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Register a new userStrong Correlation Effects on Topological Quantum Phase Transitions in Three Dimensions
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We investigate the role of short-ranged electron-electron interactions in a paradigmatic model of three dimensional topological insulators, using dynamical mean-field theory and focusing on non magnetically ordered solutions. The non-interacting band-structure is controlled by a mass term M, whose value discriminates between three different insulating phases, a trivial band insulator and two distinct topologically non-trivial phases. We characterize the evolution of the transitions between the different phases as a function of the local Coulomb repulsion U and find a remarkable dependence of the U -M phase diagram on the value of the local Hunds exchange coupling J. However, regardless the value of J, following the evolution of the topological transition line between a trivial band insulator and a topological insulator, we find a critical value of U separating a continuous transition from a first-order one. When the Hunds coupling is significant, a Mott insulator is stabilized at large U . In proximity of the Mott transition we observe the emergence of an anomalous Mott-like strong topological insulating state.
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The interest in the topological properties of materials brings into question the problem of topological phase transitions. As a control parameter is varied, one may drive a system through phases with different topological properties. What is the nature of these transitions and how can we characterize them? The usual Landau approach, with the concept of an order parameter that is finite in a symmetry broken phase is not useful in this context. Topological transitions do not imply a change of symmetry and there is no obvious order parameter. A crucial observation is that they are associated with a diverging length that allows a scaling approach and to introduce critical exponents which define their universality classes. At zero temperature the critical exponents obey a quantum hyperscaling relation. We study finite size effects at topological transitions and show they exhibit universal behavior due to scaling. We discuss the possibility that they become discontinuous as a consequence of these effects and point out the relevance of our study for real systems.
We show that four-dimensional systems may exhibit a topological phase transition analogous to the well-known Berezinskii-Kosterlitz-Thouless vortex unbinding transition in two-dimensional systems. The realisation of an engineered quantum system, where the predicted phase transition shall occur, is also presented. We study a suitable generalization of the sine-Gordon model in four dimensions and the renormalization group flow equation of its couplings, showing that the critical value of the frequency is the square of the corresponding value in $2D$. The value of the anomalous dimension at the critical point is determined ($eta=1/32$) and a conjecture for the universal jump of the superfluid stiffness ($4/pi^2$) presented.
We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological properties is richer than the two-dimensional case. In addition to the reduction of the entropy caused by non-zero vacuum expectation value of contractible loop operators a new topological invariant appears that increases the entropy if the model consists of non-trivially braiding anyons. As a result the three-dimensional topological entanglement entropy provides only partial information about the two entropic topological invariants.
Topological insulators (TIs) containing 4f electrons have recently attracted intensive interests due to the possible interplay of their non-trivial topological properties and strong electronic correlations. YbB6 and SmB6 are the prototypical systems with such unusual properties, which may be tuned by external pressure to give rise to new emergent phenomena. Here, we report the first observation, through in-situ high pressure resistance, Hall, X-ray diffraction and X-ray absorption measurements, of two pressure-induced quantum phase transitions (QPTs) in YbB6. Our data revealthat the two insulating phases are separated by a metallic phase due to the pressure-driven valence change of Yb f-orbitals. In combination with previous studies, our results suggest that the two insulating states may be topologically different in nature and originate from the d-p and d-f hybridization, respectively. The tunable topological properties of YbB6 revealed in this study may shed light on the intriguing correlation between the topology and the 4f electrons from the perspective of pressure dependent studies.
Periodical equilibrium states of magnetization exist in chiral ferromagnetic films, if the constant of antisymmetric exchange (Dzyaloshinskii-Moriya interaction) exceeds some critical value. Here, we demonstrate that this critical value can be significantly modified in curved film. The competition between symmetric and antisymmetric exchange interactions in a curved film can lead to a new type of domain wall which is inclined with respect to the cylinder axis. The wall structure is intermediate between Bloch and Neel ones. The exact analytical solutions for phase boundary curves and the new domain wall are obtained.
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