Bound states in the continuum (BICs) are quantum states with normalizable wave functions and energies that lie within the continuous spectrum for which extended or dispersive states are also available. These special states, which have shown great applicability in photonic systems for devices such as lasers and sensors, are also predicted to exist in electronic low-dimensional solid-state systems. The non-trivial topology of materials is within the known mechanisms that prevent the bound states to couple with the extended states. In this work we search for topologically protected BICs in a quantum Hall bar with an anti-dot formed by a pore far from the borders of the bar. The bound state energies and wavefunctions are calculated by means of the Recursive S-Matrix method. The resulting bound state energies coexist with extended states and exhibit a pattern complimentary to the Hofstadter butterfly. A symmetry-breaking diagonal disorder was introduced, showing that the BICs with energies far from the Landau levels remain robust. Moreover, the energy difference between consecutive BICs multiplied by the anti-dot perimeter follows the same curve despite disorder. Finally, a BIC-mediated current switching effect was found in a multi-terminal setup, which might permit their experimental detection.
We study quantum Hall interferometers in which the interference loop encircles a quantum anti-dot. We base our study on thermodynamic considerations, which we believe reflect the essential aspects of interference transport phenomena. We find that similar to the more conventional Fabry-Perot quantum Hall interferometers, in which the interference loop forms a quantum dot, the anti-dot interferometer is affected by the electro-static Coulomb interaction between the edge modes defining the loop. We show that in the Aharonov-Bohm regime, in which effects of fractional statistics should be visible,…
We report on the observation of periodic conductance oscillations near quantum Hall plateaus in suspended graphene nanoribbons. They are attributed to single quantum dots that form in the narrowest part of the ribbon, in the valleys and hills of a disorder potential. In a wide flake with two gates, a double-dot system's signature has been observed. Electrostatic confinement is enabled in single-layer graphene due to the gaps that form between Landau levels, suggesting a way to create gate-defined quantum dots that can be accessed with quantum Hall edge states.
We demonstrate a new method for locally probing the edge states in the quantum Hall regime utilizing a side coupled quantum dot positioned at an edge of a Hall bar. By measuring the tunneling of electrons from the edge states into the dot, we acquire information on the local electrochemical potential and electron temperature of the edge states. Furthermore, this method allows us to observe the spatial modulation of the electrostatic potential at the edge state due to many-body screening effect.
We study the spin ordering of a quantum dot defined via magnetic barriers in an interacting quantum spin Hall edge. The spin-resolved density-density correlation functions are computed. We show that strong electron interactions induce a ground state with a highly correlated spin pattern. The crossover from the liquid-type correlations at weak interactions to the ground state spin texture found at strong interactions parallels the formation of a one-dimensional Wigner molecule in an ordinary strongly interacting quantum dot.
We study the transport mechanisms taking place in a quantum spin Hall bar with an embedded quantum dot, where electrons localize and experience Coulomb interaction U as well as spin-flip processes λ. We solve the problem with non-equilibrium Green functions. We focus on the linear response regime and treat the many-body interactions with quantum Monte Carlo. The effects of U and λ are competitive and the induced transport takes place through different channels. The two mechanisms can be switched by changing the occupation of the dot with a gate voltage.
Quantum spin Hall insulators, recently realized in HgTe/(Hg,Cd)Te quantum wells, support topologically protected, linearly dispersing edge states with spin-momentum locking. A local magnetic exchange field can open a gap for the edge states. A quantum-dot structure consisting of two such magnetic tunneling barriers is proposed and the charge transport through this device is analyzed. The effects of a finite bias voltage beyond linear response, of a gate voltage, and of the charging energy in the quantum dot are studied within a combination of Green-function and master-equation approaches. Amon…
Graphene quantum dot with Maxwell fish eye potential energy profile is studied. A quasiclassical approximation is used given that potential energy is a slowly varying function of coordinates. Near the zero energy the spectrum of electron macroscopically degenerates. All the electron trajectories are closed circles that are classified by angular momentum and an additional integral of motion. Provided the complete filling of the lower Dirac zone, a universal value for Hall conductivity is found.
