Bulk Gap Research Articles

Hofstadter butterfly of a quasicrystal

The energy spectrum of a tight-binding Hamiltonian is studied for the two-dimensional quasiperiodic Rauzy tiling in a perpendicular magnetic field. This spectrum known as a Hofstadter butterfly displays a very rich pattern of bulk gaps that are labeled by four integers, instead of two for periodic systems. The role of phason-flip disorder is also investigated in order to extract genuinely quasiperiodic properties. This geometric disorder is found to only preserve main quantum Hall gaps.

Understanding and enhancing superconductivity in FeSe/SrTiO3 by quantum size effects

Superconductivity in one-atom-layer iron selenide (FeSe) on a strontium titanate (STO) substrate is enhanced by almost an order of magnitude with respect to bulk FeSe. There is recent experimental evidence suggesting that this enhancement persists in FeSe/STO nano-islands. More specifically, for sizes $L \sim 10$ nm, the superconducting gap is a highly non-monotonic function of $L$ with peaks well above the bulk gap value. This is the expected behavior only for weakly-coupled metallic superconductors such as Al or Sn. Here we develop a theoretical formalism to describe these experiments based on three ingredients: Eliashberg theory of superconductivity in the weak coupling limit, pairing dominated by forward scattering and periodic orbit theory to model spectral fluctuations. We obtain an explicit analytical expression for the size dependence of the gap that describes quantitatively the experimental results with no free parameters. This is a strong suggestion that superconductivity in FeSe/STO is mediated by STO phonons. We propose that, since FeSe/STO is still a weakly coupled superconductor, quantum size effects can be used to further enhance the bulk critical temperature in this interface.

Quantum interference effects in topological nanowires in a longitudinal magnetic field

We study the magnetoconductance of topological insulator nanowires in a longitudinal magnetic field, including Aharonov-Bohm, Altshuler-Aronov-Spivak, perfectly conducting channel, and universal conductance fluctuation effects. Our focus is on predicting experimental behavior in single wires in the quantum limit where temperature is reduced to zero. We show that changing the Fermi energy $E_F$ can tune a wire from from ballistic to diffusive conduction and to localization. In both ballistic and diffusive single wires we find both Aharonov-Bohm and Altshuler-Aronov-Spivak oscillations with similar strengths, accompanied by quite strong universal conductance fluctuations (UCFs), all with amplitudes between $0.3 \, G_0$ and $1\,G_0$. This contrasts strongly with the average behavior of many wires, which shows Aharonov-Bohm oscillations in the ballistic regime and Altshuler-Aronov-Spivak oscillations in the diffusive regime, with both oscillations substantially larger than the conductance fluctuations. In single wires the ballistic and diffusive regimes can be distinguished by varying $E_F$ and studying the sign of the AB signal, which depends periodically on $E_F$ in ballistic wires and randomly on $E_F$ in diffusive wires. We also show that in long wires the perfectly conducting channel is visible at a wide range of energies within the bulk gap. We present typical conductance profiles at several wire lengths, showing that conductance fluctuations can dominate the average signal. Similar behavior will be found in carbon nanotubes.

Silicon-based chalcogenide: Unexpected quantum spin Hall insulator with sizable band gap

Searching for two-dimensional (2D) silicon-based topological materials is imperative for the development of various innovative devices. Here, by using first-principles calculations, we discover the silicon-based chalcogenide Si2Te2 film to be a 2D quantum spin Hall (QSH) insulator with a fundamental band gap of 0.34 eV, which can be tunable under external strain. This nontrivial topological phase stems from band inversion between the Si-px,y and Te-px,y orbitals, demonstrated by a single pair of topologically protected helical edge states with Dirac point located in the bulk gap. Notably, the characteristic properties of edge states, such as the Fermi velocity and edge shape, can be engineered by edge modifications. Additionally, the BN sheet is an ideal substrate for the experimental realization of Si2Te2 films, without destroying its nontrivial topology. Our works open a meaningful route for designing topological spintronics devices based on 2D silicon-based films.

