Electrons at the monkey saddle: A multicritical Lifshitz point

Shtyk, A.; Goldstein, G.; Chamon, C.

doi:10.1103/physrevb.95.035137

Title: Electrons at the monkey saddle: A multicritical Lifshitz point

Journal Article · Mon Jan 23 00:00:00 EST 2017 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.95.035137· OSTI ID:1535829

Shtyk, A. ^[1]; Goldstein, G. ^[2]; Chamon, C. ^[3]

Harvard Univ., Cambridge, MA (United States)
Univ. of Cambridge (United Kingdom). Cavendish Lab.
Boston Univ., MA (United States)

In this work, we consider two-dimensional interacting electrons at a monkey saddle with dispersion $\propto p_{x}^{3} - 3 p_{x} p_{y}^{2}$ . 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 $E_{m} \propto {(B m)}^{3 / 2}$ 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 noninteracting 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 $K^{'}$ points, exhibits an interplay of competing many-body instabilities, namely, $s$ -wave superconductivity, ferromagnetism, and spin- and charge-density waves.

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Research Organization:: Boston Univ., MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Engineering and Physical Sciences Research Council (EPSRC)

Grant/Contract Number:: FG02-06ER46316; EP/M007065/1; DEF-06ER46316

OSTI ID:: 1535829

Alternate ID(s):: OSTI ID: 1341280

Journal Information:: Physical Review. B, Vol. 95, Issue 3; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 28 works

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Archetypical “push the band critical point” mechanism for peaking of the density of states in three-dimensional crystals: Theory and case study of cubic $H_{3} S$ Akashi, Ryosuke Physical Review B, Vol. 101, Issue 7 https://doi.org/10.1103/physrevb.101.075126	journal	February 2020
Optically induced Lifshitz transition in bilayer graphene Iorsh, I. V.; Dini, K.; Kibis, O. V. Physical Review B, Vol. 96, Issue 15 https://doi.org/10.1103/physrevb.96.155432	journal	October 2017
Landau-Type Theory of Planar Crystal Plasticity Baggio, R.; Arbib, E.; Biscari, P. Physical Review Letters, Vol. 123, Issue 20 https://doi.org/10.1103/physrevlett.123.205501	journal	November 2019
Origin of Magic Angles in Twisted Bilayer Graphene Tarnopolsky, Grigory; Kruchkov, Alex Jura; Vishwanath, Ashvin Physical Review Letters, Vol. 122, Issue 10 https://doi.org/10.1103/PhysRevLett.122.106405	journal	March 2019
Optically induced Lifshitz transition in bilayer graphene Iorsh, I. V.; Dini, K.; Kibis, O. V. arXiv https://doi.org/10.48550/arxiv.1707.07392	text	January 2017
Multicritical Fermi surface topological transitions Efremov, Dmitry V.; Shtyk, Alex; Rost, Andreas W. arXiv https://doi.org/10.48550/arxiv.1810.13392	text	January 2018
Magic of high order van Hove singularity Yuan, Noah F. Q.; Isobe, Hiroki; Fu, Liang arXiv https://doi.org/10.48550/arxiv.1901.05432	text	January 2019
Classification of Critical Points in Energy Bands Based on Topology, Scaling and Symmetry Yuan, Noah F. Q.; Fu, Liang arXiv https://doi.org/10.48550/arxiv.1910.10179	text	January 2019
Crystal elasto-plasticity on the Poincaré half-plane Arbib, Edoardo; Biscari, Paolo; Bortoloni, Luca International Journal of Plasticity, Vol. 130 https://doi.org/10.1016/j.ijplas.2020.102728	journal	July 2020

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