We present complete analytical and numerical results that demonstrate the anomalous universal fluctuations of the spin-Hall conductance in chiral materials such as graphene and topological insulators. We investigated both the corresponding fluctuations, the Universal Fractionated and the Universal Quantized, and also the open channels orbital number crossover between the two regimes. In particular, we show that the Wigner-Dyson symmetries does not properly describe such conductances and the preponderant role of the chiral classes on the Dirac quantum dots. The results are analytical and solve …
We evaluate the spin density oscillations arising in quantum spin Hall quantum dots created via two localized magnetic barriers. The combined presence of magnetic barriers and spin-momentum locking, the hallmark of topological insulators, leads to peculiar phenomena: a half-integer charge is trapped in the dot for antiparallel magnetization of the barriers, and oscillations appear in the in-plane spin density, which are enhanced in the presence of electron interactions. Furthermore, we show that the number of these oscillations is determined by the number of particles inside the dot, so that t…
In this work, we present the analytical solution of the effective mass Pauli equation, with Rashba and linear Dresselhaus interactions, for an electron gas moving through a semiconductor quantum dot under a longitudinal electric field, which is defined along the $x$-direction. We study the relative influence of the Rashba and Dresselhaus terms on the spin-Hall effect for the first propagating and edge channels, by analyzing the mixing between spin-up and -down states and the zero-field spin splitting along the transverse directions. When the spin rotation depends only on the $y$-coordinate, th…
Resonant tunneling through a quantum dot weakly coupled to quantum wires or quantum Hall edge states
讨论了弱耦合量子点与Tomonaga-Luttinger液体的共振隧穿。由于顺序隧穿的线性电导计算通过求解主方程的温度低于和高于平均水平间距的点。当表征Tomonaga-Luttinger液体的参数g小于1/2时，共振隧穿过程在零温度下是不相干的。在低温T下，库仑阻塞振荡中电导峰的高度和宽度分别与T^{（1/g）-2}和T成正比。隧道通过一个虚拟的中间状态（cotunneling）的贡献也包括在内。所得的电导公式可以应用于填充因子nu=1/（2 m +1）=g的分数量子霍尔液体边缘态之间的共振隧穿。
In this note we present some results concerning photon blockade and antibunching in a system consisting of a quantum dot embedded in a microcavity. We give analytic conditions for resonant and non-resonant photon blockade, valid for small values of the external pump amplitude. Starting from these results, we discuss the quantum states characteristics of the system within a master equation formalism and highlight quantities like stationary second order correlations both static and dynamic and one-photon purity.
In this work, a quantum dot that is defined asymmetrically by electrostatic means induced on a GaAs/AlGaAs heterostructure is investigated to unravel the effect of geometric constrains on the formation of spin droplets under quantised Hall conditions. The incompressibility of exciting nu = 5/2 state is explored by solving the Schrodinger equation within spin density functional theory, where the confinement potential is obtained self-consistently utilising the Thomas-Fermi approximation. Our numerical investigations show that the spatial distribution of the nu = 2 incompressible strips and elec…
Spin Hall and Edelstein effects in a ballistic quantum dot with Rashba spin-orbit coupling
CNR-SPIN（意大利国家研究委员会自旋物理研究所）；Università di Salerno（萨莱诺大学）；Dipartimento di Fisica ”E.R. Caianiello”, Università di Salerno（萨莱诺大学埃·R·卡亚涅洛物理系）；INFN, Sezione di Napoli, Gruppo collegato di Salerno（意大利国家核物理研究所那不勒斯分部萨莱诺协作组）；Dipartimento di Fisica, Università della Calabria（卡拉布里亚大学物理系）；Dipartimento di Fisica Ettore Pancini, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学埃托雷·潘奇尼物理系）；AGH University of Krakow, Faculty of Physics and Applied Computer Science（克拉科夫AGH科技大学物理与应用计算机科学系）
We show that correlated two-particle backscattering can induce fractional charge oscillations in a quantum dot built at the edge of a two-dimensional topological insulator by means of magnetic barriers. The result nicely complements recent works where the fractional oscillations were obtained employing of semiclassical treatments. Moreover, since by rotating the magnetization of the barriers a fractional charge can be trapped in the dot via the Jackiw-Rebbi mechanism, the system we analyze offers the opportunity to study the interplay between this noninteracting charge fractionalization and th…
We report on magnetoconductance measurements through a weakly coupled quantum dot, containing roughly 900 electrons, in a wide magnetic field range from 0 T to 12 T. We find modulations of the conductance resonances in the quantum Hall regime for higher integer filling factors $6> ν_\mathrm{dot} > 2$, in addition to modulations at $2> ν_\mathrm{dot} > 1$ and at fractional filling factors $ν_\mathrm{dot} \gtrsim 2/3$, $1/3$. Depending on the internal filling factor, edge reconstruction inside the quantum dot leads to the formation of multiple concentric compressible regions, which contain discr…
