Renormalization Group Analysis Of Interaction Effects In Semimetals

Semimetals are usually referred to the material with a very small overlap between the valence band and the conduction band.For example,the overlap is just one point for Dirac semimetal and Weyl semimetals.The discovery of Weyl semimetal is the most important research progress in the field of topological material after the successful com-bination of theoretical prediction and experimental discovery for topological insulator.Based on the first-principles calculations and symmetry analysis for the crystals,sev-eral important semimetals except for the Dirac and Weyl ones are predicted,including type-II Dirac/Weyl semimetal,semi-Dirac semimetal,nodal-line semimetal,multi-Weyl semimetal,triple-component Dirac/Weyl semimetal and so on.Most of the mentioned semimetal have been found in experiment.In any of these semimetals,there always exist various interactions,including Coulomb interaction between electrons,electro-magnetic fields,disorder induced by impurity,short-range four-fermion couplings and so on.Studying the influence of some kinds of interaction to several semimetals is the topic of this thesis.Based on the kind of semimetals we have investigated,this thesis is organized as follows:Chapter 1 is devoted to give an introduction to the basic concepts for semimetals,the interactions we considered,and the method we used:renormalization group.Chapter 2 and Chapter 3 focus on the interaction effects in Dirac semimetals(DSM).In Chapter 2,we study the effects of disorder on the low-energy behaviors of Dirac fermions with U(1)gauge field,i.e.,effects of disorder in three-dimensional quantum electrodynamics.Kinds of disorder include random mass(RM),random chemical po-tential(RCP),and random gauge potential(RGP).All of them substantially affect the properties of massless Dirac fermions.Adding disorder to the system explicitly breaks the Lorentz invariance,and leads to fermion velocity renormalization.We found that RCP is a marginally relevant perturbation to the system,and drives the system to un-dergo a diffusive quantum phase transition.Moreover,the role played by RM is signif-icantly enhanced by the gauge interaction but RCP and RGP seem to be insusceptible to the gauge interaction.In Chapter 3,we study the interplay of Cooper pairing interac-tion and disorder.Our main finding is that RM and RGP both lead to certain amount of increment of the critical BCS coupling,which means they will suppress the supercon-ductivity.In addition,disorders have other drastic effects on the low-energy behaviors of Dirac fermions.At the new critical value,the system would undergo a quantum phase transition between a superconducting phase and(a)a marginal-Fermi-liquid phase in the case of RM;(b)a non-Fermi liquid in the case of RGP.Our researches indicate that the existence of various interactions leads to a series of extraordinary thermodynamic and transport properties of Dirac semimetals,which can be detected by experiments.At the time,our researches provide a way to explain the observed novel quantum phenomena in Dirac and other semimetals systems.Chapter 4 and chapter 5 focus on the interaction effects in tilted Dirac semimet-als.In chapter 4,we study the disorder effects on the 2D tilted Dirac-fermion systems,in which the fennions have two distinct orbitals unrelated by any symmetry.We have presented a RG analysis of four types of disorder allowed to exist by itself in a 2D tilted Dirac-fermion system.Our results indicate that,intraorbital disorder scattering can pro-duce a bulk Fermi arc.By contrast,in the case of interorbital disorder scattering,the Dirac cone remains intact,and no bulk Fermi arc appears.Instead,interorbital disorder leads to logarithmic or power-law quantum corrections,to such quantities as DOS and specific heat of tilted Dirac fermions.We have also examined the mutual influence of different disorders,and showed that the Fermi arc does not always replace the Dirac point,even if the fermions of distinct orbitals are unrelated.We obtain a condition for the emergence of a bulk Fermi arc.The tilted Dirac-fermion system exhibits an iso-lated Dirac point if this condition is satisfied,and a bulk Fermi arc is formed when this condition is violated.In chapter 5,we have systematically studied the interplay between tilt,disorder,and Coulomb interaction in type-I Dirac fermions with particle-hole symmetry.We have shown that the interplay between ordinary tilt and disorder will dynamically generate an anomalous tilt and change the vertex of Coulomb interaction.After taking these two factors into consideration,we find that the tilt-driven topological phase transition between two types of Dirac fermions never happens.Without Coulomb interaction,an arbitrary weak x-RGP can induce the diffusive phase transition,which result is never predicted in previous studies for 2D Dirac fermions system.In addition,we have shown that the interplay between tilt and disorder generates a bulk nodal arc in the compressible diffusive metal(CDM)phase When Coulomb interaction coex-ists with the disorder,it generates a critical RCP strength to produce the diffusive phase transition and ruins the diffusive phase transition caused by x-RGP.Instead,a randomly stable state which is distinct from the DSM and CDM phase appears,and this state is also present for interplay of Coulomb interaction with y-RGP and RM.Our researches present a systematic analysis for the condition to form the bulk Fermi arc in tilted Dirac semimetal,which will be helpful to search for the bulk Fermi arc in experiment.Mean-while,our results indicate that interactions will significantly influence the properties of semimetals and even generates new quantum phenomena.Therefore,our research provides an example for predicting the interaction-driven novel quantum phenomena in various semimetals.