Pure spin current devices based on ferromagnetic topological insulators.

Two-dimensional topological insulators possess two counter propagating edge channels with opposite spin direction. Recent experimental progress allowed to create ferromagnetic topological insulators realizing a quantum anomalous Hall (QAH) state. In the QAH state one of the two edge channels disappears due to the strong ferromagnetic exchange field. We investigate heterostructures of topological insulators and ferromagnetic topological insulators by means of numerical transport calculations. We show that spin current flow in such heterostructures can be controlled with high fidelity. Specifically, we propose spintronic devices that are capable of creating, switching and detecting pure spin currents using the same technology. In these devices electrical currents are directly converted into spin currents, allowing a high conversion efficiency. Energy independent transport properties in combination with large bulk gaps in some topological insulator materials may allow operation even at room temperature.

Spectroscopic evidence for the gapless electronic structure in bulk ZrTe5

Recently, transition metal pentatellurides MTe5 (M=Zr, Hf) have inspired intensive research effort. Being predicted to be quantum spin Hall insulators (QSHI) with the bulk gap up to hundreds of meVs, it could lead to promising applications at unprecedented high temperature compared with previously discovered QSHI (e.g. HgTe/CdTe or InAs/GaSb quantum wells). However, the experimental works soon followed illustrated considerable discrepancies regarding to whether MTe5 compounds possess a full bulk gap, making their topological nature (topological insulators or Dirac semimetals) illusive. In this work, combining investigations of angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM), we systematically studied the electronic properties of ZrTe5. In intrinsic samples, we observed little evidence for the existence of topological surface states or large bulk gap. With bulk and surface doping to adjust the position of the Fermi-level, ARPES spectra indicate gapless and highly linear dispersions at the valance band top, in consistence with the STM measurements that show a V-shaped total density of states near the Fermi-level (i.e. suggesting a gapless nature of the electronic structure of ZrTe5). Moreover, near the terrace edge on the surface, we observed non-zero DOS, indicating the existence of edge states.

Topological phase transitions and a two-dimensional Weyl superconductor in a half-metal/superconductor heterostructure

We find a series of topological phase transitions in a half-metal/superconductor heterostructure, by tuning the direction of the magnetization of the half-metal film. These include transitions between a topological superconducting phase with a bulk gap and another phase without a bulk gap but has a ubiquitous local gap. At the same time, the edge states change from counter-propagating Majorana edge modes to unidirectional Majorana edge modes. In addition, we find transitions between the second phase and a nodal phase which turns out to be a two-dimensional Weyl superconductor with Fermi line edge states. We identify the topological invariants relevant to each phase and the symmetry that protects the Weyl superconductivity phase.

A bifunctional spin detector made of quantum anomalous Hall insulator

The spin selection of the topological boundary states (TBS) which are protected by the chiral-like symmetry in quantum anomalous Hall insulator (QAHI) can be used to construct a bifunctional spin detector (SD). Such device made of QAHIs in parallel with opposite chirality can divide an incoming spin-polarized current into two outgoing currents. The agreement between numerical and analytical calculation proves that the SD device functions as both spin filter and spin separator well in reflecting the spin polarization of source material from the ratio of two currents. The monotonic relation of spin polarization and current ratio suggests that using such kind of device, the spin polarization can be obtained directly. We also find that such device has a broad working energy region attributed by the TBS within the bulk gap. Combining with the result that the current ratio is barely dependent on the coupling between candidate materials and device, it is reasonable to apply this technique with a stable measuring accuracy. Furthermore, the features such as having simple geometry, being manipulated without external magnetic field, and the prospect of working at room temperature make this proposed device seem promising in developing future low-power-consumption spintronic device.

