fundamental limitation on topological phases and opens an unprecedented possibility to realize intriguing topological phases in previously impossible systems.
Using superconducting quantum circuits, we propose an approach to construct a Kitaev lattice, i.e., an anisotropic spin model on a honeycomb lattice with three types of nearest-neighbor interactions. We study two particular cases to demonstrate topological states (i.e., the vortex and bond states) and show how the braiding statistics can be revealed. Our approach provides an experimentally realizable many-body system for demonstrating exotic properties of topological phases.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
