Topological States Of Quantum Matter Research Articles

Gravitational response of topological quantum states of matter

Identifying novel topological properties of topological quantum states of matter, such as exemplified by the quantized Hall conductance, is a valuable step towards realizing materials with attractive topological attributes that guarantee their imperviousness to realistic imperfections, disorder and environmental disturbances. Is the gravitational coupling coefficient of topological quantum states of matter a promising candidate? Substantially building on well established results for quantum Hall states, using disclinations as tools for controlled creation of pristine spatial curvature free of undesirable artifacts such as would interfere with the electronic motion of interest, herein we report that a large class of lattice topological states of matter exhibit gravitational response, i.e., charge response to intrinsic spatial curvature. This phenomenon is characterized by a topologically quantized coupling constant. Remarkably, the charge-gravity relationship remains linear in the curvature, up to the maximum curvature achievable on the lattice, demonstrating absence of higher order nonlinear response. Our findings facilitate articulating the physical principles underlying the topological quantization of the gravitational coupling constant, in analogy with the insights offered by the Chern number description of the quantized Hall conductance.

Topological properties of MoP[formula omitted]N[formula omitted] (x = 0, 0.25, 0.5, 0.75, 1) compounds: A density functional approach

Triply Degenerate Point (TDP) fermions in tungsten–carbide-type materials such as MoP which represent new topological states of quantum matter, have generated great interest recently. However, the TDPs in these materials are found to be far below the Fermi level (∼ −1.5eV) leading to the TDP fermions having less contribution to low-energy quasiparticle excitations. Here, we theoretically investigate the existence of TP fermions with TDPs close to the Fermi level in MoN, which has the same structure as MoP, and the ternary MoP1−xNx ordered alloys which their crystal structure is defined by replacing P atoms by N atoms in MoP compound. The topological properties of MoP1−xNx (x = 0, 0.25, 0.5, 0.75, 1) ordered alloys are systematically investigated by combining first-principles calculations and Wannier tight-binding analysis. The obtained Wannier Charge Centers (WCCs) are applied to calculate the topological invariant Z2 number. Our calculations show that hexagonal MoP, MoP0.75N0.25, MoP0.25N0.75, and MoN compounds are topological semimetals hosting triply degenerate nodal points resulting from band crossing between degenerate and nondegenerate bands along the high-symmetry directions of the Brillouin Zone, being protected by crystalline symmetries. Among these compounds, the triple degenerate points in MoP0.75N0.25 are much closer to the Fermi level. MoP0.75N0.25 hosts some points slightly above (42 meV, 73 meV and 87 meV) the Fermi energy. On the other hand, our ab initio calculations suggest that the MoP0.5N0.5 compound with orthorhombic structure does not host any triple degenerate point. It hosts a multitude of topological features including Weyl Points and nodal lines. The calculations indicate that these nodal lines are located in the vicinity of Fermi level.

Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer's Principle.

Fidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us to formulate analogues of the four thermodynamic laws and Landauer’s principle at zero temperature. Fidelity flows, which are irreversible, are defined and may be interpreted as an alternative form of renormalization group flows. Thus, fidelity mechanics offers a means to characterize both stable and unstable fixed points: divergent fidelity temperature for unstable fixed points and zero-fidelity temperature and (locally) maximal fidelity entropy for stable fixed points. In addition, fidelity entropy behaves differently at an unstable fixed point for topological phase transitions and at a stable fixed point for topological quantum states of matter. A detailed analysis of fidelity mechanical-state functions is presented for six fundamental models—the quantum spin- XY model, the transverse-field quantum Ising model in a longitudinal field, the quantum spin- XYZ model, the quantum spin- XXZ model in a magnetic field, the quantum spin-1 XYZ model, and the spin- Kitaev model on a honeycomb lattice for illustrative purposes. We also present an argument to justify why the thermodynamic, psychological/computational, and cosmological arrows of time should align with each other, with the psychological/computational arrow of time being singled out as a master arrow of time.

