Berry curvature induced transport phenomena on crystal surfaces

Dennis Wawrzik

AutorIn

Dennis Wawrzik

Titel

Berry curvature induced transport phenomena on crystal surfaces

Zitierfähige Url:

https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa2-979413

Erstveröffentlichung

2025

Datum der Einreichung

05.09.2024

Datum der Verteidigung

29.04.2025

Abstract (EN)

The Berry curvature (BC) associated with electronic band-like states is a fundamental quantity that gives rise to an anomalous electronic velocity and interesting (nonlinear) electronic, heat, and spin-transport properties. BC is a key concept in understanding and predicting physical properties of crystalline materials and, therefore, one of central quests of modern material design is to find mechanisms that can lead to large enhancements of BC. Typically, large BC concentrations occur at points in the Brillouin zone (BZ) where two bands are exactly or nearly degenerate, leading to rapid changes of the Bloch wave functions near such hot spots. Classic examples of such BC hot spots include the Weyl nodes in 3D materials and the Dirac points in 2D graphene. Inside a solid, the anomalous velocity of Bloch electrons caused by the electronic BC leads to a sideways deflection of currents, much as an external magnetic field. Such a current deflection caused by the intrinsic electronic structure of a material and its associated Hall-type response must be allowed by the symmetries of the system. It is well-known that an absence of magnetism, and consequently a presence of time-reversal symmetry in the electronic band structure, leads to zero total BC, integrated over BZ momenta. This consequently prevents any linear Hall response. However, as long as at least lattice inversion symmetry is broken, a finite BC is associated with the electronic structure, which can then allow, e.g. a quantum nonlinear Hall effect where the observed transversal voltage is proportional to the applied current squared. This nonlinear response is related to the dipole moment of the BZ integrated BC, the BC dipole. However, for materials with both time-reversal invariance and inversion, the BC vanishes identically at all momenta in the 3D BZ. In this thesis, I show that surface states can have -compared to a pure 2D system- an additional contribution to the BC which depends on the variance of the penetration length of the state into the bulk. Large BC contributions can arise which grow as the surface state penetrates deeper into the bulk and progressively attains more bulk character. This effect and its dependence on the surface structure and symmetry distinguishes the surface states’ BC obviously from its bulk counterpart. I demonstrate that the surface Fermi arc states of tilted Weyl semimetals (WSMs) are perfect candidates to observe this enhanced surface BC. The divergence of BC occurs not at a point, but instead over an entire line in the surface BZ, which I will refer to as a BC “hot line.” These hot lines emerge in the surface BZ of WSMs, and they separate the 2D states that are localized at the surface from the continuum of 3D bulk states. The topology of the Weyl system forces the Fermi arcs to end at such a hot line leading to a gigantic contribution to the BC driven nonlinear Hall effect. It features a contribution to the BC dipole that grows linearly proportionally with the thickness of a WSM slab. Thus, these findings not only enhance the understanding of the geometrical aspects of the Fermi arcs’ electronic structure, but should also be experimentally relevant in all BC driven phenomena in WSM. At a first glance, time-reversal and inversion symmetric materials seem to become uninteresting from the BC point of view as their BC and anomalous electron velocities appear to vanish. I demonstrate that while this conclusion is valid for 3D bulk materials, at surfaces and interfaces of these the opposite holds: at a general Miller index surfaces Bloch-electrons do attain a finite anomalous velocity, also for materials with bulk inversion and time-reversal symmetry. Indeed, as a general rule of thumb, the surface BC vanishes only at unreconstructed low Miller index surfaces, whereas a finite surface BC associated with any higher index surface, including miscut and vicinal ones with surface steps that break two-fold rotations around the surface normal and, thus, lack inversion symmetry. If there is, in addition, not more than one mirror plane containing the normal, a finite surface BC dipole forms. Very many elementary surfaces fulfill this symmetry requirement. This will be demonstrated by first principles calculations of the BC at bismuth, HgTe and rhodium surfaces of various symmetries. Again, this opens up a plethora of materials to explore and harness the physical effects emerging from the electronic BC associated exclusively with their boundaries.

Freie Schlagwörter (EN)

Berry curvature, topological materials, Berry curvature dipole, Weyl semimetals

Klassifikation (DDC)

530

Klassifikation (RVK)

UP 7500

GutachterIn