arXiv subjects

Igor Burmistrov

Publications and source records attributed to Igor Burmistrov.

5 recordsLinked to original sources

arXiv2025

Bulk-edge correspondence at the spin-to-integer quantum Hall effect crossover in topological superconductors

The spin and integer quantum Hall effects are two cousins of topological phase transitions in two-dimensional electronic systems. Their close relationship makes it possible to transform spin to integer quantum Hall effect in two-dimensional topological superconductors by continuous increase in a symmetry breaking Zeeman magnetic field. We study peculiarities of bulk-edge correspondence and a fate of massless edge and bulk topological (instantons) excitations at such the crossover.

cond-mat.mes-hall↗

arXiv2025

Anderson transition symmetries at the band-edge of a correlated Sn/Si monolayer

Anderson localization is predicted to enhance the critical temperature of disordered superconductors. Despite a huge body of theoretical work based on non-linear sigma models, experiments are lacking to understand correlated electrons in disordered potentials. In this study, we investigate a tin monolayer on silicon, a material known for its likely antiferromagnetic Mott-correlated groundstate. We analyze the statistical properties of tunneling conductance maps of increasingly localized states as we approach the edge of the valence band. Using multifractal analysis, we show that the system follows an exact symmetry relation based on the algebraic structure of nonlinear sigma-models (NLsMs). We anticipate that this symmetry may be broken in specific - e.g. chiral electronic phases. Finally, we point out that multifractal analysis can equally be applied to universal conductance fluctuations in magneto-transport experiments, thus providing a powerful tool to probe the underlying symmetries of disordered electronic phases.

cond-mat.mes-hall↗

arXiv2024

Instanton analysis for the spin quantum Hall symmetry class: Non-perturbative corrections to physical observables and generalized multifractal spectrum

Recently, there has been renewed interest in studies of criticality in the spin quantum Hall effect, realized in the Altland-Zirnbauer symmetry class C of disordered, noninteracting fermions in two spatial dimensions. In our study, we develop a nonperturbative analysis of the replica two-dimensional nonlinear sigma model in class C. We explicitly construct the instanton solution with a unit topological charge. By treating fluctuations around the instanton at the Gaussian level, we calculate the instanton correction to the disorder-averaged logarithm of the partition function. We compute non-perturbative corrections to the anomalous dimensions of pure power-law scaling local operators, which determine the spectrum of generalized multifractality. We also calculate instanton corrections to the renormalized longitudinal and Hall spin conductivities and determine the topology of the phase diagram for class C. Our results demonstrate that the spin quantum Hall effect is indeed a close cousin of the integer quantum Hall effect.

cond-mat.mes-hall↗

arXiv2023

Local density of state fluctuations in 2D superconductor as a probe of quantum diffusion

The interplay of superconductivity and disorder generates a wealth of complex phenomena. In particular, the peculiar structure of diffusive electronic wavefunctions is predicted to increase the superconducting critical temperature in some range of disorder. In this work, we use an epitaxial monolayer of lead showing a simple band structure and homogenous structural disorder as a model system of a 2D superconductor in the weak-antilocalization regime. Then, we perform an extensive study of the emergent fluctuations of local density of states (LDOS) and spectral energy gap in this material and compare them with both analytical results and numerical solution of the attractive Hubbard model. We show that mesoscopic LDOS fluctuations allow to probe locally both the elastic and inelastic scattering rates which are notoriously difficult to measure in transport measurements.

cond-mat.supr-con↗

arXiv2012

A quantum dot close to Stoner instability: the role of Berry's Phase

The physics of a quantum dot with electron-electron interactions is well captured by the so called "Universal Hamiltonian" if the dimensionless conductance of the dot is much higher than unity. Within this scheme interactions are represented by three spatially independent terms which describe the charging energy, the spin-exchange and the interaction in the Cooper channel. In this paper we concentrate on the exchange interaction and generalize the functional bosonization formalism developed earlier for the charging energy. This turned out to be challenging as the effective bosonic action is formulated in terms of a vector field and is non-abelian due to the non-commutativity of the spin operators. Here we develop a geometric approach which is particularly useful in the mesoscopic Stoner regime, i.e., when the strong exchange interaction renders the system close the the Stoner instability. We show that it is sufficient to sum over the adiabatic paths of the bosonic vector field and, for these paths, the crucial role is played by the Berry phase. Using these results we were able to calculate the magnetic susceptibility of the dot. The latter, in close vicinity of the Stoner instability point, matches very well with the exact solution [I.S. Burmistrov, Y. Gefen, M.N. Kiselev, JETP Lett. 92 (2010) 179].

cond-mat.mes-hall↗