Synthetic dimension in a specially tailored photonic structure

Diplomski rad bavi se diskretnim sustavima koji mogu imati dimenziju veću od kontinuiranog prostora u kojem se nalaze. Ovo svojstvo pokazano je na jednostavnim matematičkim primjerima te su dobiveni uvjeti potrebni da se ono ostvari. Dobiveni uvjeti su zatim povezani s elektrodinamikom rešetke valovoda te je uočeno da je vezanje valovoda potrebno učiniti jako ovisnim o međusobnom položaju valovoda. Ovakvo ponašanje vezanja valovoda pokušali smo ostvariti modifikacijom presjeka svakog valovoda u kvadratnoj rešetci valovoda s dva elementa u bazi, u čijem bi presjeku time ostvarili dvosloj kvadratnih rešetki. Usporedbom vrpci dobivenih numeričkim rješavanjem jednadžbi koje opisuju dani sustav te vrpci dobivenih u ekvivalentu aproksimacije čvrste veze iz fizike čvrstog stanja koje opisuju dvosloj pokazano je da pothvat nije uspio jer se vezu između valovoda, za dane parametre, ne može učiniti dovoljno prostorno ovisnom. Na kraju su izložene neke ideje koje bi se dalje mogle koristiti u pokušaju realizacije traženog dvosloja.In this thesis we examine the property of discrete systems that their dimension can be greater than the dimension of the continous space they are embedded in. This property is shown in simple mathematical examples and the conditions to achieve it are uncovered. These conditions are recast in the language of electrodynamics of wavegude array and are shown to require strong dependance of the coupling of waveguides on their relative position. An attempt to satisfy this requirement is made by modifying the cross section of each waveguide in a square lattice of waveguides with two elements in the basis, so that the lattice would become a bilayer of square lattices instead of a twodimensional lattice. A comparison of bands calculated numerically for a given array and those determined approximately for the bilayer by method based on the tight binding approximation of solid state physics shows that the attempt is unsuccesful because the modification of the cross section of a waveguide, under the given parameters, does not produce strong enough effect on spatial dependence of coupling. Some further ideas which could be used to realise the bilayer in the cross section of waveguide array are given

Proximity-induced magnetization in graphene: Towards efficient spin gating

Gate-tunable spin-dependent properties could be induced in graphene at room temperature through magnetic proximity effect by placing it in contact with a metallic ferromagnet. Because strong chemical bonding with the metallic substrate makes gating ineffective, an intervening passivation layer is needed. Previously considered passivation layers result in a large shift of the Dirac point away from the Fermi level, so that unrealistically large gate fields are required to tune the spin polarization in graphene. We show that a monolayer of Au or Pt used as the passivation layer between Co and graphene brings the Dirac point closer to the Fermi level. In the \Co/\Pt/\Gr system the proximity-induced spin polarization in graphene and its gate control are strongly enhanced by the presence of a surface band near the Fermi level. Furthermore, the shift of the Dirac point could be eliminated entirely by selecting submonolayer coverage in the passivation layer. Our findings open a path towards experimental realization of an optimized two-dimensional system with gate-tunable spin-dependent properties.Comment: 10 page

High Chern number van der Waals magnetic topological multilayers MnBi2_2Te4_4/hBN

Chern insulators are two-dimensional magnetic topological materials that conduct electricity along their edges via the one-dimensional chiral modes. The number of these modes is a topological invariant called the first Chern number $C$, that defines the quantized Hall conductance as $S_{xy}= C e^2/h$. Increasing $C$ is pivotal for the realization of low-power-consumption topological electronics, but there has been no clear-cut solution of this problem so far, with the majority of existing Chern insulators showing $C=1$. Here, by using state-of-the-art theoretical methods, we propose an efficient approach for the realization of the high-$C$ Chern insulator state in MnBi$_2$Te$_4$/hBN van der Waals multilayer heterostructures. We show that a stack of $n$ MnBi$_2$Te$_4$ films with $C=1$ intercalated by hBN monolayers gives rise to a high Chern number state with $C=n$, characterized by $n$ chiral edge modes. This state can be achieved both under the external magnetic field and without it, both cases leading to the quantized Hall conductance $S_{xy}= C e^2/h$. Our results therefore pave way to practical high-$C$ quantized Hall systems.Comment: 10 pages, 5 figure

