Chaotic Quantum Dots Research Articles

Non-Abelian Holonomy of Majorana Zero Modes Coupled to a Chaotic Quantum Dot.

If a quantum dot is coupled to a topological superconductor via tunneling contacts, each contact hosts a Majorana zero mode in the limit of zero transmission. Close to a resonance and at a finite contact transparency, the resonant level in the quantum dot couples the Majorana modes, but a ground-state degeneracy per fermion parity subspace remains if the number of Majorana modes coupled to the dot is five or larger. Upon varying shape-defining gate voltages while remaining close to resonance, a nontrivial evolution within the degenerate ground-state manifold is achieved. We characterize the corresponding non-Abelian holonomy for a quantum dot with chaotic classical dynamics using random matrix theory and discuss measurable signatures of the non-Abelian time evolution.

Thermodynamic uncertainty relations in mesoscopic devices.

We investigate the thermodynamic uncertainty relations (TURs) in mesoscopic devices for all universal symmetry classes of Wigner-Dyson and Dirac (chiral). The observables of interest include the TUR (MS), which is defined in terms of the ratio between the mean noise and mean conductance, as well as a new TUR (R) proposed in this article, which is based on the ensemble mean of the noise-to-conductance ratio. A detailed study is made on the quantum interference corrections associated with the TURs. We also analyze the influence of orbital and sublattice/chiral degrees of freedom for the validity of the observables in these chaotic mesoscopic billiards. Our investigation is based on the concatenation between the Landauer-Büttiker theory, the Mahaux-Wendeinmüller theory, and the TURs. We simulate the universal mesoscopic chaotic quantum dots using the random-matrix theory and compare our numerical results with the pertinent experimental data. The results were obtained for a different number of channels and tunneling rates that vary from the opaque to the ideal regime and, in all cases, demonstrate a clear phenomenological distinction between the TURs. In particular, the opaque regime engenders remarkable differences between the observables, even in the semiclassical regime, which characterizes a clear violation of the central limit theorem. Furthermore, we show that the phenomenology of the quantum interference corrections is strikingly robust, surprisingly exhibiting an order of magnitude greater than the supposedly leading semiclassical term for the TUR (R).

Supercell symmetry modified spectral statistics of Kramers–Weyl fermions* *Contribution to the special issue of J. Phys. A in honour of the life and work of Fritz Haake.

We calculate the spectral statistics of the Kramers–Weyl Hamiltonian H = v∑ α σ α sin p α + tσ 0∑ α cos p α in a chaotic quantum dot. The Hamiltonian has symplectic time-reversal symmetry (H is invariant when spin σ α and momentum p α both change sign), and yet for small t the level spacing distributionP(s) ∝s β follows the β = 1 orthogonal ensemble instead of the β = 4 symplectic ensemble. We identify a supercell symmetry of H that explains this finding. The supercell symmetry is broken by the spin-independent hopping energy ∝t cos p, which induces a transition from β = 1 to β = 4 statistics that shows up in the conductance as a transition from weak localization to weak antilocalization.

Chaos Modulation Using Synchronization in Quantum Dot Light Emitting Diode with Optoelectronic Feedback

In this research, a communication scheme of chaos modulation (CMO) that depending on two chaotic quantum dot light emitting diodes (QDLEDs) synchronization was evaluated using theoretical model. The perturbation in behavior of the QDLED can be significantly increased by optoelectronic feedback. Changing the coupling strength between the transmitter and receiver in unidirectional coupling greatly contributes to creating a state of total synchronization between the two systems. Furthermore, the proposed communication model was successful by effectively receiving messages.

Influence of normal metal-superconductor interface on the statistics of conductance and shot noise power in a non-ideal chaotic quantum dot

In this paper, we apply Andreev’s reflection to study the sub-gap coherent transport properties for a quantum dot attached to normal metal and superconductor reservoirs via non-ideal leads. We use the random matrix theory to obtain numerically the conductance and shot noise power probability densities varying the transparencies and the number of open scattering channels in each lead for the three Wigner–Dyson ensembles. We obtain results from the extreme quantum limit (where the conductance is of the order of 2e 2/h, the quantum of conductance) to the semiclassical regime (conductance much larger than 2e 2/h). We observe the appearance of non-analyticities in these probability densities and an interesting invariance break under the operation of exchanging the lead labels when time-reversal symmetry is absent.

Communication in Quantum Dot Light Emitting Diode with Optoelectronic Feedback Technique

A communication scheme based on the synchronization of two chaotic quantum dot light emitting diodes is theoretically examined. The Chaos in the quantum dot light emitting is generated by means of a positive optoelectronic feedback technique. Synchronization of the chaos is achieved by varying coupling strength between the transmitter and the receiver as unidirectional coupling. We then test a proposed chaos shift keying communication scheme by successfully transmitting messages.