The gapless edge modes of the Quantum Spin Hall insulator form a helical liquid in which the direction of motion along the edge is determined by the spin orientation of the electrons. In order to probe the Luttinger liquid physics of these edge states and their interaction with a magnetic (Kondo) impurity, we consider a setup where the helical liquid is tunnel-coupled to a semiconductor quantum dot which is excited by optical absorption, thereby inducing an effective quantum quench of the tunneling. At low energy, the absorption spectrum is dominated by a power-law singularity. The correspondi…
We investigate the spectral and transport properties of a double quantum dot laterally attached to a topological superconducting nanowire, hosting the Majorana zero-energy modes. Specifically, we consider a geometry, in which the outer quantum dot is embedded between the external normal and superconducting leads, forming a circuit. First, we derive analytical expressions for the bound states in the case of an uncorrelated system and discuss their signatures in the tunneling spectroscopy. Then, we explore the case of strongly correlated quantum dots by performing the numerical renormalization g…
This paper has been updated by the author to: arXiv:1012.0060v1 [cond-mat.mes-hall], titled "Collective Nuclear Stabilization by Optically Excited Hole in Quantum Dot"
We study dephasing in electron transport through a large quantum dot (a Fabry-Perot interferometer) in the fractional quantum Hall regime with filling factor $2/3$. In the regime of sequential tunneling, dephasing occurs due to electron fractionalization into counterpropagating charge and neutral edge modes on the dot. In particular, when the charge mode moves much faster than the neutral mode, and at temperatures higher than the level spacing of the dot, electron fractionalization combined with tje fractional statistics of the charge mode leads to the dephasing selectively suppressing $h/e$ A…
The ground states of electrons in two vertically coupled quantum dots in the presence of an external magnetic field have been studied within the density functional theory. A phase diagram of the transition to the quantum Hall state in double quantum dots has been plotted for the Landau level filling factor $ν= 1$. It has been shown that the quantum Hall state can be stable for a zero tunnel splitting. The influence of the impurity potential on the stability condition for the quantum Hall state has been analyzed.
We report selective injection of both spin-up and spin-down single electrons into a quantum dot (QD) from spin-polarized non-equilibrium quantum Hall edge channels (ECs) generated by selective transmission of spin-resolved ECs using a surface gate placed at a distance from the QD. We change the spin polarization of non-equilibrium ECs by changing the bias voltages applied to different source Ohmic contacts. The efficiency of spin-up electron injection reaches 0.5, which is approximately 0.2 higher than that induced by spin-dependent tunnel coupling between QD and ECs. On the other hand, the ef…
We study a model of a quantum dot coupled to a quantum Hall edge of the Laughlin state, taking into account short-range interactions between the dot and the edge. This system has been studied experimentally in electron quantum optics in the context of single particle sources. We consider driving the dot out of equilibrium by a time-dependent bias voltage. We calculate the resulting current on the edge by applying the Kubo formula to the bosonized Hamiltonian. The Hamiltonian of this system can also be mapped to the spin-boson model and in this picture, the current can be perturbatively calcula…
This work presents theoretical demonstration of a carrier trap unit formed by dual topological insulator constrictions (TIC) on the HgTe/CdTe quantum well (QW) with inverted band structures. The sample of HgTe/CdTe QW is patterned into a Hall bar device and a topological quantum dot is created by adding split gate electrodes closely on the QW. In sharp contrast to conventional semiconductor quantum dots, the presence or absence of topological edge states in the proposed quantum hall bar system leads to distinct propagating/insulating state of the TICs with large on/off ratio. This topological …
In this work, we investigate the spatial distributions and the widths of the incompressible strips, i.e. the edgestates. The incompressible strips that correspond to ν=1,2 and 1/3 filling factors are examined in the presence of a strong perpendicular magnetic field. We present a microscopic picture of the fractional quantum Hall effect based interferometers, within a phenomenological model. We adopt Laughlin quasi-particle properties in our calculation scheme. In the fractional regime, the partially occupied lowest Landau level is assumed to form an energy gap due to strong correlations. Essen…
