Session A31: Focus Session: Topological Insulators - Exotic Phases and Phase Transitions

Quantum Anomalous Hall Effect in Magnetic Topological Insulator GdBiTe3

The quantum anomalous Hall (QAH) state is a two-dimensional bulk insulator with a non-zero Chern number in absence of external magnetic fields. Protected gapless chiral edge states enable dissipationless current transport in electronic devices. Doping topological insulators with random magnetic impurities could realize the QAH state, but magnetic order is difficult to establish experimentally in the bulk insulating limit. Here we predict that the single quintuple layer of GdBiTe$_3$ film could be a stoichiometric QAH insulator based on \emph{ab-initio} calculations, which explicitly demonstrate ferromagnetic order and chiral edge states inside the bulk gap. We further investigate the topological quantum phase transition by tuning the lattice constant and interactions. A simple low-energy effective model is presented to capture the salient physical feature of this topological material.   

First-principles study of magnetic ion doping in thin film Bi$_2$Se$_3$: electronic structure and topological phase

We study the quantum anomalous Hall state in magnetic ion-doped Bi$_2$Se$_3$ thin films. By using first-principles density functional theory, we investigate this electronic structure and identify its topological phase. We find that magnetic ion doping induces the exchange field splitting and changes the spin-orbit coupling strength. As the doping concentration increases, the exchange field splitting strength increases and the spin-orbit coupling strength may decrease depending on the type of magnetic ion. Based on these results, we show that the quantum anomalous Hall state in the doped Bi$_2$Se$_3$ thin film emerges at a certain range of doping concentration. The Hall conductance of the doped Bi$_2$Se$_3$ thin film will also be discussed with various doping concentrations.   

Charge 4e Superconductivity from Quantum Spin Hall phase

We present how to achieve charge 4e superconductor as a ground state studying non-relativistically induced quantum numbers of Skyrmions. It is shown that induced charge of Skyrmions interacting with fermion with quadratic band touching dispersion is twice bigger than one of Skyrmions with Dirac-like fermion. We also show that the former Skyrmions are always bosons while the latter ones are determined by the number of fermion flavors. Possible physical realization is discussed focusing on Skyrmions of quantum spin Hall order parameter in bi-layer graphene. Properties of quantum phase transition between charge $4e$ superconductor and quantum spin Hall phase are also discussed.   

Majorana fermions in semiconductor nanowires with realistic physical parameters

Semiconductor nanowires proximity coupled to s-wave superconductors represent a unique solid state platform for realizing and observing the elusive Majorana fermion. The existence and stability of the Majorana bound states localized at the ends of the wire depend on a set of parameters that includes the chemical potential, the external magnetic field, the spin-orbit coupling, the strength of the semiconductor-superconductor coupling, and the strengths of various types of disorder. It is critical to determine whether or not the parameter regimes that ensure the stability of the Majoranas are consistent with realistic experimental conditions. In this talk I will summarize the results of a theoretical study of multiband semiconductor nanowires that focuses on understanding the key experimental conditions required for the realization and detection of Majorana fermions. I will show that multiband occupancy not only lifts the stringent constraint of one-dimensionality, but also allows having higher carrier density in the nanowire. This significantly enhances the stability of the topologically nontrivial phase against various types of disorder, such as short-range impurities in the bulk superconductor, disorder at the semiconductor-superconductor interface, and disorder in the semiconductor nanowire. The detailed study of the parameter space for multiband semiconductor nanowires establishes the realistic likelihood of the existence of zero-energy Majorana modes within laboratory conditions.   