Superlattices of Gadolinium and Bismuth Based Thallium Dichalcogenides as Potential Magnetic Topological Insulators

Using relativistic spin-polarized density functional theory calculations we investigate magnetism, electronic structure and topology of the ternary thallium gadolinium dichalcogenides TlGdZ2 (Z= Se and Te) as well as superlattices on their basis. We find TlGdZ2 to have an antiferromagnetic exchange coupling both within and between the Gd layers, which leads to frustration and a complex magnetic structure. The electronic structure calculations reveal both TlGdSe2 and TlGdTe2 to be topologically trivial semiconductors. However, as we show further, a three-dimensional (3D) magnetic topological insulator (TI) state can potentially be achieved by constructing superlattices of the TlGdZ2/(TlBiZ2)n type, in which structural units of TlGdZ2 are alternated with those of the isomorphic TlBiZ2 compounds, known to be non-magnetic 3D TIs. Our results suggest a new approach for achieving 3D magnetic TI phases in such superlattices which is applicable to a large family of thallium rare-earth dichalcogenides and is expected to yield a fertile and tunable playground for exotic topological physics.M.M.O. and M.B. acknowledge the support by Spanish Ministerio de Ciencia e Innovación (Grant No. PID2019-103910GB-I00) and the University of the Basque Country (Grant no. IT1527-22). A.Yu.V. and E.K.P. acknowledge support from the Ministry of Education and Science of the Russian Federation within State Task No. FSWM-2020-0033 (in the part of bulk and surface electronic structure calculations). E.V.C. acknowledges support from Saint Petersburg State University (Grant ID No. 90383050). Yu.M.K. acknowledges support from the Government research assignment for ISPMS SB RAS, project FWRW-2022-0001 (in the part of the topological classification of bulk band structure)

Electronic properties of Van der Waals heterostructures from first principles

U tezi predstavljamo rezultate računa na razini teorije funkcionala gustoće za tri primjera van der Waalsovih heterostruktura. Prvo predstavljamo rezultate za 295 heterostruktura sastavljenih od dva 2D kristala. Izračunate energije, geometrijske strukture, gustoće stanja te kemijski potencijali bit će pohranjeni u bazu podataka, koja će biti javno dostupna. Analizom rezultata karakteriziramo vezanje heterostruktura te pokazujemo da je utjecaj ne fizikalne deformacije ćelija pri slaganju ulaznih struktura na izračune relativno velik. Pokazujemo i da se taj utjecaj donekle može ispraviti konstrukcijom jednostavnih modela. Potom analiziramo vezanje monosloja PtSe2 s Pt(111) radi određivanja dosad nejasne strukture tog kompleksa. Usporedbom izračunatih energija vezanja te geometrijskih i elektronskih struktura PtSe2 na čistoj i monoslojem Se prekrivenoj Pt(111) pokazujemo da je u prvoj od njih PtSe2 kemisorbiran, a u drugoj fizisorbiran. Kako temeljita eksperimentalna karakterizacija ovog kompleksa pokazuje da je PtSe2 fizisorbiran, zaključujemo da je potonja struktura točna. Naposljetku, promatramo elektronsku strukturu grafena (Gr) adsorbiranog na Co(0001) prekrivenoj monoslojem Au ili Pt. Pokazujemo da se u grafenu pojavljuje magnetizacija zbog magnetskog efekta blizine, koja se može mijenjati primjenom statičkog električnog polja. Dodatno su Co|Au|Gr te Co|Pt|Gr učinkovitiji za primjenu u spintronici od prije istraživanih Co|hBN|Gr te Co|Gr|Gr jer im za istu promjenu magnetizacije treba manje električno polje. Dodatno, u Co|Pt|Gr efekt električnog polja jako je izražen, što je posljedica spinski polariziranog površinskog stanja blizu Fermijevog nivoa. Također, pokazujemo da se promjenom pokrivenosti Co(0001) može fino upravljati magnetizacijom i osjetljivošću grafena.Rad ne sadrži sažetak na drugom jeziku