We study theoretically edge transport of a fractional quantum Hall liquid, in the presence of a quantum dot inside the Hall bar with well controlled electron density and Landau level filling factor ν, and show that such transport studies can help reveal the nature of the fractional quantum Hall liquid. In our first example we study the ν=1/3 and ν=2/3 liquids in the presence of a ν=1 quantum dot. When the quantum dot becomes large, its edge states join those of the Hall bar to reconstruct the edge states configuration. Taking randomness around the edges into account, we find that in the disord…
We report on a Kondo correlated quantum dot connected to two-dimensional leads where we demonstrate the renormalization of the g-factor in the pure Zeeman case i.e, for magnetic fields parallel to the plane of the quantum dot. For the same system we study the influence of orbital effects by investigating the quantum Hall regime i.e. a perpendicular magnetic field is applied. In this case an unusual behaviour of the suppression of the Kondo effect and of the split zero-bias anomaly is observed. The splitting decreases with magnetic field and shows discontinuous changes which are attributed to t…
We report a dual resonance feature in ballistic conductance through a quantum Hall graphene nanoribbon with a magnetic quantum dot. Such a magnetic quantum dot localizes Dirac fermions exhibiting anisotropic eigenenergy spectra with broken time-reversal symmetry. Interplay between the localized states and quantum Hall edge states is found to be two-fold, showing Breit-Wigner and Fano resonances, which is reminiscent of a double quantum dot system. By fitting the numerical results with the Fano-Breit-Wigner lineshape from the double quantum dot model, we demonstrate that the two-fold resonance …
Quantum-relativistic matter is ubiquitous in nature; however it is notoriously difficult to probe. The ease with which external electric and magnetic fields can be introduced in graphene opens a door to creating a table-top prototype of strongly confined relativistic matter. Here, through a detailed spectroscopic mapping, we provide a spatial visualization of the interplay between spatial and magnetic confinement in a circular graphene resonator. We directly observe the development of a multi-tiered "wedding cake"-like structure of concentric regions of compressible/incompressible quantum Hall…
We study the physics of electron tunneling between multiple quantum dots and the edge of a quantum Hall state. Our results generalize earlier work [G. A. Fiete, W. Bishara, C. Nayak, Phys. Rev. Lett. 101, 176801 (2008)] in which it was shown that a single quantum dot tunnel coupled to a non-Abelian quantum Hall state can realize a stable multi-channel Kondo fixed point at low-energy. In this work, we investigate the physics of multiple dots and find that a rich set of possible low-energy fixed points arises, including those with non-Fermi liquid properties. Previously unidentified fixed points…
We study the magneto-conductance of a $1.4~\mathrm{μm}$-wide quantum dot in the fractional quantum Hall regime. For a filling factor $\approx 2/3$ and $\gtrsim 1/3$ in the quantum dot the observed Coulomb resonances show a periodic modulation in magnetic field. This indicates a non-trivial reconstruction of the 2/3 fractional quantum Hall state in the quantum dot. We present a model for the charge stability diagram of the system assuming two compressible regions separated by an incompressible stripe of filling factor $2/3$ and $1/3$, respectively. From the dependence of the magnetic field peri…
We demonstrate that the experimentally observed conductance oscillations through a gate-controlled quantum dot under quantized Hall conditions originate from a true Aharonov-Bohm phase that is acquired by the electrons as they co-propagate coherently through incompressible strips at a particular filling factor and enclose a certain magnetic flux within the dot. The absence of oscillations at certain filling factors is explained. The self-consistent screening theory of the integer quantized hall effect reveals the range of experimental parameters under which further intriguing oscillation patte…
Edge states in graphene quantum dots: Fractional quantum Hall effect analogies and differences at zero magnetic field
我们研究了在自由磁场条件下，具有锯齿形边界的准圆形石墨烯量子点中的中间带隙边缘态的简并流形支持类似于分数量子霍尔效应（Fractional磁场中半导体异质结构的情况下所熟悉的强关联多体行为的方式。本文首次对5 <= N <= 8的全自旋极化电子和N（N-1）/2 <= L <= 150的总角动量进行了系统的精确对角化（EXD）数值研究。本文在前面介绍的方法的基础上推导了一个双电子分子（REM）型波函数。Yannouleas和U. Landman，Phys.Rev.B66，115315（2002）]中的方法。将EXD波函数与Laughlin型和REM型试函数进行了比较。结果发现，REM的变分扩展提供了一个更好的描述所有分数填充相比，劳克林功能（包括总能量和重叠），一个事实，反映了强大的方位角定位的边缘电子。与圆形半导体量子点中电子的多环排列相反，石墨烯REM在所有情况下都表现出单（0，N）双环分子（晶体）结构，所有电子都位于边缘上。沿着圆形边缘的锯齿形边界条件中的中断有效地充当钉扎电子分子的杂质，产生具有破坏的旋转对称性的单粒子密度，其直接描绘边缘电子的方位角定位。
We find that the confinement potential of a few electron quantum dot can be tuned to significantly increase the overlap with certain quantum Hall trial wave functions. Besides manipulating inter-electron interaction, this approach may prove useful in quantum point contact experiments, which involve narrow constrictions.