Evidence for electronic signature of a magnetic transition in the topological magnet HoSbTe

Topological insulators with intrinsic magnetic order are emerging as an exciting platform to realize fundamentally new excitations from topological quantum states of matter. To study these systems and their physics, people have proposed a variety of magnetic topological insulator systems, including HoSbTe, an antiferromagnetic weak topological insulator candidate. In this work, we use scanning tunneling microscopy to probe the electronic structure of HoSbTe with antiferromagnetic and ferromagnetic orders that are tuned by applying an external magnetic field. Although around the Fermi energy we find minor differences between the quasiparticle interferences under the ferromagnetic and antiferromagnetic orders, deep inside the valance region, a quasiparticle interference signal emerges with ferromagnetism. This observation is consistent with our first-principles calculations indicating the magnetism-driven transition of the electronic states in this spin-orbit coupled topological magnet.

Magnetic Weyl Semimetallic Phase in Thin Films of Eu_{2}Ir_{2}O_{7}.

The interplay between electronic interactions and strong spin-orbit coupling is expected to create a plethora of fascinating correlated topological states of quantum matter. Of particular interest are magnetic Weyl semimetals originally proposed in the pyrochlore iridates, which are only expected to reveal their topological nature in thin film form. To date, however, direct experimental demonstrations of these exotic phases remain elusive, due to the lack of usable single crystals and the insufficient quality of available films. Here, we report on the discovery of signatures for the long-sought magnetic Weyl semimetallic phase in (111)-oriented Eu_{2}Ir_{2}O_{7} high-quality epitaxial thin films. We observed an intrinsic anomalous Hall effect with colossal coercivity but vanishing net magnetization, which emerges right below the onset of a peculiar magnetic phase with all-in-all-out (AIAO) antiferromagnetic ordering. The anomalous Hall conductivity obtained experimentally is consistent with the theoretical prediction, likely arising from the nonzero Berry curvature emanated by Weyl node pairs near the Fermi level that act as sources and sinks of Berry flux, activated by broken cubic crystal symmetry at the top and bottom terminations of the thin film.

Roton pair density wave in a strong-coupling kagome superconductor.

The transition metal kagome lattice materials host frustrated, correlated and topological quantum states of matter1-9. Recently, a new family of vanadium-based kagome metals, AV3Sb5 (A = K, Rb or Cs), with topological band structures has been discovered10,11. These layered compounds are nonmagnetic and undergo charge density wave transitions before developing superconductivity at low temperatures11-19. Here we report the observation of unconventional superconductivity and a pair density wave (PDW) in CsV3Sb5 using scanning tunnelling microscope/spectroscopy and Josephson scanning tunnelling spectroscopy. We find that CsV3Sb5 exhibits a V-shaped pairing gap Δ ~ 0.5 meV and is a strong-coupling superconductor (2Δ/kBTc ~ 5) that coexists with 4a0 unidirectional and 2a0 × 2a0 charge order. Remarkably, we discover a 3Q PDW accompanied by bidirectional 4a0/3 spatial modulations of the superconducting gap, coherence peak and gap depth in the tunnelling conductance. We term this novel quantum state a roton PDW associated with an underlying vortex-antivortex lattice that can account for the observed conductance modulations. Probing the electronic states in the vortex halo in an applied magnetic field, in strong field that suppresses superconductivity and in zero field above Tc,reveals that the PDW is a primary state responsible for an emergent pseudogap and intertwined electronic order. Our findings show striking analogies and distinctions to the phenomenology of high-Tc cuprate superconductors, and provide groundwork for understanding the microscopic origin of correlated electronic states and superconductivity in vanadium-based kagome metals.

