New Quantum States Of Semi-metallic Graphite And Bismuth In High Magnetic Fields

A longstanding open question in condensed matter physics is the fate of three-dimensional elec-tron gas in high magnetic fields.When electrons are confined to their lowest Landau level and reach the quantum limit,the Coulomb interaction,neglected in the single-particle treatment of electrons,is expected to play a significant role,leading to the emergence of many new quantum states.Graphite,bismuth and Bi-rich Bi-Sb alloys,as typical semi-metals,have very low carrier density and a moderate magnetic field can push the carriers to their quantum limit.Hence,these two kinds of semi-metals are ideal materials to study the behavior of three-dimensional electron gas in high magnetic fields.In this thesis,we have studied Nernst effect of graphite,angle dependent magnetoresistance of bismuth and Bi-rich Bi-Sb alloys in high magnetic fields.When the field is high enough,the electron systems would enter the excitonic insulator state in graphite and the 100%valley polarization state in bismuth as well as Bi-rich Bi-Sb alloys.The main content of this thesis is as follows:First,we have successfully overcome the difficulties of the thermoelectric measurement in pulsed magnetic fields and measured the Nernst effect of graphite up to 60 T.And we find that there is a critical point(T=9.2 K,B=47 T)in the Nernst effect.At this critical field,hole and electron Landau subbands simultaneously cross the Fermi level and allow exciton formation.By quantifying the effective mass and the spatial separation of the excitons in the basal plane,we show that the degeneracy temperature of the excitonic fluid corresponds to this critical temperature.Therefore,we conclude that at this critical point,the excitons in graphite will undergo Bose–Einstein condensation and enter the excitonic insulator state.This identification would explain why the field-induced transition observed in graphite is not a universal feature of three-dimensional electron systems pushed beyond the quantum limit.Second,we present a study of a comprehensive angle dependent magnetoresistance of bismuth up to 65 T and detect a large anisotropic drop in magnetoresistance above 30 T.Previously,it was suggested due to the evacuation of the 1_hhole Landau level and predicted a metal–insulator transition at88 T using a theoretical model.However,we do not find any evidence of metal–insulator transition in our magnetoresistance measurements up to 90 T.By modifying the theoretical model with considering the interband coupling between the last Landau levels,we obtain the Landau spectrum of bismuth,which agrees well with the experimental data.By comparing the experimental data and theoretical calculation,we argue that this drop in magnetoresistance directly relates to the Dirac valleys.Above the threshold field,B_empty,one or two electron valleys are completely emptied,thus the valley system enters the 100%polarization state.The electrons transfer from the valley with higher mobility to the lower one,which causes overall decrease of mobility and the drastic drop of magnetoresistance.We also discuss the mobilities in magnetic fields and find an abrupt change near the threshold magnetic field,which is attributed to the possible trion state.Third,as bismuth and antimony have similar lattice parameters,Bi-Sb alloys can form a solid solution over the entire composition range.When the content of antimony is less than 4%,the band structure of bismuth and Bi-Sb alloys is same,the Fermi surface of Bi-Sb alloys decrease gradually with the doping of Sb.Thus,we also measured the angle dependent magnetoresistance of Bi_1-xSb_xalloys with x=1.6%and x=3%under high magnetic fields.We find that the doping of Sb weakens the anisotropy of Bi-Sb alloy,and leads the decrease of threshold field B_empty.The Landau spectrum of Bi_1-xSb_xfor x=3%alloy has been obtained by comparing with bismuth spectrum.We also discuss the possible trion states which may determine the fate of magnetoresistance in high magnetic fields.In this thesis,we find two new quantum states in high magnetic fields:excitonic insulator state and 100%valley polarization state,as well as a new possible quantum state:trion state.These studies have enriched our understanding of the behavior of three-dimensional electron gas in high magnetic fields.