Tuning ferromagneticBaFe2(PO4)2through a high Chern number topological phase

There is strong interest in discovering or designing wide gap Chern insulators. Here we follow a Chern insulator to trivial Mott insulator transition versus interaction strength U in a honeycomb lattice Fe-based transition metal oxide, discovering that a spin-orbit coupling energy scale $\xi$=40 meV can produce and maintain a topologically entangled Chern insulating state against large band structure changes arising from an interaction strength U up to 60 times as large. Within the Chern phase the minimum gap switches from the zone corner K to the zone center $\Gamma$ while maintaining the topological structure. At a critical strength $U_c$, the continuous evolution of the electronic structure encounters a gap closing then reopening, upon which the system reverts to a trivial Mott insulating phase. This Chern insulator phase of honeycomb lattice Fe$^{2+}$ BaFe$_2$(PO$_4$)$_2$ corresponds to a large Chern number C=-3 that will provide enhanced anomalous Hall conductivity due to the associated three edge states threading through the bulk gap of 80 meV.

Krein signatures of transfer operators for half-space topological insulators

We propose a complementary point of view on the topological invariants of two-dimensional tight-binding models restricted to half-spaces. The transfer operators for such systems are J-unitary on a infinite dimensional Krein space and, for energies in the bulk gap, only have discrete spectrum on the unit circle. These eigenvalues have Krein inertia which can be used to define topological invariants determining the nature of the surface modes and allowing to distinguish different topological phases. This is illustrated by numerical results.

Interaction-driven topological superconductivity in one dimension

We study one-dimensional topological superconductivity in the presence of time-reversal symmetry. This phase is characterized by having a bulk gap, while supporting a Kramers' pair of zero-energy Majorana bound states at each of its ends. We present a general simple model which is driven into this topological phase in the presence of repulsive electron-electron interactions. We further propose two experimental setups and show that they realize this model at low energies. The first setup is a narrow two-dimensional topological insulator partially covered by a conventional s-wave superconductor, and the second is a semiconductor wire in proximity to an s-wave superconductor. These systems can therefore be used to realize and probe the time-reversal invariant topological superconducting phase. The effect of interactions is studied using both a mean-field approach and a renormalization group analysis.

Finite-Size and Composition-Driven Topological Phase Transition in (Bi1-xInx)2Se3 Thin Films.

In a topological insulator (TI), if its spin-orbit coupling (SOC) strength is gradually reduced, the TI eventually transforms into a trivial insulator beyond a critical point of SOC, at which point the bulk gap closes: this is the standard description of the topological phase transition (TPT). However, this description of TPT, driven solely by the SOC (or something equivalent) and followed by closing and reopening of the bulk band gap, is valid only for infinite-size samples, and little is known how TPT occurs for finite-size samples. Here, using both systematic transport measurements on interface-engineered (Bi1-xInx)2Se3 thin films and theoretical simulations (with animations in the Supporting Information), we show that description of TPT in finite-size samples needs to be substantially modified from the conventional picture of TPT due to surface-state hybridization and bulk confinement effects. We also show that the finite-size TPT is composed of two separate transitions, topological-normal transition (TNT) and metal-insulator transition (MIT), by providing a detailed phase diagram in the two-dimensional phase space of sample size and SOC strength.

Quantum anomalous Hall effect in atomic crystal layers from in-plane magnetization

We theoretically report that, with \textit{in-plane} magnetization, the quantum anomalous Hall effect (QAHE) can be realized in two-dimensional atomic crystal layers with preserved inversion symmetry but broken out-of-plane mirror reflection symmetry. We take the honeycomb lattice as an example, where we find that the low-buckled structure, which makes the system satisfy the symmetric criteria, is crucial to induce QAHE. The topologically nontrivial bulk gap carrying a Chern number of $\mathcal{C}=\pm1$ opens in the vicinity of the saddle points $M$, where the band dispersion exhibits strong anisotropy. We further show that the QAHE with electrically tunable Chern number can be achieved in Bernal-stacked multilayer systems, and the applied interlayer potential differences can dramatically decrease the critical magnetization to make the QAHE experimentally feasible.