Time-Reversal Symmetry Breaking Driven Topological Phase Transition in EuB6

The interplay between time-reversal symmetry (TRS) and band topology plays a crucial role in topological states of quantum matter. In time-reversal-invariant (TRI) systems, the inversion of spin-degenerate bands with opposite parity leads to nontrivial topological states, such as topological insulators and Dirac semimetals. When the TRS is broken, the exchange field induces spin splitting of the bands. The inversion of a pair of spin-splitting subbands can generate more exotic topological states, such as quantum anomalous Hall insulators and magnetic Weyl semimetals. So far, such topological phase transitions driven by the TRS breaking have not been visualized. In this work, using angle-resolved photoemission spectroscopy, we have demonstrated that the TRS breaking induces a band inversion of a pair of spin-splitting subbands at the TRI points of Brillouin zone in EuB$_6$, when a long-range ferromagnetic order is developed. The dramatic changes in the electronic structure result in a topological phase transition from a TRI ordinary insulator state to a TRS-broken topological semimetal (TSM) state. Remarkably, the magnetic TSM state has an ideal electronic structure, in which the band crossings are located at the Fermi level without any interference from other bands. Our findings not only reveal the topological phase transition driven by the TRS breaking, but also provide an excellent platform to explore novel physical behavior in the magnetic topological states of quantum matter.

Faithful simulation and detection of quantum spin Hall effect on superconducting circuits

Topological states of quantum matter have inspired both fascinating physics findings and exciting opportunities for applications. Due to the over-complicated structure of, as well as interactions between, real materials, a faithful quantum simulation of topological matter is very important in deepening our understanding of these states. This requirement puts the quantum superconducting circuits system as a good option for mimicking topological materials, owing to their flexible tunability and fine controllability. As a typical example herein, we realize a $\mathbb{Z}_2$-type topological insulator featuring the quantum spin Hall effect state, using a coupled system of transmission-line resonators and transmons. The single-excitation eigenstates of each unit cell are used as a pseudo-spin 1/2 system. The boundary of the topological phase transition is fixed in the phase diagram. Topological edge states are shown, which can be experimentally verified by detecting the population at the boundary of the plane. Compared to the previous simulations, this compositional system is fairly controllable, stable and less limited. Therefore, our scheme provides a reliable platform for faithful quantum simulations of topological matter.

Field-free platform for Majorana-like zero mode in superconductors with a topological surface state

Superconducting materials exhibiting topological properties are emerging as an exciting platform to realize fundamentally new excitations from topological quantum states of matter. In this work, we explore the possibility of a field-free platform for generating Majorana zero energy excitations by depositing magnetic Fe impurities on the surface of candidate topological superconductors, LiFeAs and PbTaSe$_2$. We use scanning tunneling microscopy to probe localized states induced at the Fe adatoms on the atomic scale and at sub-Kelvin temperatures. We find that each Fe adatom generates a striking zero-energy bound state inside the superconducting gap, which do not split in magnetic fields up to 8T, underlining a nontrivial topological origin. Our findings point to magnetic Fe adatoms evaporated on bulk superconductors with topological surface states as a new platform for exploring Majorana zero modes and quantum information science under field-free conditions.

Emergence of a new symmetry class for Bogoliubov–de Gennes (BdG) Hamiltonians: expanding 10-fold symmetry classes

ABSTRACTSymmetry plays an important role in the topological states of quantum matter. Cartan found three symmetry classes, Altland and Zirnbauer extended it to the 10-fold symmetry class for mesoscopic systems. We observe the emergence of a new symmetry class for BdG Hamiltonians. This new symmetry class appears for the BdG Hamiltonian in spinful background. We also observe the interesting feature that there is no evidence of Kramers's degeneracy for this BdG model Hamiltonian either in spinless or in spinful background. We call the extra symmetry class X, i.e. expanding the 10-fold symmetry classes for topological states of quantum matter. These BdG Hamiltonians show many new, interesting and insightful results.

Nanoscale topological defects and improper ferroelectric domains in multiferroic barium hexaferrite nanocrystals