Communication in Quantum Dot Light Emitting Diode with Optoelectronic Feedback Technique

A communication scheme based on the synchronization of two chaotic quantum dot light emitting diodes is theoretically examined. The Chaos in the quantum dot light emitting is generated by means of a positive optoelectronic feedback technique. Synchronization of the chaos is achieved by varying coupling strength between the transmitter and the receiver as unidirectional coupling. We then test a proposed chaos shift keying communication scheme by successfully transmitting messages.

Mesoscopic Fluctuations: Nuclei, Quantum Dots, and Beyond

This paper is dedicated to review the contributions of Prof. Mahir Hussein to the theory of random matrices and its applications to mesoscopic systems, with focus on his more recent works on conductance fluctuations of chaotic quantum dots.

Quantum state transfer of electrons in chaotic quantum dots

Abstract In this paper, we study theoretically the transmission of the two-electron quantum state between the leads of a chaotic quantum dot in the presence or absence of time-reversal symmetry. The system we consider in this work is constituted by two-channel non-ideal leads connecting the cavity to two reservoirs of electrons. Quantum fidelity was used to quantify the success of the transference of states between the leads. We show that the quantum fidelity of the system is equal to the product of the transmission eigenvalues. We obtained its average and probability density function via random matrix theory by two approaches: sample simulation and exact integration. The results show that the quantum state transference is enhanced for ideal leads with broken time-reversal symmetry.

Encrypted Chaos in Quantum Dot Light Emitting Diode

A communication scheme based on the synchronization of two chaotic quantum dot light emitting diodes (QD-LEDs) is theoretically examined. The Chaos in the QD-LED is generated by means of an optical feedback. Synchronization of the chaos is achieved by varying coupling strength between the transmitter and the receiver as unidirectional coupling. The proposed communication schemes is test a by successfully transmitting messages.

Statistics of orbital entanglement for the full scattering state in a chaotic quantum dot

We study the statistical properties of orbital entanglement for the full scattering state in a chaotic quantum dot attached to two nonideal two-channel leads via random matrix theory. Using the entanglement entropy as the entanglement quantifier, we obtain its average and probability density function varying the opacity of each lead in the presence and absence of time-reversal symmetry by two methods: (a) exact integration over random matrix ensembles when one contact is ideal and (b) random matrix simulations for arbitrary opacity values. All results show that these two methods are in agreement with each other. The Person correlation coefficient between the entanglement entropy and the entanglement production factor was also analyzed. We verify that the latter predicts a good level of entanglement of the full scattering state.

Wigner–Smith time-delay matrix in chaotic cavities with non-ideal contacts

We consider wave propagation in a complex structure coupled to a finite number N of scattering channels, such as chaotic cavities or quantum dots with external leads. Temporal aspects of the scattering process are analysed through the concept of time delays, related to the energy (or frequency) derivative of the scattering matrix . We develop a random matrix approach to study the statistical properties of the symmetrised Wigner–Smith time-delay matrix , and obtain the joint distribution of and for the system with non-ideal contacts, characterised by a finite transmission probability (per channel) . We derive two representations of the distribution of in terms of matrix integrals specified by the Dyson symmetry index (the general case of unequally coupled channels is also discussed). We apply this to the Wigner time delay , which is an important quantity providing the density of states of the open system. Using the obtained results, we determine the distribution of the Wigner time delay in the weak coupling limit and identify the following three regimes. (i) The large deviations at small times (measured in units of the Heisenberg time) are characterised by the limiting behaviour for . (ii) The distribution shows the universal behaviour in some intermediate range . (iii) It has a power law decay for large .

Josephson currents in chaotic quantum dots

We study theoretically the Josephson current-phase relationship in a chaotic quantum dot coupled to superconductors by ballistic contacts. In this regime, strong proximity effect induces superconductivity in the quantum dot that leads to a significant modification in the electron density of states and formation of multiple sub-gaps. The magnitude of the resulting supercurrent depends on the phase difference of the superconducting order parameter in the leads and shows strongly anharmonic skewed behavior. We find that when the Thouless energy on the dot exceeds the superconducting energy gap, the second harmonic of the supercurrent becomes comparable in magnitude to the first harmonic. To address these effects on the technical level, we use the nonlinear $\sigma$-model Keldysh formalism in the framework of the circuit theory to compute dependence of the density of states, Josephson energy, and current on the superconducting phases in the leads. We analyze how these quantities change as a function of the Thouless energy and the superconducting gap. Finally, we briefly discuss sub-gap tail states, mesoscopic supercurrent fluctuations, weak localization correction, and also touch on anharmonicity of gatemon qubits with quantum dot Josephson junctions.

Spin-to-charge conversion in 2D electron gas and single-layer graphene devices

We investigate the spin-to-charge conversion emerging from a mesoscopic device connected to multiple terminals. We obtain analytical expressions to the characteristic coefficient of spin-to-charge conversion, which are applied in two kinds of ballistic chaotic quantum dots at low temperature. We perform analytical diagrammatic calculations in the universal regime for two-dimensional electron gas and single-layer graphene with the strong spin-orbit interaction in the universal regime. Furthermore, our analytical results are confirmed by numerical simulations. Finally, we connect our analytical findings to recent experimental measures giving a conceptual explanation about the apparent discrepancies between them.