Breakdown of the Kondo insulating state inSmB6by introducing Sm vacancies

SmB6 is a proposed topological Kondo insulator where the presence of topological nontriviality can be tuned by variations in the Sm valence. Experimentally, Sm valence can be changed by tuning stoichiometry of SmB6. We show that Raman scattering can detect vacancies lower than 1% of Sm sites in SmB6 crystal by probing the intensity of defect-induced scattering of the acoustic phonon branch at 10~meV. In the electronic Raman spectra of SmB6 at temperatures below 130~K, we observe features developing in A$_{1g}$ and E$_g$ symmetries at 100 and 41~meV which we assign to excitations between hybridized bands, and depressed spectral weight below 20~meV associated with the hybridization gap. With the increased number of Sm vacancies up to 1% we observe an increase of spectral weight below 20~meV showing that the gap is filling in with electronic states. For the sample with the lowest number of vacancies the in-gap exciton excitations with long lifetimes protected by hybridization gap are observed at 16-18~meV in E$_g$ and T$_{2g}$ symmetries. These excitations broaden as a decrease in the lifetime with increasing number of vacancies and are quenched by the presence of in-gap states at concentration of Sm vacancies of about 1%. Based on this study we suggest that only the most stoichiometric SmB6 samples have a bulk gap necessary for topological Kondo insulators.

Classical impurities and boundary Majorana zero modes in quantum chains

We study the response of classical impurities in quantum Ising chains. The Z2 degeneracy they entail renders the existence of two decoupled Majorana modes at zero energy, an exact property of a finite system at arbitrary values of its bulk parameters. We trace the evolution of these modes across the transition from the disordered phase to the ordered one and analyze the concomitant qualitative changes of local magnetic properties of an isolated impurity. In the disordered phase, the two ground states differ only close to the impurity, and they are related by the action of an explicitly constructed quasi-local operator. In this phase the local transverse spin susceptibility follows a Curie law. The critical response of a boundary impurity is logarithmically divergent and maps to the two-channel Kondo problem, while it saturates for critical bulk impurities, as well as in the ordered phase. The results for the Ising chain translate to the related problem of a resonant level coupled to a 1d p-wave superconductor or a Peierls chain, whereby the magnetic order is mapped to topological order. We find that the topological phase always exhibits a continuous impurity response to local fields as a result of the level repulsion of local levels from the boundary Majorana zero mode. In contrast, the disordered phase generically features a discontinuous magnetization or charging response. This difference constitutes a general thermodynamic fingerprint of topological order in phases with a bulk gap.

Realization and detection of Weyl semimetals and the chiral anomaly in cold atomic systems

In this work, we describe a method to realize 3D Weyl semimetal by coupling multilayers of honeycomb optical lattice in the presence of a pair of Raman lasers. The Raman lasers render each isolated honeycomb layer a Chern insulator. With finite interlayer coupling, the bulk gap of the system closes at certain out-of-plane momenta due to Raman assisted tunnelling and result in the Weyl semimetal phase. Using experimentally relevant parameters, we show that both one and two pairs of Weyl points can be realized by tuning the interlayer coupling strength. We suggest that Landau-Zener tunnelling can be used to detect Weyl points and show that the transition probability increases dramatically when Weyl point emerges. The realization of chiral anomaly by using a magnetic field gradient is also discussed.

Hard gap in a normal layer coupled to a superconductor

The ability to induce a sizable gap in the excitation spectrum of a normal layer placed in contact with a conventional superconductor has become increasingly important in recent years in the context of engineering a topological superconductor. The quasiclassical theory of the proximity effect shows that Andreev reflection at the superconductor/normal interface induces a nonzero pairing amplitude in the metal but does not endow it with a gap. Conversely, when the normal layer is atomically thin, the tunneling of Cooper pairs induces an excitation gap that can be as large as the bulk gap of the superconductor. We study how these two seemingly different views of the proximity effect evolve into one another as the thickness of the normal layer is changed. We show that a fully quantum-mechanical treatment of the problem predicts that the induced gap is always finite but falls off with the thickness of the normal layer $d$. If $d$ is less than a certain crossover scale, which is much larger than the Fermi wavelength, the induced gap is comparable to the bulk gap. As a result, a sizable excitation gap can be induced in normal layers that are much thicker than the Fermi wavelength.