Se intercalation between Pt Se 2 and the Pt surface during synthesis of Pt Se 2 by direct selenization of Pt(111)

Using the first principles calculations, we analyze the structural and electronic properties of a PtSe2 monolayer on Pt substrate, obtained by direct selenization of the Pt(111) surface [Wang et al., Nano Lett. 15, 4013 (2015)]. We demonstrate that in order to reproduce the experimental result that PtSe2 is physisorbed on the surface, the surface must be passivated. We propose that this passivation is most likely due to intercalation of Se atoms between PtSe2 and Pt surface during the selenization process. In this case the mean distance between the Se-passivated surface and PtSe2 is found to be 3.24Å, which is consistent with the distance that can be extracted from the scanning transmission electron microscopy image of the hybrid system, and the adsorption energy is found to fall into physisorption range. Therefore, our findings provide an insight into the synthesis of PtSe2 by direct selenization: A realistic structural model should include a Se-passivated surface and not a clean one

High Chern number van der Waals magnetic topological multilayers MnBi2Te4/hBN

Chern insulators are two-dimensional magnetic topological materials that conduct electricity along their edges via the one-dimensional chiral modes. The number of these modes is a topological invariant called the first Chern number C that defines the quantized Hall conductance as Sxy = Ce2/h. Increasing C is pivotal for the realization of low-power-consumption topological electronics, but there has been no clear-cut solution to this problem so far, with the majority of existing Chern insulators showing C = 1. Here, by using state-of-the-art theoretical methods, we propose an efficient approach for the realization of the high-C state in MnBi2Te4/hBN van der Waals multilayer heterostructures. We show that a stack of n MnBi2Te4 films with C = 1 intercalated by hBN monolayers gives rise to a high Chern number state with C = n, characterized by n chiral edge modes. This state can be achieved both under the external magnetic field and without it, both cases leading to the quantized Hall conductance Sxy = Ce2/h. Our results, therefore, pave the way to practical high-C quantized Hall systems.The authors thank J. Ibañez-Azpiroz, S.S. Tsirkin, I. Souza, and M. Garnica for stimulating discussions. M.B. and M.M.O. acknowledge the support of the Spanish Ministerio de Ciencia e Innovacion (Grant no. PID2019-103910GB-I00) and the University of the Basque Country (Grant no. IT1527-22). A.Y.V. and E.K.P. acknowledge the Ministry of Science and Higher Education of the Russian Federation (state task № FSWM-2020-0033). E.V.C. acknowledges support from Saint Petersburg State University (Grant ID 94031444).Peer reviewe

Superlattices of Gadolinium and Bismuth Based Thallium Dichalcogenides as Potential Magnetic Topological Insulators

Using relativistic spin-polarized density functional theory calculations we investigate magnetism, electronic structure and topology of the ternary thallium gadolinium dichalcogenides TlGdZ2 (Z= Se and Te) as well as superlattices on their basis. We find TlGdZ2 to have an antiferromagnetic exchange coupling both within and between the Gd layers, which leads to frustration and a complex magnetic structure. The electronic structure calculations reveal both TlGdSe2 and TlGdTe2 to be topologically trivial semiconductors. However, as we show further, a three-dimensional (3D) magnetic topological insulator (TI) state can potentially be achieved by constructing superlattices of the TlGdZ2/(TlBiZ2)n type, in which structural units of TlGdZ2 are alternated with those of the isomorphic TlBiZ2 compounds, known to be non-magnetic 3D TIs. Our results suggest a new approach for achieving 3D magnetic TI phases in such superlattices which is applicable to a large family of thallium rare-earth dichalcogenides and is expected to yield a fertile and tunable playground for exotic topological physics