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Criticality of Nodal Point Semimetals

Uryszek, Mikolaj D; (2023) Criticality of Nodal Point Semimetals. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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In this thesis we investigate interaction driven quantum phase transitions of semimetals with a point-like Fermi surface. The most famous example of a member of this family is graphene, which at half-filling hosts gapless fermionic excitations that are Dirac like, i.e. disperse linearly. Unlike in con- ventional metals the density of states vanishes at the Fermi level, which in turn promises novel correlations due to the reduced phase space available to fluctuations. When subject to strong short-ranged interactions these systems undergo a phase transition into a broken symmetry phase where the excita- tions become gapped. However due to the gapless nature of the fermionic excitations in the semimetallic phase it is not possible to describe the crit- icality using a Ginzburg-Landau type theory which only contains bosonic order parameter degrees of freedom. The low-energy theory best equipped for these so-called fermionic quantum criticality problems is a Yukawa-type effective field theory which couples the dynamical order parameter field to the fermions. With the use of Renormalisation Group (RG) we study the critical phe- nomena of the quantum phase transition from a nodal-point semimetal to charge density wave (CDW) insulator. We show that the screening of or- der parameter fluctuations by particle-hole excitations is crucial. Without inclusion of this non-perturbative effect the RG flows contain non-universal dependence on the momentum shell cutoff scheme. We compute the exact critical exponents for the case of Dirac and semi-Dirac fermions in two spatial dimensions up to linear order in 1/N f where N f is the number of fermionic flavours. Lastly we consider the effects of non-magnetic disorder on a Dirac semimetal to CDW phase transition, and find a new disordered interacting fixed point which gives rise to non-Fermi liquid behaviour. We investigate the scaling of physical observables at this critical fixed point.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Criticality of Nodal Point Semimetals
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Copyright © The Author 2023. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
URI: https://discovery.ucl.ac.uk/id/eprint/10168496
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