Multicritical Fermi Surface Topological Transitions

Abstract

A wide variety of complex phases in quantum materials are driven by electron-electron interactions, which are magnified by regions in momentum space where the density of states is enhanced. 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 leafs 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 further boost the formation of complex quantum phases via interactions. As a concrete example, we demonstrate these theoretical ideas in the analysis of experimental data on Sr3Ru2O7 in the vicinity of the metamagnetic quantum critical point, resolving several previously puzzling aspects of the data.Introduction. The properties of unconventional density waves in quantum materials are generally connected to features of the electronic band structure. Characteristic wave vectors of emergent order parameters can for example often be related to nesting-type features of the underlying Fermi surface as discussed for e.g. iron pnictides 1 , organics 2 , and transition metal dichalcogenides 3 . Yet these nesting features in themselves usually cannot account for the observed thermodynamic stability of such correlated quantum phases. Intriguingly in a range of these materials the band structure hosts energetically close-by singularities in the density of states (DOS), which have been conjectured to be crucial ingredients stabilising the emergent phases.Singularities in the DOS occur naturally at Fermi surface (FS) topological Lifshitz transitions (LT). A prominent example is the van Hove singularity (vHs) formed at a saddle point in the energy-momentum dispersion (see fig. 1a). A two-dimensional (2D) vHs has a relatively weak logarithmic divergence in the DOS but is known to lead to a wealth of phenomena such as ferromagnetism driven by the Stoner mechanism (see eg. Ref. 4). An important yet under-appreciated point is that the thermodynamic stability of the emergent phases does not only depend on the magnitude but also shape of the singularity as a function of energy 4 (i.e. gradient and curvature). As a consequence stronger power law divergences can have a much more dramatic impact on the formation of complex ordered phases than the relatively weak vHs.Building on this insight, we explore a generalisation of these concepts to multicritical topological transitions where multiple disjoint parts of a FS merge. Such multicritical FS topological transitions naturally occur at points of high crystal symmetry, where the number n of FS components merging depends on the particular symmetry. In fig. 1a-c we illustrate the symmetries associated with the n = 2 (vHs), 3 and 4 cases in 2D. When the singularity occurs at an edge of a Brillouin zone there are generically two pieces (n = 2) of the Fermi surface that join at the sin...

Classification of critical points in energy bands based on topology, scaling, and symmetry

“…x − p 2 y = 0 if h < 0. This type of critical point and topological transition can be realized in Sr 3 Ru 2 O 7 by changing magnetization of Ru atoms [11,12].…”

“…without constraints from symmetry etc. ), then the maximal number µ ≡ max{m} of critical points in (11) is only determined by scaling property of canonical dispersion [36][37][38][39]…”

“…To summarize, based on general principles of topology, scaling and symmetry, we systematically describe and classify critical points from 1D to 3D, especially highorder critical points in 2D. Our results include ordinary VHS as a natural corollary, and could be relevant in realistic materials such as 2D moiré systems [13,17], ruthenate [11,12,[41][42][43][44] and cuprate [2][3][4][45][46][47][48][49][50] materials. As the DOS near high-order critical points can be power-law divergent and particle-hole asymmetric, we expect highorder critical points can play important roles in transport phenomena and interaction effects, which may help us to understand correlated phases such as unconventional superconductivity and non-Fermi liquid.…”

“…The high-order critical points have been proposed occasionally in specific materials under different names in the context of DOS singularity, including the so-called extended VHS [2][3][4][5][6][7][8], multicritical points [9][10][11][12] and highorder VHS [13]. At the energy of a high-order critical point, the DOS can be power-law divergent, stronger than ordinary VHS, and hence we call it a high-order VHS of DOS.…”

Supermetal

“…The existence of high-order VHS has recently been identified in a variety of materials including twisted bilayer graphene near a magic angle, trilayer graphenehexagonal BN heterostructure [2], and Sr 3 Ru 2 O 7 [5]. In particular, scanning tunneling spectroscopy measurements [6] on twisted bilayer graphene found power-law divergent DOS at the magic twist angle, providing direct evidence for high-order VHS [2].…”