Topological Insulator Quantum Dots Research Articles

Edge States and Strain-Driven Topological Phase Transitions in Quantum Dots in Topological Insulators.

We present here a theory of the electronic properties of quasi two-dimensional quantum dots made of topological insulators. The topological insulator is described by either eight band k→·p→ Hamiltonian or by a four-band k→·p→ Bernevig-Hughes-Zhang (BHZ) Hamiltonian. The trivial versus topological properties of the BHZ Hamiltonian are characterized by the different topologies that arise when mapping the in-plane wavevectors through the BHZ Hamiltonian onto a Bloch sphere. In the topologically nontrivial case, edge states are formed in the disc and square geometries of the quantum dot. We account for the effects of compressive strain in topological insulator quantum dots by means of the Bir-Pikus Hamiltonian. Tuning strain allows topological phase transitions between topological and trivial phases, which results in the vanishing of edge states from the energy gap. This may enable the design of a quantum strain sensor based on strain-driven transitions in HgTe topological insulator square quantum dots.

Surface states and breaking down of spin-to-surface locking on a conical topological insulator quantum dot

Surface states and breaking down of spin-to-surface locking on a conical topological insulator quantum dot

Interference effect in the electronic transport of a topological insulator quantum dot

Edge and bulk energy levels can coexist in a quantum dot (QD) made of a topological insulator. Interference effect will occur between bulk and edge levels and also between degenerate edge levels. It can be observed in the transport behavior. For the former, it acts as Fano interference with edge and bulk levels contributing continuous and resonant transport channels, respectively. Generally speaking, Fano interference can be realized in a two-armed junction with a single QD or a one-armed junction with at least two QDs. But here it is realized in a one-armed junction with a single QD. As for the interference between degenerate edge levels, it leads to a spin and space dependent scattering process. Spin of an incident electron will either be conserved or rotate about an axis for transmitting into different leads. It is determined by the local spin polarization of edge levels and the accumulated phase in transport paths in the QD. It may be used in the design of a spin field-effect transistor.

Electrically pumped terahertz laser based on a topological insulator quantum dot array

The energy level separation between the edge states in topological insulator quantum dots lies in the terahertz (THz) range. Quantum confinement ensures the nonuniformity of the energy level separation near the Dirac point. Based on these features, we propose that a topological insulator quantum dot array can be operated as an electrically pumped continuous-wave THz laser. The proposed device can operate at room temperature, with power exceeding 10 mW and quantum efficiency reaching ∼50%. This study may promote the usage of topological insulator quantum dots as an important source of THz radiation.

Optical intersubband properties of a core–shell semiconductor–topological insulator quantum dot described by θ-electrodynamics

The optical properties of a spherical topological insulator embedded concentrically in a single-electron system consisting of a core-shell GaAs quantum dot are analyzed, when the system is under a uniform external magnetic field. The topological insulator's magnetoelectric response is computed in the effective framework of $\theta$-electrodynamics, which allows analytical calculations for the induced electric and magnetic potentials by Green's Function method. The GaAs Hamiltonian is constructed in the effective-mass approximation, and its corresponding Schr\"odinger equation is numerically solved through the Lagrange-mesh method. We compute the total absorption coefficients and refractive index changes given by the non-linear iterative density matrix formalism up to third order. Our results show that the presence of the magnetoelectric material causes new dipolar transitions otherwise not allowed. Also, an enhancement of the photon absorption is found when the incident light polarization is oriented parallel to the external magnetic field, in comparison with perpendicular polarization. Moreover, we report an appreciable blue shift in the optical functions when the values of the $\theta$-parameter are increased. These results can be useful for indirect experimental measures of the magnetoelectric polarizability which is proportional to the QED fine-structure constant $\alpha$.

THz Emission by Frequency Down-conversion in Topological Insulator Quantum Dots

Terahertz waves are useful in many fields, including imaging, spectroscopy, and telecommunication. However, an effective source of THz radiation source for real-world applications is still lacking. This study proposes using the approximately equidistant helical edge states in topological-insulator quantum dots for frequency down-conversion, to produce light covering most of the ``THz gap'', from 3 to 10 THz. Such a topological-insulator quantum-dot array can form a continuous-wave THz laser that works at room temperature, with an output power of 28 mW. This study expands both the application of topological phenomena and THz device physics.

