scholarly journals The bulk-corner correspondence of time-reversal symmetric insulators

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Sander Kooi ◽  
Guido van Miert ◽  
Carmine Ortix
Keyword(s):  
Time Reversal ◽  
Real Space ◽  
Topological Phases ◽  
Spin Orbit Coupling ◽  
Topological Properties ◽  
Many Body ◽  
Boundary Correspondence ◽  
Berry Phases ◽  
The Many ◽  
Do So

AbstractThe topology of insulators is usually revealed through the presence of gapless boundary modes: this is the so-called bulk-boundary correspondence. However, the many-body wavefunction of a crystalline insulator is endowed with additional topological properties that do not yield surface spectral features, but manifest themselves as (fractional) quantized electronic charges localized at the crystal boundaries. Here, we formulate such bulk-corner correspondence for the physical relevant case of materials with time-reversal symmetry and spin-orbit coupling. To do so we develop partial real-space invariants that can be neither expressed in terms of Berry phases nor using symmetry-based indicators. These previously unknown crystalline invariants govern the (fractional) quantized corner charges both of isolated material structures and of heterostructures without gapless interface modes. We also show that the partial real-space invariants are able to detect all time-reversal symmetric topological phases of the recently discovered fragile type.

scholarly journals Many-body topological invariants from randomized measurements in synthetic quantum matter

2020 ◽  
Vol 6 (15) ◽  
pp. eaaz3666 ◽  
Author(s):  
Andreas Elben ◽  
Jinlong Yu ◽  
Guanyu Zhu ◽  
Mohammad Hafezi ◽  
Frank Pollmann ◽  
...  
Keyword(s):  
Body Wave ◽  
Complete Classification ◽  
Theoretical Description ◽  
Spin Model ◽  
Topological Invariants ◽  
Topological Phases ◽  
Many Body ◽  
Topological Quantum ◽  
The Many ◽  
Symmetry Protected

Many-body topological invariants, as quantized highly nonlocal correlators of the many-body wave function, are at the heart of the theoretical description of many-body topological quantum phases, including symmetry-protected and symmetry-enriched topological phases. Here, we propose and analyze a universal toolbox of measurement protocols to reveal many-body topological invariants of phases with global symmetries, which can be implemented in state-of-the-art experiments with synthetic quantum systems, such as Rydberg atoms, trapped ions, and superconducting circuits. The protocol is based on extracting the many-body topological invariants from statistical correlations of randomized measurements, implemented with local random unitary operations followed by site-resolved projective measurements. We illustrate the technique and its application in the context of the complete classification of bosonic symmetry-protected topological phases in one dimension, considering in particular the extended Su-Schrieffer-Heeger spin model, as realized with Rydberg tweezer arrays.

Critical topological nodal points and nodal lines/rings in Kagome graphene

2020 ◽  
Vol 22 (16) ◽  
pp. 8713-8718
Author(s):  
Jun Zhou ◽  
Yuee Xie ◽  
Shengbai Zhang ◽  
Yuanping Chen
Keyword(s):  
Transport Phenomena ◽  
Topological Phases ◽  
Topological Properties ◽  
Many Body ◽  
Body Effect ◽  
Nodal Lines ◽  
Flat Bands ◽  
Nodal Points

Critical topological phases, possessing flat bands, provide a platform to study unique topological properties and transport phenomena under a many-body effect.

scholarly journals Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models

2019 ◽  
Vol 7 (5) ◽  
Author(s):  
Loïc Herviou ◽  
Nicolas Regnault ◽  
Jens H Bardarson
Keyword(s):  
Two Dimensions ◽  
Topological Properties ◽  
Many Body ◽  
Energy Bands ◽  
Entanglement Spectrum ◽  
Body State ◽  
Left And Right ◽  
The Many ◽  
The Right ◽  
Hamiltonian Map

We study the properties of the entanglement spectrum in gapped non-interacting non-Hermitian systems, and its relation to the topological properties of the system Hamiltonian. Two different families of entanglement Hamiltonians can be defined in non-Hermitian systems, depending on whether we consider only right (or equivalently only left) eigenstates or a combination of both left and right eigenstates. We show that their entanglement spectra can still be computed efficiently, as in the Hermitian limit. We discuss how symmetries of the Hamiltonian map into symmetries of the entanglement spectrum depending on the choice of the many-body state. Through several examples in one and two dimensions, we show that the biorthogonal entanglement Hamiltonian directly inherits the topological properties of the Hamiltonian for line gapped phases, with characteristic singular and energy zero modes. The right (left) density matrix carries distinct information on the topological properties of the many-body right (left) eigenstates themselves. In purely point gapped phases, when the energy bands are not separable, the relation between the entanglement Hamiltonian and the system Hamiltonian breaks down.

