Stephan Rachel

Giant magnetoresistance and perfect spin filter in silicene, germanene, and stanene

Silicene, germanene and stanene are two-dimensional topological insulators exhibiting helical edge states. We investigate global and local manipulations at the edges by exposing them to (i) a charge-density-wave order, (ii) a superconductor, (iii) an out-of-plane antiferromagnetic, and (iv) an in-plane antiferromagnetic field. We show that these perturbations affect the helical edge states in a different fashion. As a consequence one can realize quantum spin-Hall effect without edge states. In addition, these edge manipulations lead to very promising applications: a giant magnetoresistance and a perfect spin filter. We also investigate the effect of manipulations on a very few edge-sites of a topological insulator nanodisk.

Inelastic Electron Backscattering in a Generic Helical Edge Channel

We evaluate the low-temperature conductance of a weakly interacting one-dimensional helical liquid without axial spin symmetry. The lack of that symmetry allows for inelastic backscattering of a single electron, accompanied by forward scattering of another. This joint effect of weak interactions and potential scattering off impurities results in a temperature-dependent deviation from the quantized conductance, δG ∝ T4. In addition, δG is sensitive to the position of the Fermi level. We determine numerically the parameters entering our generic model for the Bernevig-Hughes-Zhang Hamiltonian of a HgTe/CdTe quantum well in the presence of Rashba spin-orbit coupling.

Quantum spin Hall insulators with interactions and lattice anisotropy

We investigate the interplay between spin-orbit coupling and electron-electron interactions on the honeycomb lattice, combining the cellular dynamical mean-field theory and its real-space extension with analytical approaches. We provide a thorough analysis of the phase diagram and temperature effects at weak spin-orbit coupling. We systematically discuss the stability of the quantum spin Hall phase toward interactions and lattice anisotropy, resulting in the plaquette-honeycomb model. We also show the evolution of the helical edge states characteristic of quantum spin Hall insulators as a function of Hubbard interaction and anisotropy. At very weak spin-orbit coupling and intermediate electron-electron interactions, we substantiate the existence of a quantum spin liquid phase.

General relation between entanglement and fluctuations in one dimension

In one dimension very general results from conformal field theory and exact calculations for quantum spin chains have established universal scaling properties of the entanglement entropy between two parts of a critical system. Using both analytical and numerical methods, we show that if particle number or spin is conserved, fluctuations in a subsystem obey identical scaling as a function of subsystem size in one dimension. We investigate the effects of boundaries and subleading corrections for critical spin and bosonic chains.

Spiral order in the honeycomb iridate Li2IrO3

The honeycomb iridates A_2IrO_3 (A = Na, Li) constitute promising candidate materials to realize the Heisenberg-Kitaev model (HKM) in nature, hosting unconventional magnetic as well as spin-liquid phases. Recent experiments suggest, however, that Li_2IrO_3 exhibits a magnetically ordered state of incommensurate spiral type which has not been identified in the HKM. We show that these findings can be understood in the context of an extended Heisenberg-Kitaev scenario satisfying all tentative experimental evidence: (i) the maximum of the magnetic susceptibility is located inside the first Brillouin zone, (ii) the Curie-Weiss temperature is negative relating to dominant antiferromagnetic fluctuations, and (iii) significant second-neighbor spin exchange is involved.

Time-reversal-invariant Hofstadter-Hubbard Model with ultracold fermions

We consider the time-reversal-invariant Hofstadter-Hubbard model which can be realized in cold-atom experiments. In these experiments, an additional staggered potential and an artificial Rashba-type spin-orbit coupling are available. Without interactions, the system exhibits various phases such as topological and normal insulator, metal as well as semi-metal phases with two or even more Dirac cones. Using a combination of real-space dynamical mean-field theory and analytical techniques, we discuss the effect of on-site interactions and determine the corresponding phase diagram. In particular, we investigate the semi-metal to antiferromagnetic insulator transition and the stability of different topological insulator phases in the presence of strong interactions. We compute spectral functions which allow us to study the edge states of the strongly correlated topological phases.

Rashba spin-orbit coupling in the Kane-Mele-Hubbard model

Spin-orbit (SO) coupling is the crucial parameter to drive topological-insulating phases in electronic band models. In particular, the generic emergence of SO coupling involves the Rashba term which fully breaks the SU(2) spin symmetry. As soon as interactions are taken into account, however, many theoretical studies have to content themselves with the analysis of a simplified U(1)-conserving SO term without Rashba coupling. We intend to fill this gap by studying the Kane-Mele-Hubbard (KMH) model in the presence of Rashba SO coupling and present the first systematic analysis of the effect of Rashba SO coupling in a correlated two-dimensional topological insulator. We apply the variational cluster approach (VCA) to determine the interacting phase diagram by computing local density of states, magnetization, single particle spectral function, and edge states. Preceded by a detailed VCA analysis of the KMH model in the presence of U(1)-conserving SO coupling, we find that the additional Rashba SO coupling drives new electronic phases such as a metallic regime and a weak topological-semiconductor phase which persist in the presence of interactions.

Detecting quantum critical points using bipartite fluctuations.

We show that the concept of bipartite fluctuations F provides a very efficient tool to detect quantum phase transitions in strongly correlated systems. Using state-of-the-art numerical techniques complemented with analytical arguments, we investigate paradigmatic examples for both quantum spins and bosons. As compared to the von Neumann entanglement entropy, we observe that F allows us to find quantum critical points with much better accuracy in one dimension. We further demonstrate that F can be successfully applied to the detection of quantum criticality in higher dimensions with no prior knowledge of the universality class of the transition. Promising approaches to experimentally access fluctuations are discussed for quantum antiferromagnets and cold gases.

Phase diagram and quantum order by disorder in the kitaev K1 - K2 honeycomb magnet

We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling K2, which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iridate Na2IrO3, and may also play a role in α-RuCl3and Li2IrO3. This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in Na2IrO3. Moreover, the minimal K1- K2model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.

Tunneling spectra simulation of interacting Majorana wires

Recent tunneling experiments on InSb hybrid superconductor-semiconductor devices have provided hope for a stabilization of Majorana edge modes in a spin-orbit quantum wire subject to a magnetic field and superconducting proximity effect. Connecting the experimental scenario with a microscopic description poses challenges of a different kind, such as accounting for the effect of interactions on the tunneling properties of the wire. We develop a density matrix renormalization group (DMRG) analysis of the tunneling spectra of interacting Majorana chains, which we explicate for the Kitaev chain model. Our DMRG approach allows us to calculate the spectral function down to zero frequency, where we analyze how the Majorana zero-bias peak is affected by interactions. For topological phase transitions between the topological and trivial superconducting phase in the Majorana wire, the bulk gap closure generically affects the proximity peaks and the Majorana peak.