Topological States and Adiabatic Pumping in Quasicrystals

We find a connection between quasicrystals and topological matter, namely that quasicrystals exhibit non-trivial topological phases attributed to dimensions higher than their own [1]. Quasicrystals are materials which are neither ordered nor disordered, i.e. they exhibit only long-range order [2]. This long-range order is usually expressed as a projection from a higher dimensional ordered system. Recently, the unrelated discovery of Topological Insulators [3] defined a new type of materials classified by their topology. We show theoretically and experimentally using photonic lattices, that one-dimensional quasicrystals exhibit topologically-protected boundary states equivalent to the edge states of the two-dimensional Integer Quantum Hall Effect. We harness this property to adiabatically pump light across the quasicrystal, and generalize our results to higher dimensional systems. Hence, quasicrystals offer a new platform for the study of topological phases while their topology may better explain their surface properties.\\[4pt] [1] Y.~E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, arXiv:1109.5983 (2011).\\[0pt] [2] C. Janot, \textit{Quasicrystals} (Clarendon, Oxford, 1994), 2nd ed.\\[0pt] [3] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. \textbf{82}, 3045 (2010).   

Skyrmion quantum numbers and quantized pumping in two dimensional topological chiral magnets

We investigate the general conditions to achieve the adiabatic charge and spin polarizations and quantized pumping in 2D magnetic insulators possessing inhomogeneous spin structures. In particular, we focus on the chiral ferrimagnetic insulators which are generated via spontaneous symmetry breaking from correlated two dimensional topological insulators. Adiabatic deformation of the inhomogeneous spin structure generates the spin gauge flux, which induces adiabatic charge and spin polarization currents. The unit pumped charge/spin are determined by the product of two topological invariants which are defined in momentum and real spaces, respectively. The same topological invariants determine the charge and spin quantum numbers of skyrmion textures. It is found that in noncentrosymmetric systems, a new topological phase, dubbed the topological chiral magnetic insulator, exists in which a skyrmion defect is a spin-1/2 fermion with electric charge $e$. Considering the adiabatic current responses of generic inhomogeneous systems, it is shown that the quantized topological response of chiral magnetic insulators is endowed with the second Chern number.   

Beyond Floquet theory: new paradigms for robust topological phenomena in strongly driven systems

The discoveries of the quantized Hall effect [1] and Thouless' quantized adiabatic pumping [2] revealed the existence of a new class of extremely robust quantum phenomena which can be observed with high fidelity, largely independent of sample details. The immunity of these remarkable effects to a variety of perturbations can be understood in terms of a topological structure associated with the systems' wave functions. The rapid development of powerful tools for controlling solid state and atomic systems over the last decade has motivated the exploration of topological phenomena in driven systems. Recently, Kitagawa and coworkers [3] discussed analogs of previously known topological phenomena in terms of the Floquet operators of periodically-driven systems. Intriguingly, this work also revealed new robust phenomena, such as the existence of robust chiral edge modes in a 2D system with vanishing Chern numbers for all bulk Floquet bands. Here we construct the topological invariant which distinguishes phases with and without chiral edge modes, and discuss generalizations to other 1D and 2D systems. \\[4pt] [1] K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).\\[0pt] [2] D. J. Thouless, Phys. Rev. B 27, 6083 (1983).\\[0pt] [3] T. Kitagawa, et al., Phys. Rev. B 82, 235114 (2010).   

Emergent Topological Phases with Multiple Bands and Artificial Gauge Fields

Particles on a two-dimensional Kagome lattice have attracted growing attention recently in relation to topological insulators and topological phases. Such Kagome structures can be engineered in optical lattices and can also be loaded with bosons. Similar tight-binding models might also be realized in photonic QED circuits. In this work, we investigate in detail the 3-band model emerging from such a tight-binding model on the two-dimensional Kagome lattice in the presence of artificial gauge fields and identify novel phases of matter such as bulk metals with helical edge states. We investigate the stability of edge modes inside a topological metallic phase and the role of lattice anisotropies and disorder, as well as relation to current experiments.   

Possible interaction driven topological phases in (111) bilayers of LaNiO$_3$

We use the variational mean-field approach to systematically study the phase diagram of a bilayer heterostructure of the correlated transition metal oxide LaNiO$_3$, grown along the (111) direction. The Ni$^{3+}$ ions with $d^7$ (or $e_g^1$) configuration form a buckled honeycomb lattice. We show that as a function of the strength of the on-site interactions, various topological phases emerge. In the presence of a reasonable size of the Hund's coupling, as the correlation is tuned from intermediate to strong, the following sequence of phases is found: (1) a Dirac half-semimetal phase, (2) a quantum anomalous Hall insulator (QAHI) phase with Chern number one, and (3) a ferromagnetic nematic phase breaking the lattice point group symmetry. The spin-orbit couplings and magnetism are both dynamically generated in the QAHI phase.   