Multiferroic materials that demonstrate magnetically driven ferroelectricity have fascinating properties such as magnetic (electric) field-controlled ferroelectric (magnetic) response that can be used in transformative applications including fast-writing, power-saving, and nondestructive data storage technologies in next-generation computing devices. However, since multiferroicity is typically observed at low temperatures, it is highly desirable to design multiferroic materials that can operate at room temperature. Here we show that $\mathrm{BaF}{\mathrm{e}}_{12}{\mathrm{O}}_{19}$ is a promising room-temperature multiferroic material, and we unravel in three dimensions (3D) the dynamics of topological defects, strain, and improper ferroelectric domains driven by electric fields in individual $\mathrm{BaF}{\mathrm{e}}_{12}{\mathrm{O}}_{19}$ nanocrystals. Using Bragg coherent diffractive imaging in combination with group-theoretical analysis, first-principles density functional calculations of phonons, and Landau phase-field theory we uncover in 3D the dynamics of topological defects, strain, and improper ferroelectric domains driven by electric fields in individual $\mathrm{BaF}{\mathrm{e}}_{12}{\mathrm{O}}_{19}$ nanocrystals. Our results show that $\mathrm{BaF}{\mathrm{e}}_{12}{\mathrm{O}}_{19}$ is an improper ferroelectric, in contrast to the current paradigm that adheres to the absence of improper ferroelectricity. Moreover, the fine structure of the reconstructed Bragg electron density suggests that $\mathrm{BaF}{\mathrm{e}}_{12}{\mathrm{O}}_{19}$ may be able to harbor novel topological quantum states of matter and a pathway to transform information technologies.

Topological Axion States in the Magnetic Insulator MnBi_{2}Te_{4} with the Quantized Magnetoelectric Effect.

Topological states of quantum matter have attracted great attention in condensed matter physics and materials science. The study of time-reversal-invariant topological states in quantum materials has made tremendous progress. However, the study of magnetic topological states falls much behind due to the complex magnetic structures. Here, we predict the tetradymite-type compound MnBi_{2}Te_{4} and its related materials host topologically nontrivial magnetic states. The magnetic ground state of MnBi_{2}Te_{4} is an antiferromagetic topological insulator state with a large topologically nontrivial energy gap (∼0.2 eV). It presents the axion state, which has gapped bulk and surface states, and the quantized topological magnetoelectric effect. The ferromagnetic phase of MnBi_{2}Te_{4} might lead to a minimal ideal Weyl semimetal.

Choreographed entanglement dances: Topological states of quantum matter

It has long been thought that all different phases of matter arise from symmetry breaking. Without symmetry breaking, there would be no pattern, and matter would be featureless. However, it is now clear that for quantum matter at zero temperature, even symmetric disordered liquids can have features, giving rise to topological phases of quantum matter. Some of the topological phases are highly entangled (that is, have topological order), whereas others are weakly entangled (that is, have symmetry-protected trivial order). This Review provides a brief summary of these zero-temperature states of matter and their emergent properties, as well as their importance in unifying some of the most basic concepts in nature.

Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces

A new class of phenomena stemming from topological states of quantum matter has recently found a variety of analogies in classical systems. Spin-locking and one-way propagation have been shown to drastically alter scattering of electromagnetic waves, thus offering an unprecedented robustness to defects and disorder. Despite these successes, bringing these new ideas to practical grounds meets a number of serious limitations. In photonics, when it is crucial to implement topological photonic devices on a chip, two major challenges are associated with electromagnetic dissipation into heat and out-of-plane radiation into free space. Both these mechanisms may destroy the topological state and seriously affect the device performance. Here, we demonstrate experimentally that the topological order for light can be implemented in all-dielectric on-chip prototype metasurfaces, which mitigate the effect of Ohmic losses by using exclusively structured dielectric materials, and we reveal that coupling of the system to the radiative continuum does not affect topological properties. We demonstrate the spin-Hall effect of light for spin-polarized topological edge states through near-field spectroscopy measurements.

Topological quantum states of matter in iron-based superconductors: from concept to material realization.

We review recent progress in the exploration of topological quantum states of matter in iron-based superconductors. In particular, we focus on the non-trivial topology existing in the band structures and superconducting states of iron’s 3d orbitals. The basic concepts, models, materials and experimental results are reviewed. The natural integration between topology and high-temperature superconductivity in iron-based superconductors provides great opportunities to study topological superconductivity and Majorana modes at high temperature.

