Magnetic and charge order in cuprate superconductors

Glavna tema rada je magnetski odziv itinerantnih fermiona u nekoliko modela vodljivih ravnina u kupratnim visokotemperaturnim supravodičima. Poseban naglasak stavljamo na razlike u spektrima ispod i iznad temperature otvaranja pseudoprocjepa. Na početku predstavljamo kuprate i njihov poprilično složen fazni dijagram. U fazi sa pseudoprocjepom, koja se javlja ispod karakteristične temperature T*, samo dio Fermijeve plohe je u procjepu, a u njoj se pronalazi i mnoštvo različitih magnetskih i nabojnih uređenja. Postoje dvije osnovne vrste magnetskih spektara u kupratima: prvi koji nalikuje pješčanom satu, s dvije grane sa suprotnim disperzijama, i drugi sa samo jednom granom na visokim frekvencijama, karakterističan za živin kuprat Hg1201. Eksperimenti upućuju na moguće magnetsko porijeklo pseudoprocjepa, pa pretpostavljamo da on nastaje kondenzacijom neke vrste magnetskih fluktuacija s plauzibilnom disperzijom koja odgovara gornjoj grani opaženoj u eksperimentima. Takav dinamički otvoreni pseudoprocjep parametriziramo konstantnim statičkim procjepom na valnom vektoru q = QAF. Eksplicitna k-ovisnost procjepa nije potrebna za reprodukciju eksperimentalnih ARPES spektara, no gušenje procesa raspršenja elektrona na magnonima mora rasti s temperaturom. Pokazujemo kako modeli bez međudjelovanja predviđaju i nekomenzurabilne magnetske faze, u suprotnosti s eksperimentima neutronskog raspršenja u kojima su opaženi signali samo na komenzurabilnom vektoru QAF na temperaturama blizu T*. Uvođenje korelacija, uzrokovanih jakim kulonskim odbijanjem na bakrovim orbitalama, razrješava ovu nekonzistentnost i predviđa isključivo komenzurabilno AF uređenje na visokim temperaturama. Procjep oko vH točaka bilo kojeg porijekla, otvoren na QAF ispod T* dovodi do stvaranja potrebnog procjepa u magnetskom spektru. Gornju granu pobuđenja, točno iznad tog procjepa, stoga pripisujemo čestično-šupljinskim pobuđenjima, a ne nekom kolektivnom modu, što je uobičajeno u literaturi. Pokušaj interpretacije faze s pseudoprocjepom kao pravog AF prijelaza, rješavanjem Dysonove jednadžbe, kvari ove rezultate i udaljava ih od eksperimentalnog režima. Ovo je sukladno pretpostavci da pseudoprocjep nije fazni prijelaz, već postupni prijelaz. Isti procjep predviđa i korektnu vrijednost valnog vektora nabojnih uređenja, koja je viša od one u modelima bez međudjelovanja. Pitanje nabojnog uređenja koje se u nekim kupratima poput Bi2201 javlja blizu T* ostaje otvoreno.The main focus of the thesis are magnetic responses of itinerant fermions in several models relevant for the CuO2 plane in cuprate superconductors. In particular, we study the changes in magnetic spectra on passing through the pseudogap phase. First we introduce the cuprate superconductors and their rather complicated phase diagram. The pseudogap phase, appearing below a characteristic temperature T*, features a partially gapped Fermi surface and the coexistence of several fluctuating spin and charge density waves. Magnetic spectra can be divided into two groups: one shaped like the hourglass, with two branches, and the other with only one, high energy branch (in the mercury cuprate Hg1201). As suggested by experiments, this phase is most likely magnetic, so we assume it is brought on by a condensation of some magnetic mode with a plausible dispersion conforming with the upper branch of the magnetic excitations. The dynamically opened pseudogap is parametrised as a static gap at q = QAF and no explicit k-dependence is required to describe the gap shape measured in ARPES. The damping rate of this electron-magnon scattering, used here as a parameter, is required to increase with temperature. Non-interacting metallic models are shown to predict incommensurate phases, in sharp contrast with neutron scattering experiments which observe only commensurate signals at QAF at very high temperatures, close to T*. Introducing strong correlations, caused by a strong Coulomb repulsion on the copper orbitals, resolves this inconsistency and recovers the tendency towards commensurate AF order at high temperatures. A gap of any origin, opening around the antinodal parts of the Fermi surface below T* around QAF opens a spin gap in the magnetic spectrum. The part of the upper branch of magnetic excitations, just above the gap, is therefore identified as interband particle-hole excitations, rather than the usual collective modes of some ordered state. Attempts to interpret the low-temperature response as a real phase transition, by solving the Dyson equation for an AF state, result in magnetic spectra differing greatly from the experimental ones. This is consistent with the assumption that the pseudogap phase boundary is a crossover rather than real phase transition. The same constant gap function reproduces the correct wave vector for the low-temperature charge density wave order, which is higher than the antinodal nesting of the non-ineracting models. The bismuth cuprate Bi2201 may, however, feature a CDW gap opening at the antinode already at T*, therefore leaving open the question of the correct nesting vector for this class of cuprates