Electric field tuning of spin splitting in topological insulator quantum dots doped with a single magnetic ion

We investigate theoretically the electron spin states in a disk-shaped topological insulator quantum dot (TIQD) containing a single magnetic Mn2+ ion. We demonstrate that the energy spectra and the density distributions of the symmetry-protected edge states in a HgTe TIQD can be modulated effectively by a single magnetic impurity Mn2+. Additionally, when an in-plane external electric field is applied., it not only tunes the spin splittings of edge states via the s(p)-d exchange interaction between the electron (hole) and the magnetic Mn2+ ion respectively, but also gives rise to the bright-to-dark transitions in the optical transition spectrum. Such spin properties of TIQDs with single Mn2+ ion as illustrated in this work could offer a new platform for topological electro-optical devices.

Suppressed Stark shift of helical edge states in topological-insulator quantum dots

We study the stability of the electronic states in circular two-dimensional topological-insulator quantum dots against electric perturbations, as quantified by the susceptibility $\ensuremath{\chi}$ of the Stark shift $\mathrm{\ensuremath{\Delta}}E=\ensuremath{\chi}{F}^{2}/2$ of each energy level due to a small electric field $F$. We find the typical susceptibility ${\ensuremath{\chi}}_{\mathrm{edge}}\ensuremath{\sim}1$ meV/(mV/${\mathrm{nm})}^{2}$ for edge states is 4 orders of magnitude smaller than ${\ensuremath{\chi}}_{\mathrm{bulk}}\ensuremath{\sim}{10}^{4}$ meV/(mV/${\mathrm{nm})}^{2}$ for normal bulk states. We show that the origin of this strong stability of the edge states is the equidistance nature of the edge states, which follows from the linear dispersion of the one-dimensional edge channel. Therefore, we expect this strong stability to be a general feature for edge states in relatively large topological-insulator quantum dots. This finding identifies a new physical mechanism for protecting the edge states against electrical perturbations, which may be relevant to the applications of these edge states in quantum technologies.

Topological protection of electronic states against disorder probed by their magnetic moment

Magnetic moments (MMs) of electrons in topological insulator quantum dots (TI-QDs) are investigated using a model system, namely a multiorbital honeycomb lattice. Their nature and orientation with respect to the spin are studied. We show that large MMs are not specific to edge states in nontrivial gaps, as band states can host even larger MMs. However, we demonstrate that edge-state and band-state MMs have a totally different sensitivity to disorder. Measuring the MMs in TI-QDs is therefore a direct way to probe the nontrivial to trivial topological transition under increasing disorder.

Electronic structure of rectangular HgTe quantum dots

We theoretically investigate the single- and few-electron ground-states properties of HgTe topological insulator quantum dots with rectangular hard-wall confining potential using configuration interaction method. For the case of single electron, the edge states is robust against the deformation from a square quantum dot to a rectangular ones, in contrast to the bulk states, the energy gap of the QDs increased due to the coupling of the opposite edge states; for the case of few electrons, the electrons first fill the edge states in the bulk band gap and the addition energy exhibit universal even-odd oscillation due to the shape-independent two-fold degeneracy of the edge states. The size of this edge shell can be controlled by tuning the dot size, shape or the bulk band gap via lateral or vertical electric gating respectively of the HgTe quantum dot.

Spin-polarized charge trapping cell based on a topological insulator quantum dot

We demonstrate theoretically that a topological insulator quantum dot can be formed via double topological insulator constrictions (TICs), and can be used as a charge and/or spin carrier trap memory element.

