arXiv subjects

Sonja Predin

Publications and source records attributed to Sonja Predin.

7 recordsLinked to original sources

arXiv2026

On the relation between the areal rate of Zitterbewegung and Berry curvature in two-band systems

We introduce the Zitterbewegung areal rate operator to study the relation between the orientation of trembling motion and band topology. Constructed from the oscillatory interband displacement and velocity, this operator distinguishes clockwise from anticlockwise motion. For a generic gapped two-band Hamiltonian in two dimensions, we show that the Zitterbewegung areal rate is proportional to the Berry curvature. The derivation uses only spectral projectors and is therefore gauge invariant. We also demonstrate that the Zitterbewegung areal rate operator is time-independent and a constant of motion at each momentum, although the displacement and velocity from which it is constructed oscillate in time. Its sign distinguishes anticlockwise from clockwise Zitterbewegung and coincides with the sign of the Berry curvature. For wave packets narrowly localized around the isolated massive Dirac points, the Zitterbewegung chirality equals the sign of the local Chern contribution. The Chern number can therefore be reconstructed from the orientations of the Zitterbewegung motion around the individual Dirac points.

cond-mat.mes-hall↗

arXiv2024

Dipole representation of composite fermions in graphene quantum Hall systems

The even denominator fractional quantum Hall effect has been experimentally observed in graphene in the fourth Landau level ($n = 3$). This paper is motivated by recent studies regarding the possibility of pairing and the nature of the ground state in this system. By extending the dipole representation of composite fermions, we adapt this framework to the context of graphene's quantum Hall systems, with a focus on half-filled Landau levels. We derive an effective Hamiltonian that incorporates the key symmetry of half-filled Landau levels, particularly particle-hole symmetry. At the Fermi level, the energetic instability of the dipole state is influenced by the interplay between topology and symmetry, driving the system towards a critical state. We explore the possibility that this critical state stabilizes into one of the paired states with well-defined pairing solutions. However, our results demonstrate that the regularized state which satisfies boost invariance at Fermi level and lacks well-defined pairing instabilities emerges as energetically more favorable. Therefore, we find no well-defined pairing instabilities of composite fermions in the dipole representation in the half-filled fourth Landau level ($ n = 3 $) of electrons in graphene. Although the theory of composite fermions has its limitations, further research is required to investigate other possible configurations. We discuss the consistency of our results with experimental and numerical studies, and their relevance for future research efforts.

cond-mat.str-el↗

arXiv2023

Quantum Hall bilayer in dipole representation

The quantum Hall bilayer (QHB) at filling factor $ \nu = 1 $ represents a competition between Bose-Einstein condensation (BEC) at small distances between layers and fermionic condensation, whose influence grows with distance and results in two separate Fermi liquid states for the underlying quasiparticles at very large (or infinite) distances. The question that can be raised is whether, at intermediate distances between layers, a distinct phase exists, or if a singular transition occurs, with the possibility that this happens at infinite distances. Here, using a dipole representation for fermionic quasiparticles, we find support for the latter scenario: Within a large and relevant range of distances, BEC condensation, identified as Cooper $ s $-wave pairing of dipole quasiparticles, prevails over both Cooper $ p $-wave pairing and $ s $-wave excitonic pairing of the same quasiparticles.

cond-mat.str-el↗

arXiv2021

Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities

Building on previous work [N. Read, Phys. Rev. B 58, Z. Dong and T. Senthil, 16262 (1998); Phys. Rev. B 102, 205126 (2020)] on the system of bosons at filling factor $ν= 1$, we derive the Dirac composite fermion theory for a half-filled Landau level from first principles and applying the Hartree-Fock approach in a preferred representation. On the basis of the microscopic formulation, in the long-wavelength limit, we propose a noncommutative field-theoretical description, which in a commutative limit reproduces the Son's theory, with additional terms that may be expected on physical grounds. The microscopic representation of the problem is also used to discuss pairing instabilities of composite fermions. We find that a presence of a particle-hole symmetry breaking leads to a weak (BCS) coupling $p$-wave pairing in the lowest Landau level, and strong coupling $p$-wave pairing in the second Landau level that occurs in a band with nearly flat dispersion, a third power function of momentum.

cond-mat.str-el↗

arXiv2017

Entanglement spectrum of the degenerative ground state of Heisenberg ladders in a time-dependent magnetic field

We investigate of the relationship between the entanglement and subsystem Hamiltonians in the perturbative regime of strong coupling between subsystems. One of the two conditions that guarantees the proportionality between these Hamiltonians obtained by using the nondegenerate perturbation theory within the first order is that the unperturbed ground state has a trivial entanglement Hamiltonian. Furthermore, we study the entanglement Hamiltonian of the Heisenberg ladders in a time-dependent magnetic field using the degenerate perturbation theory, where couplings between legs are considered as a perturbation. In this case, when the ground state is two-fold degenerate, and the entanglement Hamiltonian is proportional to the Hamiltonian of a chain within first-order perturbation theory, even then also the unperturbed ground state has a nontrivial entanglement spectrum.

cond-mat.str-el↗

arXiv2017

Entanglement spectra of superconductivity ground states on the honeycomb lattice

We analytically evaluate the entanglement spectra of the superconductivity states in graphene, primarily focusing on the s-wave and chiral $ d_{x^{2}-y^{2}}+id_{xy} $ superconductivity states. We demonstrate that the topology of the entanglement Hamiltonian can differ from that of the subsystem Hamiltonian. In particular, the topological properties of the entanglement Hamiltonian of the chiral $ d_{x^{2}-y^{2}}+id_{xy} $ superconductivity state obtained by tracing out one spin direction clearly differ from those of the time-reversal invariant Hamiltonian of noninteracting fermions on the honeycomb lattice.

cond-mat.mes-hall↗

arXiv2016

Trigonal Warping in Bilayer Graphene: Energy versus Entanglement Spectrum

We present a mainly analytical study of the entanglement spectrum of Bernal-stacked graphene bilayers in the presence of trigonal warping in the energy spectrum. Upon tracing out one layer, the entanglement spectrum shows qualitative geometric differences to the energy spectrum of a graphene monolayer. However, topological quantities such as Berry phase type contributions to Chern numbers agree. The latter analysis involves not only the eigenvalues of the entanglement Hamiltonian but also its eigenvectors. We also discuss the entanglement spectra resulting from tracing out other sublattices. As a technical basis of our analysis we provide closed analytical expressions for the full eigensystem of bilayer graphene in the entire Brillouin zone with a trigonally warped spectrum.

cond-mat.mes-hall↗