arXiv subjects

Zory Davoyan

Publications and source records attributed to Zory Davoyan.

3 recordsLinked to original sources

arXiv2026

Topological instability and reentrant crystallization in active solids

We extend the KTHNY theory of defect-mediated melting in two dimensions to the case of active solids exhibiting both non-reciprocal (odd) elasticity and Cosserat (micropolar) coupling. For perturbatively small values of non-reciprocity, melting still proceeds via defect unbinding, but the melting temperature shifts due to activity. However, at a threshold value of non-reciprocity, we discover a qualitatively distinct mechanism for 2D melting, which we call topological instability. This melting occurs through the proliferation of defect pairs at any temperature. We use a combination of field theory and simulations to characterize this zero-temperature transition in terms of the defect-pair fugacity. Surprisingly, for higher activity values, we find reentrant crystallization, where the quasi-long-range order survives even at temperatures for which the equilibrium crystal would melt. Although active solids present one realization of this topological instability, we envision core-energy-driven defect proliferation as a generic and unexplored route for two-dimensional melting.

cond-mat.stat-mech↗

arXiv2024

Non-Abelian Hopf-Euler insulators

We discuss a class of three-band non-Abelian topological insulators in three dimensions that carry a single bulk Hopf index protected by spatiotemporal ($\mathcal{PT}$) inversion symmetry. These phases may also host subdimensional topological invariants given by the Euler characteristic class, resulting in real Hopf-Euler insulators. Such systems naturally realize helical nodal structures in the three-dimensional Brillouin zone, providing a physical manifestation of the linking number described by the Hopf invariant. We show that, by opening a gap between the valence bands of these systems, one finds a fully-gapped ``flag'' phase, which displays a three-band multi-gap Pontryagin invariant. Unlike the previously reported $\mathcal{PT}$-symmetric four-band real Hopf insulator, which hosts a $\mathbb{Z} \oplus \mathbb{Z}$ invariant, these phases are not unitarily equivalent to two copies of a complex two-band Hopf insulator. We show that such uncharted phases can be obtained through dimensional extension of two-dimensional Euler insulators, and that they support (i) an optical bulk integrated circular shift effect quantized by the Hopf invariant, (ii) quantum-geometric breathing in the real space Wannier functions, and (iii) surface Euler topology on boundaries. Consequently, our findings pave the way for novel experimental realizations of real-space quantum-geometry, as these systems may be directly simulated by utilizing synthetic dimensions in metamaterials or ultracold atoms.

cond-mat.mes-hall↗

arXiv2024

Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index

We report on a certain class of three-dimensional topological insulators and semimetals protected by spinless $\mathcal{P}\mathcal{T}$ symmetry, hosting an integer-valued bulk invariant. We show using homotopy arguments that these phases host multi-gap topology, providing a realization of a single $\mathbb{Z}$ invariant in three spatial dimensions that is distinct from the Hopf index. We identify this invariant with the Pontryagin index, which describes BPST instantons in particle physics contexts and corresponds to a 3-sphere winding number. We study naturally arising multi-gap linked nodal rings, topologically characterized by split-biquaternion charges, which can be removed by non-Abelian braiding of nodal rings, even without closing a gap. We additionally connect the describing winding number in terms of gauge-invariant combinations of non-Abelian Berry connection elements, indicating relations to Pontryagin characteristic class in four dimensions. These topological configurations are furthermore related to fully non-degenerate multi-gap phases that are characterized by a pair of winding numbers relating to two isoclinic rotations in the case of four bands and can be generalized to an arbitrary number of bands. From a physical perspective, we also analyze the edge states corresponding to this Pontryagin index as well as their dissolution subject to the gap-closing disorder. Finally, we elaborate on the realization of these novel non-Abelian phases, their edge states and linked nodal structures in acoustic metamaterials and trapped-ion experiments.

cond-mat.mes-hall↗