Session K03: Quantum Effects in Topological Systems

Classification and construction of higher-order symmetry protected topological phases of interacting bosons

Motivated by the recent discovery of higher-order topological insulators, we study their counterparts in strongly interacting bosons: `higher-order symmetry protected topological (HOSPT) phases'. While the usual (1st-order) SPT phases in d spatial dimensions support anomalous (d-1)-dimensional surface states, HOSPT phases in d dimensions are characterized by topological boundary states of dimension (d-2) or smaller, protected by certain global symmetries and robust against disorders. Based on a dimensional reduction analysis, we show that HOSPT phases can be built from lower-dimensional SPT phases in a way that preserves the associated crystalline symmetries. When the total symmetry is a direct product of global and crystalline symmetry groups, we are able to classify the HOSPT phases using the Künneth formula of group cohomology. Based on a decorated domain wall picture of the Künneth formula, we show how to systematically construct the HOSPT phases, and demonstrate our construction with many examples in two and three dimensions.   

Intrinsically interacting topological crystalline insulators and superconductor

Motivated by recent progress in crystalline symmetry protected topological (SPT) phases of interacting bosons, we study topological crystalline insulators/superconductors (TCIs) of strongly interacting fermions. We construct a class of intrinsically interacting fermionic TCIs, and show that they are beyond both free-fermion TCIs and bosonic crystalline SPT phases. We also show how these phases can be characterized by symmetry protected gapless corner/hinge states.   

Disorder-induced helical phase in magnetic topological insulators

In magnetically doped thin-film topological insulators, aligning the magnetic moments generates a quantum anomalous Hall phase with a single chiral edge state. We study the de-magnetization process and show that disorder from randomly oriented magnetic moments can produce a quantum-spin-Hall-like phase with counter-propagating helical edge modes protected by a unitary reflection symmetry. This phase is analogous to the quantum spin Hall effect observed in the zeroth Landau level of graphene, which is also protected by a unitary symmetry (spin rotation). We show that introducing superconductivity, combined with selective breaking of reflection symmetry by a gate, allows for creation and manipulation of Majorana zero modes via purely electrical means.   

Topological states from topological crystals

We show that crystalline symmetry protected topological states is adiabatically connected to a real-space crystalline pattern of lower-dimensional topological states, which we refer to as a topological crystal. As a demonstration of principle, we explicitly enumerate all inequivalent topological crystals for non-interacting time-reversal symmetric electronic insulators with significant spin-orbit coupling and any one of the 230 space groups in three dimensions. Because every topological crystalline insulator can be deformed into a topological crystal, the enumeration of the latter gives topological crystalline insulators a full classification and for each class an explicit real-space construction.   

Landau levels of topological surface states probed by quantum capacitance

Three-dimensional topological insulator (3D TI) is known by its unique Dirac dispersion surface states arising from band inversion of its bulk. Development of discrete Landau levels (LLs) in strong perpendicular magnetic field provides strong evidence of quantization from two-dimensional nature of the topological surface states. Density of states of the surface states’ LLs can be quantitatively determined through a quantum capacitance measurement. However, quantum capacitance in 3D TI is relatively less explored primarily due to mixing signals from the bulk or narrow bulk bandgap such as strained HgTe. In this work, we study the quantum capacitance of a truly bulk insulating 3D TI via a TI-based van der Waals heterostructures configuration. The quantum capacitance data are compared to the quantum Hall conductance in transport. By controlling the dual-gate voltages, we access the LLs from each surface states. The chemical potentials as function of charge density are extracted to quantify the LL spacings.   