Effective spin dephasing mechanism in confined two-dimensional topological insulators

A Kramers pair of helical edge states in quantum spin Hall effect (QSHE) is robust against normal dephasing but not robust to spin dephasing. In our work, we provide an effective spin dephasing mechanism in the puddles of two-dimensional (2D) QSHE, which is simulated as quantum dots modeled by 2D massive Dirac Hamiltonian. We demonstrate that the spin dephasing effect can originate from the combination of the Rashba spin-orbit coupling and electron-phonon interaction, which gives rise to inelastic backscattering in edge states within the topological insulator quantum dots, although the time-reversal symmetry is preserved throughout. Finally, we discuss the tunneling between extended helical edge states and local edge states in the QSH quantum dots, which leads to backscattering in the extended edge states. These results can explain the more robust edge transport in InAs/GaSb QSH systems.

Reverse Stark effect, anomalous optical transitions, and control of spin in topological insulator quantum dots

Formed through a closed domain magnetic heterostructure on the surface of a three-dimensional topological insulator, a quantum dot permits a class of quantized interfacial states of topological origin. We find that these states exhibit a remarkable reverse Stark effect in response to an applied electric field. In particular, those topological states whose energies are within the gap exhibit peculiar electrical alignments that are opposite to those associated with the conventional quantum-confined Stark effect in that the positive- (negative-) energy states tend to align with (against) the direction of the field. The phenomenon has unusual implications for the associated optical transitions. Furthermore, the exotic topological states exhibit polarized spin textures that can be effectively controlled electrically or optically, opening an avenue for potential applications in Dirac-material-based spintronics.

Kondo effect in a topological insulator quantum dot

We investigate theoretically the nonequilibrium transport properties of a topological insulator quantum dot (TIQD) in the Coulomb blockade and Kondo regime. An Anderson impurity model is applied to a TIQD system coupled to two external leads, and we show that the model realizes the spin-orbital Kondo effect at the Dirac point where the edge states are not split by a finite-size effect, leading to an additional $SU(4)$ symmetry because of the presence of strong mixture among four internal degrees of freedom. In a more realistic situation where the degeneracy is lifted due to the finite-size effect, we demonstrate that there is a richer structure in transport measurements. We illustrate a continuous crossover from four (spin and orbital) Coulomb peaks with large interpair spacing and small intrapair spacing to a double-peak structure in the local density of states (LDOS) as increasing the hybridization strength $\ensuremath{\Gamma}$ within the Coulomb blockade regime. When temperature falls below the Kondo temperature ${T}_{K}$, four Kondo peaks show up in the nonequilibrium LDOS. Two of them are located at the chemical potential of each lead, and the other two are shifted away from the chemical potential by an amount proportional to the TIQD's bare energy level, leading to a triple-peak structure in the differential conductance when a bias voltage is applied.

Single- and Few-Electron States in Deformed Topological Insulator Quantum Dots**Supported by the National Natural Science Foundation of China under Grant No 11434010, and the National Basic Research Program of China under Grant No 2011CB922204.

We theoretically investigate the single- and few-electron states in deformed HgTe quantum dots (QDs) with an inverted band structure using the full configuration interaction method. For the circular and deformed QD, it is found that the energy of edge states is robust against the shape from the circular QD in various elliptic ones. For the few electron states, electrons will firstly fill the edge states localized at the short axis, then the states localized at the long axis of the QD before filling the bulk states. The filling of the edge states can be controlled by tuning the dot size or the deformation of the geometry of the HgTe QD, respectively.

Single- and few-electron states in topological-insulator quantum dots

We theoretically investigate the single- and few-electron states of HgTe topological insulator quantum dots using the configuration interaction method and find distinguishing features for both cases. For a single electron, the kinetic energy of the edge states follows an ``edge'' quantization rule and is robust against the deformation of the circular quantum dot into various elliptic ones, in contrast to the bulk states of the quantum dot. For two electrons, the ratio between the kinetic energy and the Coulomb energy is insensitive to the dot size when the dot is circular, but can be tuned over a relatively wide range by deforming the circular dot into elliptic ones, in contrast to conventional quantum dots, where the kinetic (Coulomb) energy dominates for small (large) dots. For a few electrons, the electrons first fill the edge states in the bulk band gap, and the addition energy and ground state spin exhibit universal even-odd oscillation due to the shape-independent two-fold degeneracy of the edge states. The size of this edge shell can be controlled by tuning the dot size or the band gap of the HgTe quantum well via lateral or vertical electric gating, respectively.