Theoretical paradigm for the quantum spin Hall effect at high temperatures

The quantum spin Hall effect (QSHE) has formed the seed for contemporary research on topological quantum states of matter. Since its discovery in HgTe/CdTe quantum wells and AlGaAs/GaAs heterostructures, all such systems have so far been suffering from extremely low operating temperatures, rendering any technological application out of reach. We formulate a theoretical paradigm to accomplish the high temperature QSHE in monolayer-substrate heterostructures. Specifically, we explicate our proposal for hexagonal compounds formed by monolayers of heavy group-V elements (As, Sb, Bi) on a SiC substrate. We show how orbital filtering due to substrate hybridization, a tailored multi-orbital density of states at low energies, and large spin-orbit coupling can conspire to yield QSH states with bulk gaps of several hundreds of meV. Combined with the successful realization of Bi/SiC (0001), with a measured bulk gap of 800 meV reported previously [Reis et al., 10.1126/science.aai8142 (2017)], our paradigm elevates the QSHE from an intricate quantum phenomenon at low temperatures to a scalable effect amenable to device design and engineering.

A possible candidate for triply degenerate point fermions in trigonal layered PtBi2

Triply degenerate point (TP) fermions in tungsten–carbide-type materials (e.g., MoP), which represent new topological states of quantum matter, have generated immense interest recently. However, the TPs in these materials are found to be far below the Fermi level, leading to the TP fermions having less contribution to low-energy quasiparticle excitations. Here, we theoretically predict the existence of TP fermions with TP points close to the Fermi level in trigonal layered PtBi2 by ab initio calculations, and experimentally verify the predicted band topology by magnetotransport measurements under high magnetic fields up to 40 T. Analyses of both the pronounced Shubnikov–de Haas and de Haas–van Alphen oscillations reveal the existence of six principal Fermi pockets. Our experimental results, together with those from ab initio calculations, reveal the interplay between transport behaviors and unique electronic structures, and support the existence of TP fermions in trigonal layered PtBi2.

Spontaneous Hall effect in the Weyl semimetal candidate of all-in all-out pyrochlore iridate

Topological quantum states of matter, characterized by geometrical features of electronic band structures, have been extensively studied. Among them, the topological electronic state with magnetic order remains elusive because of a scarce number of examples. Here we present experimental observations proving that the pyrochlore iridate, when electronically tuned, can be a topological Weyl semimetal as predicted by recent theories. We observe a sizable spontaneous Hall conductivity with minimal magnetization only within a few Kelvin below the all-in all-out magnetic ordering temperature. Our theoretical calculation, which is quantitatively consistent with the observation, suggests that the presence of linearly-dispersing crossing points (Weyl points), acting as a source/sink of a quantized magnetic flux, potentially gives rise to such an enormous effect. The manifestation of the salient Hall response provides one important example of topological states, which promotes a better understanding of Weyl semimetal and indicates the new research direction for the topological-materials design.

Topological states of condensed matter.

Topological states of quantum matter have been investigated intensively in recent years in materials science and condensed matter physics. The field developed explosively largely because of the precise theoretical predictions, well-controlled materials processing, and novel characterization techniques. In this Perspective, we review recent progress in topological insulators, the quantum anomalous Hall effect, chiral topological superconductors, helical topological superconductors and Weyl semimetals.

Surface Kondo effect and non-trivial metallic state of the Kondo insulator YbB12.

A synergistic effect between strong electron correlation and spin–orbit interaction has been theoretically predicted to realize new topological states of quantum matter on Kondo insulators (KIs), so-called topological Kondo insulators (TKIs). One TKI candidate has been experimentally observed on the KI SmB6(001), and the origin of the surface states (SS) and the topological order of SmB6 has been actively discussed. Here, we show a metallic SS on the clean surface of another TKI candidate YbB12(001) using angle-resolved photoelectron spectroscopy. The SS shows temperature-dependent reconstruction corresponding to the Kondo effect observed for bulk states. Despite the low-temperature insulating bulk, the reconstructed SS with c–f hybridization is metallic, forming a closed Fermi contour surrounding on the surface Brillouin zone and agreeing with the theoretically expected behaviour for SS on TKIs. These results demonstrate the temperature-dependent holistic reconstruction of two-dimensional states localized on KIs surface driven by the Kondo effect.