Band structure and superconductivity in In-doped topological insulator (Pb0.5Sn0.5)1-xInxTe probed by NMR spectroscopy

The bulk band structure and superconductivity in the In-doped topological crystalline insulators (Pb_0.5Sn_0.5)_1-xIn_xTe, for x = 0, 0.1, 0.2, and 0.3, have been investigated by nuclear magnetic resonance (NMR) techniques. We found that the NMR frequency shifts of ¹¹⁷Sn, and ²⁰⁷Pb are dominated by the spins of free charge carriers, whereas the ¹²⁵Te frequency shift is determined by the magnetic orbital moments of the binding electrons. By analyzing these shifts, we conclude that In substitution for 0 ≤ x ≤ 0.3 provides not just hole carriers but also lifts the chemical potential from the valence bands to the conduction bands, in consistent with the results from the electric transport measurements. The superconductivity in the x = 0.3 sample is investigated by the nuclear spin-lattice relaxation rate (1/T₁) as a function of temperature, where a Hebel-Slichter coherence peak is observed near the critical temperature. This suggests that the superconducting gap in the bulk is fully opened and this feature may favor that (Pb_0.5Sn_0.5)_0.7In_0.3Te is a conventional superconductor rather than a chiral p-wave topological superconductor.   

Disorder-driven phase transitions in chiral-symmetric topological insulators

Chiral-symmetric topological insulators exhibit properties, such as polarization, that are robust to translation-symmetric perturbations provided the perturbations do not close the energy gap. However, it's unclear to what extent these topologically protected properties are robust to disorder, as disorder breaks the translation symmetry. Here we study a collection of 2D chiral-symmetric models with disorder using a covariant real space formula for the topological invariant. Generically, we find that the topological invariants remain precisely quantized until a critical value of disorder, at which point it smoothly decreases to zero. Furthurmore, we find that the critical disorder occurs exactly when states at the Fermi energy become delocalized. We therefore demonstrate that the topological characteristics are robust, and that in the presence of disorder the topology is protected by a mobility gap in place of an energy gap.   

Low Temperature Terahertz Nano Imaging of WTe2 Thin Film

We discuss the development of cryogenic scanning near-field microscope suitable for nano-scale imaging and spectroscopy at terahertz frequency range with the spatial resolution below 130 nm[1]. We report terahertz near-field measurement of WTe2 thin film of 1 to 3 layers[2] above and below the metal-insulator transition. Clear contrast in near-field signal can be observed among regions with different layer numbers and between metallic and insulating state.
[1] Stinson, H. T., et al. "Infrared nanospectroscopy and imaging of collective superfluid excitations in anisotropic superconductors." Physical Review B 90.1 (2014): 014502.
[2] Fei, Zaiyao, et al. "Edge conduction in monolayer WTe 2." Nature Physics 13.7 (2017): 677.   

Detection of higher order topological phase in a disordered breathing Kagome model by using machine learning

A higher order topological insulator is a new concept of topological states of matter, which is characterized by the emergent boundary states whose dimensionality is lower by more than two compared with that of the bulk, and draws a considerable interest. Yet, its robustness against disorders is still unclear. Here we investigate a phase diagram of higher order topological insulator phases in a breathing Kagome model in the presence of disorders, by using a state-of-the-art machine learning technique. We find that the corner states survive against the finite strength of disorder potential as long as the energy gap is not closed, indicating the stability of the higher order topological phases against the disorders. We also discuss the relation between the higher order topological phase and the Z_3 Berry phase, which is a bulk topological invariant.   

Double-frequency Aharonov-Bohm effect and non-Abelian braiding property of Jackiw-Rebbi zero-mode

Ever since its first proposal in 1976, Jackiw-Rebbi zero-mode has been drawing extensive attention for its charming properties including charge fractional quantization, topologically protected zero-energy and possible non-Abelian statistics. We numerically investigate the Jackiw-Rebbi zero-mode in a quantum spin Hall insulator heterostructure and show that its zero-energy nature leads to a double-frequency Aharonov-Bohm effect in electronic transport. Such observation suggests that Majorana zero-mode could be viewed as a special case of Jackiw-Rebbi zero-mode. Moreover, similar to the Majorana zero-modes, Jackiw-Rebbi zero-modes also show non-Abelian braiding properties in a cross-shaped junction. However, such non-Abelian property can be destroyed by infinitesimal disorder breaking charge-conjugation symmetry, implying the presence of charge-conjugation symmetry is of equal importance as the topological gap in the topological quantum computation.   

