arXiv subjects

Alex Shtyk

Publications and source records attributed to Alex Shtyk.

4 recordsLinked to original sources

arXiv2019

Catastrophe theory classification of Fermi surface topological transitions in two dimensions

We classify all possible singularities in the electronic dispersion of two-dimensional systems that occur when the Fermi surface changes topology, using catastrophe theory. For systems with up to seven control parameters (i.e., pressure, strain, bias voltage, etc), the theory guarantees that the singularity belongs to to one of seventeen standard types. We show that at each of these singularities the density of states diverges as a power law, with a universal exponent characteristic of the particular catastrophe, and we provide its universal ratio of amplitudes of the prefactors of energies above and below the singularity. We further show that crystal symmetry restricts which types of catastrophes can occur at the points of high symmetry in the Brillouin zone. For each of the seventeen wallpaper groups in two-dimensions, we list which catastrophes are possible at each high symmetry point.

cond-mat.str-el↗

arXiv2018

Multicritical Fermi surface topological transitions

A wide variety of complex phases in quantum materials are driven by electron-electron interactions, which are enhanced through density of states peaks. A well known example occurs at van Hove singularities where the Fermi surface undergoes a topological transition. Here we show that higher order singularities, where multiple disconnected leaves of Fermi surface touch all at once, naturally occur at points of high symmetry in the Brillouin zone. Such multicritical singularities can lead to stronger divergences in the density of states than canonical van Hove singularities, and critically boost the formation of complex quantum phases via interactions. As a concrete example of the power of these Fermi surface topological transitions, we demonstrate how they can be used in the analysis of experimental data on Sr$_3$Ru$_2$O$_7$. Understanding the related mechanisms opens up new avenues in material design of complex quantum phases.

cond-mat.str-el↗

arXiv2017

Topological electronic properties of silicon

The central role that materials play in human history is exemplified by the three-age division of prehistory into the stone, bronze, and iron ages. References to our present time as the information age or silicon age epitomizes the important role that this semiconducting material came to play in the development of computers and devices that permeate our daily lives. Here we show that the electronic states in silicon have nontrivial topological structures that are captured by a network of Berry flux lines that link at points of high symmetry in the Brillouin zone. This complex network has ice-nodal points where fluxes satisfy ice rules, making silicon a "nodal-chain insulator". Fixing the longitudinal momentum parallel to such flux lines yields a two-dimensional Dirac Hamiltonian for the transverse degrees of freedom. This complex Berry-flux network implies a topologically stable two-fold degeneracy along the X-W direction in all of silicon bands, a fact that is supported by crystal symmetry arguments as well as direct inspection of the vast literature on silicon band structures. Similarly to nodal-chain semimetals, we find drumhead-like states in the regions that are delimited by the projections of the bulk Berry flux network on the surface Brillouin zone.

cond-mat.mes-hall↗

arXiv2016

Electrons at the monkey saddle: a multicritical Lifshitz point

We consider 2D interacting electrons at a monkey saddle with dispersion $\propto p_x^3-3p_xp_y^2$. Such a dispersion naturally arises at the multicritical Lifshitz point when three van Hove saddles merge in an elliptical umbilic elementary catastrophe, which we show can be realized in biased bilayer graphene. A multicritical Lifshitz point of this kind can be identified by its signature Landau level behavior $E_m\propto (Bm)^{3/2}$ and related oscillations in thermodynamic and transport properties, such as de Haas-van Alphen and Shubnikov-de Haas oscillations, whose period triples as the system crosses the singularity. We show, in the case of a single monkey saddle, that the non-interacting electron fixed point is unstable to interactions under the renormalization group flow, developing either a superconducting instability or non-Fermi liquid features. Biased bilayer graphene, where there are two non-nested monkey saddles at the $K$ and $K^\prime$ points, exhibits an interplay of competing many-body instabilities, namely s-wave superconductivity, ferromagnetism, and spin- and charge-density wave.

cond-mat.str-el↗