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Τίτλος Hall effect in 2D spin-orbit and topological materials with Van Hove singularities
Άλλος τίτλος Φαινόμενο Hall σε 2D spin-orbit και τοπολογικά υλικά με Van Hove ανωμαλίες
Συγγραφέας Κοκκίνης Εμμανουήλ
Σύμβουλος διατριβής Ζώτος, Ξενοφών
Περίληψη As we know, the classical Hall effect arises when we apply an external magnetic field perpendicular to the direction of the current density. One can define the Hall coefficient RH = Ey/ (jxBz), where Ey is the induced electric field. For a single band the Hall number depends only on the sign and density of carriers. That is why, at low temperatures, it can be used to determine the number of electrons or holes in electron and hole-like pockets respectively. However, in systems with multiple bands or near Fermi-surface topological transitions, the Hall coefficient starts to deviate from its exclusive counting nature. This anomalous behavior can be attributed to singularities in the density of states, called Van Hove singularities [1, 2]. Most materials show logarithmic-type Van Hove singularities, which correspond to a logarithmic divergence of the density of states at the Lifshitz transition. In our work, we are interested in higher order Van Hove singularities, which arise from more complicated Lifshitz transitions. Such singularities can be observed, for example, in Sr3Ru2O7 which exhibits a more complicated singularity when an external magnetic field is applied [3, 4]. Another example is highly overdoped graphene and twisted bilayer graphene [5–8]. In the first section of this thesis (Chapters 1-2), we extend the well-known Chambers’ formula [9] to the case of a time-dependent electric field as well as a band with non-zero Berry Curvature. To this end, we study the solution of the Boltzmann equation to first order in the magnetic field B and to quadratic order in the electric field E2. We note that the equations of motion used in this work are valid to leading order in the electric and magnetic fields. We also neglect Zeeman splitting and spin orbit coupling which would result in more complicated expressions. We then apply our generalized Chambers’ formula to study three different systems. The first is a simple rectangular lattice [10], the second is a simple model for highly doped graphene and the last is the Haldane model as an example of a system with non-zero Berry Curvature. In all of the above cases, we study the effect of the high order Van Hove singularities to the Hall coefficient of the system. In the second section of the work (Chapter 3), we study the Reactive Hall response [11] (T→0, ω→0) for the case of a rectangular lattice, to which we have added a spin-orbit coupling in the form of Rashba interaction. To do this, we consider a magnetic field in the ydirection modulated by a one component wave vector q. Furthermore, we study the “screening” (or slow) response, by first taking the ω→0 limit and then the q→0 limit. Through our analysis, we analytically derive an equation that connects the Hall constant RH with the Drude weight D of the system. We then apply our formula to study the behavior of the Hall constant of our system for different values of the hopping elements. This gives us a qualitative image of the sign change of the carriers close to a metal-insulator transition. Once again, we observe that closely to the Van Hove singularity points, the behavior of the Hall constant rapidly changes.
Γλώσσα Αγγλικά
Ημερομηνία έκδοσης 2022-07-22
Συλλογή   Σχολή/Τμήμα--Σχολή Θετικών και Τεχνολογικών Επιστημών--Τμήμα Φυσικής--Πτυχιακές εργασίες
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