arXiv subjects

Anton Talkachov

Publications and source records attributed to Anton Talkachov.

5 recordsLinked to original sources

arXiv2025

Multiple correlation lengths and type-1.5 superconductivity in $U(1)$ superconductors due to hidden competition between irreducible representations of nonlocal pairing

A fundamental characteristic of a superconducting state is the coherence length $ξ$. Multicomponent superconductors, particularly ones breaking multiple symmetries, are characterized by multiple coherence lengths. Here we show that even, nominally $single$-component superconductors under certain conditions are characterized by multiple coherence lengths. We consider nearest-neighbor pairing interactions on a square lattice that leads to $s$-wave and $d$-wave representations of link superconducting order parameter. We show that even if the subdominant order parameter is completely suppressed in the ground state, it results in multiple correlation lengths with nontrivial hierarchy, resulting in important physical consequences in inhomogeneous solutions. Under certain conditions, this leads to type-1.5 superconductivity, where magnetic field penetration length falls between two coherence lengths, leading to vortex clustering in an external magnetic field.

cond-mat.supr-con↗

arXiv2025

Microscopic theory of strain-controlled split superconducting and time-reversal symmetry-breaking transitions in $s+id$ superconductor

We study conditions of the appearance of $U(1)\times \mathbb{Z}_2$ superconducting states that spontaneously break time-reversal symmetry (BTRS) on a square lattice as a function of applied stress. Calculations show that if critical temperatures coincide at zero stress, they exhibit a linear kink and no kink otherwise for uniaxial and isotropic strain. Linear kink is absent for shear strain. We find that in general, the microscopic calculations show a complex phase diagram, for example, non-monotonic behavior of BTRS transition. Another beyond-Ginzburg-Landau theory result is that $U(1)$ critical temperature can decrease under compressional [100] uniaxial strain for small Poisson ratio materials. In the second part of the paper, we consider the effects of boundaries and finiteness of the sample on the strain-induced splitting of $T_c^{U(1)}$ and $T_c^{\mathbb{Z}_2}$ transitions. A finite sample has BTRS boundary states with persistent superconducting currents over a wide range of band filling. Overall, the BTRS dome occupies a larger band filling--temperature phase space region for a mesoscopic sample with [110] surface compared to an infinite system. Hence, the presence of boundaries helps to stabilize the BTRS phase.

cond-mat.supr-con↗

arXiv2024

A microscopic approach to the problem of enhancement and suppression of superconductivity on twinning planes

Using a microscopic approach, we revisit the problem of superconducting critical temperature change in the presence of twin boundaries. We show that both critical temperature enhancement and suppression can come purely from geometric effects. These include aspects of scattering of electrons on these crystalline defects even when the coupling constant is unchanged. We consider two dimensional rectangular and three dimensional body centered cubic lattices with onsite s-wave superconducting pairing, nearest and next-to-nearest neighbor hoppings. In the considered two dimensional lattice with twin boundaries, the superconducting critical temperature associated with twinning planes is suppressed for moderate band filling and enhanced for an almost empty/filled band. The superconducting phase diagram is more diverse for the three dimensional lattice, which is caused by the interplay of van Hove singularity, changing coordination number, and modification of distances to nearest and next-to-nearest neighbors.

cond-mat.supr-con↗

arXiv2022

A microscopic study of boundary superconducting states on a honeycomb lattice

We address the problem of boundary s-wave superconductivity on rectangular honeycomb lattices: nanoflakes, armchair and zigzag nanotubes. We discuss how the presence of edges and corners in these systems can significantly alter the superconducting correlations at a macroscopic length scale, leading to either nontrivial enhancement or suppression of the superconducting gap value near the boundaries. This in turn results in different critical temperatures of the gap closure at boundaries compared to the bulk gap. The effects are macroscopic but strongly depend on the atomic-level structure of the boundaries.

cond-mat.supr-con↗

arXiv2022

Wave functions and edge states in rectangular honeycomb lattices revisited: nanoflakes, armchair and zigzag nanoribbons and nanotubes

Properties of bulk and boundaries of materials can, in general, be quite different, both for topological and non-topological reasons. One of the simplest boundary problems to pose is the tight-binding problem of noninteracting electrons on a finite honeycomb lattice. Despite its simplicity, the problem is quite rich and directly related to the physics of graphene. We revisit this long-studied problem and present an analytical derivation of the electron spectrum and wave functions for graphene rectangular derivatives. We provide an exact analytical description of extended and localized states, the transition between them, and a special case of a localized state when the wave function is nonzero only at the edge sites. The later state has zero energy, we discuss its existence in zigzag nanoribbons, zigzag nanotubes with number of sites along a zigzag edge divisible by 4, and rectangular graphene nanoflakes with an odd number of sites along both zigzag and armchair edges.

cond-mat.mes-hall↗