Quasi-particle Interference on the Step Edges of Epitaxial Stanene on InSb (111)

Stanene (single-layer of tin), having an atomic structure similar to graphene, offers a promising platform for achieving room-temperature quantum spin Hall effect with a gap of 0.3 eV [1-3]. We have performed the in-situ scanning tunneling microscopy experiments on stanene which was epitaxially grown on the InSb (111). Several types of step edges have been observed in the atomic-resolution STM topographic image. The quasi-particle interference near the steps has been detected by STS, allowing us to study the electron scattering behavior along the edge in relation to the topological property of the edge state.

Reference:
[1] Y. Xu, et al, Phys. Rev. Lett. 111, 1 (2013).
[2] F. F. Zhu, et al, Nat. Mater. 14, 1020 (2015).
[3] C. Z. Xu et al, Phys. Rev. Lett. 118, 1 (2017).   

Experimental demonstration of the robustness of topological surface states on a PbTaSe2 superconductor

Conventional semiconductor electronic surface states are determined by the details of its surface geometry, and the chemical nature of the surface atoms. Conversely, topological surface states arise entirely from the non-trivial bulk band topology. In topological insulators, the bulk electronic structure is always gapped while the surface is metallic everywhere independent of surface details. This bulk-boundary correspondence is the key manifestation of topology in a condensed matter system.
Unfortunately, there has yet to be solid experimental demonstrated in a real material. Here, on superconducting Z₂ topological insulator PbTaSe₂(001), we uncover two types of surfaces with distinct surface geometry and chemistry, namely 1 × 1-Se and 2 × 2-Pb surfaces. By means of scanning tunneling microscopy, we find metallic surface states on both types of surfaces. Moreover, we discern the superconducting gap to be uniform on both surfaces. Our research serves as the first experimental proof that the topological surface state is robust against surface geometry reconstruction, variation in chemical termination of the surface, and superconducting interactions, possibly opening new pathways for research in topological materials.   

Chiral Phonon Transport Induced by Topological Magnons

The plethora of recent discoveries in the field of topological electronic insulators has inspired a search for boson systems with similar properties. There are predictions that ferromagnets on a two-dimensional honeycomb lattice may host chiral edge magnons. In such systems, we theoretically study how magnons and phonons couple. We find topological magneto-polarons around the avoided crossings between phonons and topological magnons. Exploiting this feature along with our finding of Rayleigh edge phonons in armchair ribbons, we demonstrate the existence of chiral edge modes with a phononic character. We predict that these modes mediate a chirality in the coherent phonon response and suggest to measure this effect via elastic transducers. These findings reveal a possible approach towards heat management in future devices.   

First-order topological quantum phase transitions in strongly correlated one-dimensional systems

Topological quantum phase transitions, such as the transition between a topological insulator and a trivial gapped phase, are hallmarked by the
change of a topological invariant [1]. For non-interacting fermions, such transitions between insulating phases are continuous since they are accompanied by the closing of the band gap as long as the symmetries of the system are maintained. For interacting fermions, by contrast, this paradigm is altered and first-order topological quantum transitions can occur [2].

In my talk I discuss the first example of a first-order topological quantum phase transition in a strongly correlated one-dimensional system [3].
Specifically, I consider a four-leg ladder which supports a symmetry protected topological phase in the presence of an on-site repulsive interaction, but is driven towards a trivial phase by a nearest-neighbor interaction. Employing a DMRG approach, I investigate at a numerically exact level the first-order nature of the transition.

References
[1] X. -L. Qi and S. -C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
[2] A. Amaricci, et al; Phys. Rev. Lett. 114, 185701 (2015).
[3] S. Barbarino, et al; in preparation.