Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFaithful derivation of symmetry indicators: A case study for topological superconductors with time-reversal and inversion symmetries
125
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Topological crystalline superconductors have attracted rapidly rising attention due to the possibility of higher-order phases, which support Majorana modes on boundaries in $d-2$ or lower dimensions. However, although the classification and bulk topological invariants in such systems have been well studied, it is generally difficult to faithfully predict the boundary Majoranas from the band-structure information due to the lack of well-established bulk-boundary correspondence. Here we propose a protocol for deriving symmetry indicators that depend on a minimal set of necessary symmetry data of the bulk bands and can diagnose boundary features. Specifically, to obtain indicators manifesting clear bulk-boundary correspondence, we combine the topological crystal classification scheme in the real space and a twisted equivariant K group analysis in the momentum space. The key step is to disentangle the generally mixed strong and weak indicators through a systematic basis-matching procedure between our real-space and momentum-space approaches. We demonstrate our protocol using an example of two-dimensional time-reversal odd-parity superconductors, where the inversion symmetry is known to protect a higher-order phase with corner Majoranas. Symmetry indicators derived from our protocol can be readily applied to ab initio database and could fuel material predictions for strong and weak topological crystalline superconductors with various boundary features.
rate research
Read More
Topological crystalline superconductors are known to have possible higher-order topology, which results in Majorana modes on $d-2$ or lower dimensional boundaries. Given the rich possibilities of boundary signatures, it is desirable to have topological invariants that can predict the type of Majorana modes from band structures. Although symmetry indicators, a type of invariants that depends only on the band data at high-symmetry points, have been proposed for certain crystalline superconductors, there exist symmetry classes in which symmetry indicators fail to distinguish superconductors with different Majorana boundaries. Here, we systematically obtain topological invariants for an example of this kind, the two-dimensional time-reversal symmetric superconductors with two-fold rotational symmetry $C_2$. First, we show that the non-trivial topology is independent of band data on the high-symmetry points by conducting a momentum-space classification study. Then from the resulting K groups, we derive calculable expressions for four $mathbb{Z}_2$ invariants defined on the high-symmetry lines or general points in the Brillouin zone. Finally, together with a real-space classification study, we establish the bulk-boundary correspondence and show that the four $mathbb{Z}_2$ invariants can predict Majorana boundary types from band structures. Our proposed invariants can fuel practical material searches for $C_2$-symmetric topological superconductors featuring Majorana edge and corner modes.
The collective mode spectrum of a symmetry-breaking state, such as a superconductor, provides crucial insight into the nature of the order parameter. In this context, we present a microscopic weak-coupling theory for the collective modes of a generic multi-component time-reversal symmetry breaking superconductor, and show that fluctuations in the relative amplitude and phase of the two order parameter components are well-defined underdamped collective modes, even in the presence of nodal quasiparticles. We then demonstrate that these generalized clapping modes can be detected using a number of experimental techniques including ac electronic compressibility measurements, electron energy loss spectroscopy, microwave spectroscopy, and ultrafast THz spectroscopy. Finally, we discuss the implications of our work as a new form of collective mode spectroscopy that drastically expands the number of experimental probes capable of detecting time-reversal symmetry breaking in unconventional superconductors such as Sr$_{text{2}}$RuO$_{text{4}}$, UTe$_{text{2}}$, and moire heterostructures.
We present results of numerical studies of spin quantum Hall transitions in disordered superconductors, in which the pairing order parameter breaks time-reversal symmetry. We focus mainly on p-wave superconductors in which one of the spin components is conserved. The transport properties of the system are studied by numerically diagonalizing pairing Hamiltonians on a lattice, and by calculating the Chern and Thouless numbers of the quasiparticle states. We find that in the presence of disorder, (spin-)current carrying states exist only at discrete critical energies in the thermodynamic limit, and the spin-quantum Hall transition driven by an external Zeeman field has the same critical behavior as the usual integer quantum Hall transition of non-interacting electrons. These critical energies merge and disappear as disorder strength increases, in a manner similar to those in lattice models for integer quantum Hall transition.
Fascinating phenomena have been known to arise from the Dirac theory of relativistic quantum mechanics, which describes high energy particles having linear dispersion relations. Electrons in solids usually have non-relativistic dispersion relations but their quantum excitations can mimic relativistic effects. In topological insulators, electrons have both a linear dispersion relation, the Dirac behavior, on the surface and a non-relativistic energy dispersion in the bulk. Topological phases of matter have attracted much interest, particularly broken-symmetry phases in topological insulator materials. Here, we report by Nb doping that the topological insulator Bi2Se3 can be turned into a bulk type-II superconductor while the Dirac surface dispersion in the normal state is preserved. A macroscopic magnetic ordering appears below the superconducting critical temperature of 3.2 K indicating a spontaneous spin rotation symmetry breaking of the Nb magnetic moments. Even though such a magnetic order may appear at the edge of the superconductor, it is mediated by superconductivity and presents a novel phase of matter which gives rise to a zero-field Hall effect.
In the recent search for unconventional- and topological superconductivity, noncentrosymmetric superconductors (NCSCs) rank among the most promising candidate materials. Surprisingly, some of them -- especially those containing rhenium -- seem to exhibit also time-reversal symmetry (TRS) breaking in their superconducting state, while TRS is preserved in many other isostructural NCSCs. To date, a satisfactory explanation for such discrepant behavior, albeit crucial for understanding the unconventional superconductivity of these materials, is still missing. Here we review the most recent developments regarding the Re-based class, where the muon-spin relaxation ($mu$SR) technique plays a key role due to its high sensitivity to the weak internal fields associated with the TRS breaking phenomenon. We discuss different cases of Re-containing superconductors, comprising both centrosymmetric- and noncentrosymmetric crystal structures and ranging from pure rhenium, to Re$T$ ($T$ = 3$d$-5$d$ early transition metals), to the dilute-Re case of ReBe$_{22}$. $mu$SR results suggest that the rhenium presence and its amount are two key factors for the appearance and the extent of TRS breaking in Re-based superconductors. Besides summarizing the existing findings, we also put forward future research ideas regarding the exciting field of materials showing TRS breaking.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