Correlation between peak-height modulation and phase lapses in transport through quantum dots.

We show that two intriguing features of mesoscopic transport, namely, the modulation of Coulomb blockade peak heights and the transmission phase lapses occurring between subsequent peaks, are closely related. Our analytic arguments are corroborated by numerical simulations for chaotic ballistic quantum dots. The correlations between the two properties are experimentally testable. The statistical distribution of the partial-width amplitude, at the heart of the previous relationship, is determined, and its characteristic parameters are estimated from simple models.

Truncated Linear Statistics Associated with the Eigenvalues of Random Matrices II. Partial Sums over Proper Time Delays for Chaotic Quantum Dots

Invariant ensembles of random matrices are characterized by the distribution of their eigenvalues $\{\lambda_1,\cdots,\lambda_N\}$. We study the distribution of truncated linear statistics of the form $\tilde{L}=\sum_{i=1}^p f(\lambda_i)$ with $p<N$. This problem has been considered by us in a previous paper when the $p$ eigenvalues are further constrained to be the largest ones (or the smallest). In this second paper we consider the same problem without this restriction which leads to a rather different analysis. We introduce a new ensemble which is related, but not equivalent, to the "thinned ensembles" introduced by Bohigas and Pato. This question is motivated by the study of partial sums of proper time delays in chaotic quantum dots, which are characteristic times of the scattering process. Using the Coulomb gas technique, we derive the large deviation function for $\tilde{L}$. Large deviations of linear statistics $L=\sum_{i=1}^N f(\lambda_i)$ are usually dominated by the energy of the Coulomb gas, which scales as $\sim N^2$, implying that the relative fluctuations are of order $1/N$. For the truncated linear statistics considered here, there is a whole region (including the typical fluctuations region), where the energy of the Coulomb gas is frozen and the large deviation function is purely controlled by an entropic effect. Because the entropy scales as $\sim N$, the relative fluctuations are of order $1/\sqrt{N}$. Our analysis relies on the mapping on a problem of $p$ fictitious non-interacting fermions in $N$ energy levels, which can exhibit both positive and negative effective (absolute) temperatures. We determine the large deviation function characterizing the distribution of the truncated linear statistics, and show that, for the case considered here ($f(\lambda)=1/\lambda$), the corresponding phase diagram is separated in three different phases.

Effective production of orbital quantum entanglement in chaotic quantum dots with nonideal contacts

We study orbital entanglement production in a chaotic quantum dot with two-channel leads by varying the opacity of the contacts in the unitary and orthogonal Wigner-Dyson ensembles. We computed the occurrence probability of entangled states (squared norm) and its concurrence (entanglement level). We also define an entanglement production factor to properly evaluate the entanglement behavior in the system considering effective aspects. The results are numerically obtained through (i) integrations over random matrix ensembles (exact results) for the scenario of one contact ideally fixed and (ii) random matrix simulations for arbitrary contact opacities (sampling). Those outcomes are in mutual agreement and indicate that the optimum effective production of orbital entanglement is achieved when both contacts are ideal and the time-reversal symmetry is broken.

Fluctuation phenomena in chaotic Dirac quantum dots: Artificial atoms on graphene flakes

We develop the stub model for the Dirac Quantum Dot, an electron confining device on a grapheme surface. Analytical results for the average conductance and the correlation functions are obtained and found in agreement with those found previously using semiclassical calculation. Comparison with available data are presented. The results reported here demonstrate the applicability of Random Matrix Theory in the case of Dirac electrons confined in a stadium.

Reprint of : Effect of a tunnel barrier on the scattering from a Majorana bound state in an Andreev billiard

We calculate the joint distribution P(S,Q) of the scattering matrix S and time-delay matrix Q=−iℏS†dS/dE of a chaotic quantum dot coupled by point contacts to metal electrodes. While S and Q are statistically independent for ballistic coupling, they become correlated for tunnel coupling. We relate the ensemble averages of Q and S and thereby obtain the average density of states at the Fermi level. We apply this to a calculation of the effect of a tunnel barrier on the Majorana resonance in a topological superconductor. We find that the presence of a Majorana bound state is hidden in the density of states and in the thermal conductance if even a single scattering channel has unit tunnel probability. The electrical conductance remains sensitive to the appearance of a Majorana bound state, and we calculate the variation of the average conductance through a topological phase transition.

Universal spin Hall conductance fluctuations in chaotic Dirac quantum dots

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 investigate both the corresponding fluctuations, the universal fractionated and the universal quantized, and also the open channel orbital number crossover between the two regimes. In particular, we show that the Wigner-Dyson symmetries do not properly describe such conductances and the preponderant role of the chiral classes on the Dirac quantum dots. The results are analytical and solve outstanding issues.