scholarly journals Effects of spin–orbit coupling and many-body correlations in STM transport through copper phthalocyanine

2015 ◽  
Vol 6 ◽  
pp. 2452-2462 ◽  
Author(s):  
Benjamin Siegert ◽  
Andrea Donarini ◽  
Milena Grifoni
Keyword(s):  
Copper Phthalocyanine ◽  
Second Step ◽  
Scanning Tunneling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Many Body ◽  
Tunneling Microscopy ◽  
Frontier Orbitals ◽  
Model Hamiltonian ◽  
The Many

The interplay of exchange correlations and spin–orbit interaction (SOI) on the many-body spectrum of a copper phtalocyanine (CuPc) molecule and their signatures in transport are investigated. We first derive a minimal model Hamiltonian in a basis of frontier orbitals that is able to reproduce experimentally observed singlet–triplet splittings. In a second step SOI effects are included perturbatively. Major consequences of the SOI are the splitting of former degenerate levels and a magnetic anisotropy, which can be captured by an effective low-energy spin Hamiltonian. We show that scanning tunneling microscopy-based magnetoconductance measurements can yield clear signatures of both these SOI-induced effects.

scholarly journals Imaging the electronic Wigner crystal in one dimension

Science ◽  
2019 ◽  
Vol 364 (6443) ◽  
pp. 870-875 ◽  
Author(s):  
I. Shapir ◽  
A. Hamo ◽  
S. Pecker ◽  
C. P. Moca ◽  
Ö. Legeza ◽  
...  
Keyword(s):  
Real Space ◽  
Wigner Crystal ◽  
One Dimension ◽  
Many Body ◽  
Quantum Crystal ◽  
Electronic Density ◽  
Eugene Wigner ◽  
Minimal Invasiveness ◽  
Wigner Crystals ◽  
The Many

The quantum crystal of electrons, predicted more than 80 years ago by Eugene Wigner, remains one of the most elusive states of matter. In this study, we observed the one-dimensional Wigner crystal directly by imaging its charge density in real space. To image, with minimal invasiveness, the many-body electronic density of a carbon nanotube, we used another nanotube as a scanning-charge perturbation. The images we obtained of a few electrons confined in one dimension match the theoretical predictions for strongly interacting crystals. The quantum nature of the crystal emerges in the observed collective tunneling through a potential barrier. These experiments provide the direct evidence for the formation of small Wigner crystals and open the way for studying other fragile interacting states by imaging their many-body density in real space.

scholarly journals Bulk-Boundary Correspondence for Disordered Free-Fermion Topological Phases

2019 ◽  
Vol 377 (3) ◽  
pp. 1761-1821 ◽  
Author(s):  
Alexander Alldridge ◽  
Christopher Max ◽  
Martin R. Zirnbauer
Keyword(s):  
Classification Scheme ◽  
Topological Phases ◽  
Free Fermion ◽  
Space Theory ◽  
Symmetry Classes ◽  
Boundary Class ◽  
Boundary Correspondence ◽  
Interacting Systems ◽  
Bulk System ◽  
The Many

Abstract Guided by the many-particle quantum theory of interacting systems, we develop a uniform classification scheme for topological phases of disordered gapped free fermions, encompassing all symmetry classes of the Tenfold Way. We apply this scheme to give a mathematically rigorous proof of bulk-boundary correspondence. To that end, we construct real C$$^*$$ ∗ -algebras harbouring the bulk and boundary data of disordered free-fermion ground states. These we connect by a natural bulk-to-boundary short exact sequence, realising the bulk system as a quotient of the half-space theory modulo boundary contributions. To every ground state, we attach two classes in different pictures of real operator $$K$$ K -theory (or $$KR$$ KR -theory): a bulk class, using Van Daele’s picture, along with a boundary class, using Kasparov’s Fredholm picture. We then show that the connecting map for the bulk-to-boundary sequence maps these $$KR$$ KR -theory classes to each other. This implies bulk-boundary correspondence, in the presence of disorder, for both the “strong” and the “weak” invariants.

