Increasing the number of topological nodal lines in semimetals via uniaxial pressure

The application of pressure has been demonstrated to induce intriguing phase transitions in topological nodal-line semimetals. In this work we analyze how uniaxial pressure affects the topological character of BaSn$$_2$$ 2 , a Dirac nodal-line semimetal in the absence of spin-orbit coupling. Using calculations based on the density functional theory and a model tight-binding Hamiltonian, we find the emergence of a second nodal line for pressures higher than 4 GPa. We examine the topological features of both phases demonstrating that a nontrivial character is present in both of them. Thus, providing evidence of a topological-to-topological phase transition in which the number of topological nodal lines increases. The orbital overlap increase between Ba $$d_{xz}$$ d xz and $$d_{yz}$$ d yz orbitals and Sn $$p_z$$ p z orbitals and the preservation of crystal symmetries are found to be responsible for the advent of this transition. Furthermore, we pave the way to experimentally test this kind of transition by obtaining a topological relation between the zero-energy modes that arise in each phase when a magnetic field is applied.

Fonctions zêta ℓ-modulaires

Let F be a non-Archimedean locally compact field, of residual characteristic p, and let D be a finite-dimensional central division F-algebra. Let ℓ be a prime number different from p. In this article, generalizing the results of [GJ], we associate, to each ℓ-modular smooth irreducible representation π of GLm(D), two invariants L(T,π), ε(T,π,ψ), where T is an indeterminate and ψ is a nontrivial character of F.

Monodromy group for a strongly semistable principal bundle over a curve, II

Let X be a geometrically irreducible smooth projective curve defined over a field k. Assume that X has a k–rational point; fix a k–rational point x ε X. From these data we construct an affine group scheme X defined over the field k as well as a principal X–bundle over the curve X. The group scheme X is given by a ℚ–graded neutral Tannakian category built out of all strongly semistable vector bundles over X. The principal bundle is tautological. Let G be a linear algebraic group, defined over k, that does not admit any nontrivial character which is trivial on the connected component, containing the identity element, of the reduced center of G. Let EG be a strongly semistable principal G–bundle over X. We associate to EG a group scheme M defined over k, which we call the monodromy group scheme of EG, and a principal M–bundle EM over X, which we call the monodromy bundle of EG. The group scheme M is canonically a quotient of X, and EM is the extension of structure group of . The group scheme M is also canonically embedded in the fiber Ad(EG)x over x of the adjoint bundle.

TWISTED CHARACTER OF A SMALL REPRESENTATION OF GL(4)

We compute by a purely local method the (elliptic) θ-twisted character χπY of the representation πY = I(3, 1)(13 × χY) of G = GL (4, F), where F is a p-adic field, p ≠ 2, and Y is an unramified quadratic extension of F; χY is the nontrivial character of F×/NY/FY×. The representation πY is normalizedly induced from [Formula: see text], mi ∈ GL (i, F), on the maximal parabolic subgroup of type (3, 1); θ is the "transpose-inverse" involution of G. We show that the twisted character χπY of πY is an unstable function: its value at a twisted regular elliptic conjugacy class with norm in CY = CY(F)="( GL (2, Y)/F×)F" is minus its value at the other class within the twisted stable conjugacy class. It is 0 at the classes without norm in CY. Moreover πY is the endoscopic lift of the trivial representation of CY. We deal only with unramified Y/F, as globally this case occurs almost everywhere. The case of ramified Y/F would require another paper. Our CY = "( R Y/F GL (2)/ GL (1))F" has Y-points CY(Y) = {(g, g′) ∈ GL (2, Y) × GL (2, Y); det (g) = det (g′)}/Y× (Y× embeds diagonally); σ(≠ 1) in Gal (Y/F) acts by σ(g, g′) = (σg′, σg). It is a θ-twisted elliptic endoscopic group of GL(4). Naturally this computation plays a role in the theory of lifting of CY and GSp(2) to GL(4) using the trace formula, to be discussed elsewhere. Our work extends — to the context of nontrivial central characters — the work of [7], where representations of PGL (4, F) are studied. In [7] we develop a 4-dimensional analogue of the model of the small representation of PGL (3, F) introduced by the first author and Kazhdan in [5] in a 3-dimensional case, and we extend the local method of computation introduced in [6]. As in [7] we use here the classification of twisted (stable) regular conjugacy classes in GL (4, F) of [4], motivated by Weissauer [13].

INDUCED QUANTUM GRAVITY ON A RIEMANN SURFACE

Induced quantum gravity dynamics built over a Riemann surface is studied in arbitrary dimension. Local coordinates on the target space are given by means of the Laguerre–Forsyth construction. A simple model is proposed and perturbatively quantized. In doing so, the classical [Formula: see text]-symmetry turns out to be preserved on-shell at any order of the ℏ perturbative expansion. As a main result, due to quantum corrections, the target coordinates acquire a nontrivial character.