Quantum Phase Transitions in the Kane-Mele-Hubbard Model

We study the ground state phase diagram of the Kane-Mele-Hubbard model on the two-dimensional honeycomb lattice. At half-filling the phase diagram is mapped out using projective auxiliary field quantum Monte Carlo simulations. We present a refined phase boundary for the quantum spin liquid. The topological (quantum spin-Hall) insulator at finite Hubbard interaction strength is adiabatically connected to the ground state of the Kane-Mele model. For the magnetic phase at large Hubbard interaction strength, we show that the magnetic order is restricted to the transverse direction. The transition from the topological band insulator to the antiferromagnetic Mott insulator is in the universality class of the three-dimensional XY model. The numerical data also suggest that the spin liquid to topological insulator and spin liquid to Mott insulator transitions are both continuous.   

Topological Phase Transitions for Interacting Finite Systems

We investigate topological phase transitions in interacting systems via the observation of a topologically protected level crossing. This level crossing is robust and sharply defines a topological transition even in finite-size systems. For Chern insulators, this technique gives the same topological transition point as obtained in the Chern number calculation (via flux insertion). However, in the presence of space inversion symmetry, we proved that if the topological index changes by an odd integer at the topological transition, the level crossing can only arise under (some of) the four high-symmetry boundary conditions. This discovery provides a very efficient way to detect topological phase transitions, which reduces the computational load dramatically. In contrast to the standard Chern number technique, which requires to compute the ground state wave function for hundreds of different boundary conditions, our technique achieves the same result by calculating the excitation gap for only four different boundary conditions. We demonstrate this technique in the Haldane-Fermi-Hubbard model utilizing exact diagonalization. Generalization to time-reversal invariant Z$_2$topological insulators will also be discussed.   

Topological phases and phase transitions in a two-dimensional fermionic lattice

A topological state of matter is characterized by a topological invariant, which is protected against disorder effects. For the quantum Hall effect, the Hall conductivity is protected since it is carried by chiral edge states, induced by a magnetic field. Systems with large spin-orbit coupling exhibit the quantum spin Hall effect, where the protected quantity is the spin Hall conductivity, carried by helical edge states. In our theoretical study of a fermionic tight-binding model we show that the interplay between the magnetic field and the spin-orbit coupling generates spin-imbalanced chiral phases and exotic phase transitions between helical and chiral spin textures. We explore the experimental possibilities to observe these phase transitions in cold-atom systems, for which the necessary strengths of the magnetic field and spin-orbit coupling are accessible. As a second application, we investigate the spectrum of topological phases in HgTe quantum wells doped with Mn ions (in collaboration with Molenkamp's group). We show that this doping leads to interesting reentrant effects of both the Hall and spin Hall conductivities.   

Phase Structure of the Topological Anderson Insulator

We report the phase structure of disordered HgTe topological Anderson insulator in a 2-D geometry. We use exact diagonalization to calculate the spectrum and eigenstate structure, and recursive green's functions to calculate the conductance. All observables are measured at several system sizes, allowing us to determine phase transitions and two critical points. The quantized-conductance TAI phase contains two phases: TAI-I lying in a bulk band gap, and TAI-II where bulk states exist but are localized. We find that the TAI-II phase persists at disorder strengths where there is no bulk band gap; a bulk band gap is not necessary to obtain conductance quantization. In a previous work the weak-disorder edge of the TAI phase was explained as a transition into the bulk gap (TAI-I), but we find also a direct transition into the ungapped (TAI-II) quantized phase. Effective medium theory (SCBA) predicts well the boundaries and interior of the TAI-I phase, but fails at larger disorders including the interior of the TAI-II phase. When the system size is smaller than the bulk localization length, the quantized TAI region is bounded by either the bulk band edge or the localization length, but when the system size is large it is bounded by a transition of edge states.