scholarly journals Bandgap Correction and Spin-Orbit Coupling Induced Absorption Spectra of Dimethylammonium Lead Iodide for Solar Cell Absorber

2021 ◽  
Vol 9 ◽  
Author(s):  
Ridwan O. Agbaoye ◽  
Sherifdeen Bolarinwa ◽  
Kolawole Olubunmi Akiode ◽  
Abibat A. Adekoya-Olowofela ◽  
Lateefat Modupe Habeeb ◽  
...  
Keyword(s):  
Solar Cell ◽  
Orbit Coupling ◽  
Maximum Efficiency ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Many Body ◽  
Lead Iodide ◽  
Many Body Perturbation Theory ◽  
The Many ◽  
Efficient Solar Cell

The search for stable and highly efficient solar cell absorbers has revealed interesting materials; however, the ideal solar cell absorber is yet to be discovered. This research aims to explore the potentials of dimethylammonium lead iodide (CH3NH2CH3PbI3) as an efficient solar cell absorber. (CH3NH2CH3PbI3) was modeled from the ideal organic–inorganic perovskite cubic crystal structure and optimized to its ground state. Considering the spin-orbit coupling (SOC) effects on heavy metals, the electronic band structure and bandgaps were calculated using the density functional theory (DFT). In contrast, bandgap correction was achieved by using the GW quasiparticle methods of the many-body perturbation theory. The optical absorption spectra were calculated from the real and imaginary dielectric tensors, which are determined by solving the Bethe–Salpeter equations of the many-body perturbation theory. Spin-orbit coupling induces band splitting and bandgap reduction in both DFT and GW methods, while the GW method improves the DFT bandgap. We report a DFT band gap of 1.55 eV, while the effect of spin-orbit coupling reduces the bandgap to 0.50 eV. Similarly, the self-consistent GW quasiparticle method recorded a bandgap of 2.27 eV, while the effect of spin-orbit coupling on the self-consistent GW quasiparticle method reported a bandgap of 1.20 eV. The projected density of states result reveals that the (CH3NH2CH3PbI3) does not participate in bands around the gap, with the iodine (I) p orbital and the lead (Pb) p orbital showing most prominence in the valence band and the conduction band. The absorption coefficient reaches 106 in the ultraviolet, visible, and near-infrared regions, which is higher than the absorption coefficient of CH3NH3PbI3. The spectroscopic limited maximum efficiency predicts a high maximum efficiency of about 62% at room temperature and an absorber thickness of about 10–1 to 102 μm, suggesting that (CH3NH2CH3PbI3) has an outstanding prospect as a solar cell absorber.

A Simple Real-Space Channelling Theory for Electron Diffraction and HREM

1990 ◽  
Vol 48 (1) ◽  
pp. 64-65
Author(s):  
D. Van Dyck
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Direct Method ◽  
Real Space ◽  
Zone Axis ◽  
Phase Object ◽  
High Resolution Images ◽  
The Many ◽  
Analytical Expressions ◽  
Electron Wavefunction

The computation of the many beam dynamical electron diffraction amplitudes or high resolution images can only be done numerically by using rather sophisticated computer programs so that the physical insight in the diffraction progress is often lost. Furthermore, it is not likely that in this way the inverse problem can be solved exactly, i.e. to reconstruct the structure of the object from the knowledge of the wavefunction at its exit face, as is needed for a direct method [1]. For this purpose, analytical expressions for the electron wavefunction in real or reciprocal space are much more useful. However, the analytical expressions available at present are relatively poor approximations of the dynamical scattering which are only valid either for thin objects ((weak) phase object approximation, thick phase object approximation, kinematical theory) or when the number of beams is very limited (2 or 3). Both requirements are usually invalid for HREM of crystals. There is a need for an analytical expression of the dynamical electron wavefunction which applies for many beam diffraction in thicker crystals. It is well known that, when a crystal is viewed along a zone axis, i.e. parallel to the atom columns, the high resolution images often show a one-to-one correspondence with the configuration of columns provided the distance between the columns is large enough and the resolution of the instrument is sufficient. This is for instance the case in ordered alloys with a column structure [2,3]. From this, it can be suggested that, for a crystal viewed along a zone axis with sufficient separation between the columns, the wave function at the exit face does mainly depend on the projected structure, i.e. on the type of atom columns. Hence, the classical picture of electrons traversing the crystal as plane-like waves in the directions of the Bragg beams which historically stems from the X-ray diffraction picture, is in fact misleading.

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