Three-dimensional topological insulator quantum dot for optically controlled quantum memory and quantum computing

We present the model of a quantum dot (QD) consisting of a spherical core-bulk heterostructure made of 3D topological insulator (TI) materials, such as PbTe/Pb$_{0.31}$Sn$_{0.69}$Te, with bound massless and helical Weyl states existing at the interface and being confined in all three dimensions. The number of bound states can be controlled by tuning the size of the QD and the magnitude of the core and bulk energy gaps, which determine the confining potential. We demonstrate that such bound Weyl states can be realized for QD sizes of few nanometers. We identify the spin locking and the Kramers pairs, both hallmarks of 3D TIs. In contrast to topologically trivial semiconductor QDs, the confined massless Weyl states in 3D TI QDs are localized at the interface of the QD and exhibit a mirror symmetry in the energy spectrum. We find strict optical selection rules satisfied by both interband and intraband transitions that depend on the polarization of electron-hole pairs and therefore give rise to the Faraday effect due to Pauli exclusion principle. We show that the semi-classical Faraday effect can be used to read out spin quantum memory. When a 3D TI QD is embedded inside a cavity, the single-photon Faraday rotation provides the possibility to implement optically mediated quantum teleportation and quantum information processing with 3D TI QDs, where the qubit is defined by either an electron-hole pair, a single electron spin, or a single hole spin in a 3D TI QD. Remarkably, the combination of inter- and intraband transition gives rise to a large dipole moment of up to 450 Debye. Therefore, the strong-coupling regime can be reached for a cavity quality factor of $Q\approx10^{4}$ in the infrared wavelength regime of around $10\:\mu$m.

NUMERICAL STUDY OF TRANSPORT PROPERTIES IN TOPOLOGICAL INSULATOR QUANTUM DOTS UNDER MAGNETIC FIELD

In this paper, we investigate the transport properties of HgTe / CdTe -based topological insulator quantum dots (TIQDs) under magnetic field. Both disk and square shaped TIQDs are considered and the magneto-conductance are calculated numerically for various magnetic field strength. The magnetic field lifts the spin degeneracy, leading to spin polarized current at given Fermi energy. Meanwhile, the magneto-conductance demonstrates the Aharonov–Bohm (AB) oscillation with a period of one flux quantum [Formula: see text]. Numerical results for AB oscillation features indicate the mismatch between electron (e) and hole (h) doping conditions, which can be attributed to the e–h asymmetry in the full band Hamiltonian. Further, interference effect emerges around bulk and edge energy degenerate points, subsequently suppressing the magneto-conductance in both shaped systems. All these physical characteristics are qualitatively consistent for disk and square shaped TIQDs due to the topological nature of edge modes.

Topological Insulator Quantum Dot with Tunable Barriers

Thin (6-7 quintuple layer) topological insulator Bi(2)Se(3) quantum dot devices are demonstrated using ultrathin (2-4 quintuple layer) Bi(2)Se(3) regions to realize semiconducting barriers which may be tuned from ohmic to tunneling conduction via gate voltage. Transport spectroscopy shows Coulomb blockade with large charging energy >5 meV and additional features implying excited states.

Energy spectrum and broken spin-surface locking in topological insulator quantum dots

We consider the energy spectrum and the spin-parity structure of the eigenstates for a quantum dot made of a strong topological insulator. Using the effective low-energy theory in a finite-length cylinder geometry, numerical calculations show that even at the lowest energy scales, the spin direction in a topologically protected surface mode is not locked to the surface. We find "zero-momentum" modes, and subgap states localized near the "caps" of the dot. Both the energy spectrum and the spin texture of the eigenstates are basically reproduced from an analytical surface Dirac fermion description. Our results are compared to microscopic calculations using a tight-binding model for a strong topological insulator in a finite-length nanowire geometry.