Two-dimensional topological insulators in group-11 chalcogenide compounds:M2Te(M=Cu,Ag)

Two-dimensional (2D) topological insulators (TIs) are recently recognized states of quantum matter that are highly interesting for lower-power-consuming electronic devices owing to their nondissipative transport properties protected from backscattering. So far, only few 2D TIs, suffering from small bulk band gap ($l10\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$), have been experimentally confirmed. Here, through first-principles calculations, we propose a family of 2D TIs in group-11 chalcogenide 2D crystals, ${M}_{2}\mathrm{Te}\phantom{\rule{0.28em}{0ex}}(M=\mathrm{Cu},\phantom{\rule{0.16em}{0ex}}\mathrm{Ag})$. The nontrivial topological states in $\mathrm{C}{\mathrm{u}}_{2}\mathrm{Te}$ and $\mathrm{A}{\mathrm{g}}_{2}\mathrm{Te}$ 2D crystals, identified by topological invariant and edge state calculations, exhibit sizeable bulk gaps of 78 and 150 meV, respectively, suggesting that they are candidates for room-temperature applications. Moreover, strain engineering leads to effective control of the nontrivial gaps of $\mathrm{C}{\mathrm{u}}_{2}\mathrm{Te}$ and $\mathrm{A}{\mathrm{g}}_{2}\mathrm{Te}$, and a topological phase transition can be realized in $\mathrm{C}{\mathrm{u}}_{2}\mathrm{Te}$, while the nontrivial phase in $\mathrm{A}{\mathrm{g}}_{2}\mathrm{Te}$ is stable against strain. Their dynamic and thermal stabilities are further confirmed by employing phonon calculations and ab initio molecular dynamic simulations.

Defect energetics and magnetic properties of 3d-transition-metal-doped topological crystalline insulator SnTe

The introduction of magnetism in SnTe-class topological crystalline insulators is a challenging subject with great importance in the quantum device applications. Based on the first-principles calculations, we have studied the defect energetics and magnetic properties of 3d transition-metal (TM)-doped SnTe. We find that the doped TM atoms prefer to stay in the neutral states and have comparatively high formation energies, suggesting that the uniform TMdoping in SnTe with a higher concentration will be difficult unless clustering. In the dilute doping regime, all the magnetic TMatoms are in the high-spin states, indicating that the spin splitting energy of 3d TM is stronger than the crystal splitting energy of the SnTe ligand. Importantly, Mn-doped SnTe has relatively low defect formation energy, largest local magnetic moment, and no defect levels in the bulk gap, suggesting that Mn is a promising magnetic dopant to realize the magnetic order for the theoretically-proposed large-Chern-number quantum anomalous Hall effect (QAHE) in SnTe.

Optoelectronic properties of Ni–GaP diodes with a modified surface

We report the promising results for Ni–GaP Schottky diode structures manufactured on the substrates with chemically-etched nano-scale surface formations that are responsible for a clearly marked luminescence band located at the energy exceeding the band gap of the bulk GaP. The other peculiarity produced by surface patterning concerns a remarkable redshift of material's optical absorption edge. At the room temperature, the height of potential barrier for Ni–GaP structure is 1.8eV, with the monochromatic sensitivity peaking at 0.35A/W. The comparative study of diode performance under different light sources exhibited the pronounced linear photocurrent-illumination dependence for about five orders of illumination magnitude, evidencing good optical and electrical quality of Ni–GaP diodes with surface-modified semiconductor substrate.