Disordered Quantum Wires Research Articles

Random-Matrix Models of Monitored Quantum Circuits

We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born probabilities. The latter generalizes the Porter–Thomas distribution for random unitary circuits to the monitored setting and is log-normal at long times. We also consider weak measurements that interpolate between identity quantum channels and projective measurements. In this setting, we derive an exactly solvable Fokker–Planck equation for the joint distribution of singular values of Kraus operators, analogous to the Dorokhov–Mello–Pereyra–Kumar (DMPK) equation modelling disordered quantum wires. We expect that the statistical properties of Kraus operators we have established for these simple systems will serve as a model for the entangling phase of monitored quantum systems more generally.

Exceptional non-Hermitian phases in disordered quantum wires

We demonstrate the occurrence of nodal non-Hermitian (NH) phases featuring exceptional degeneracies in chiral-symmetric disordered quantum wires, where NH physics naturally arises from the self-energy in a disorder-averaged Green's function description. Notably, we find that at least two nodal points in the clean Hermitian system are required for exceptional points to be effectively stabilized upon adding disorder. We identify and study experimental signatures of our theoretical findings both in the spectral functions and in mesoscopic quantum transport properties of the considered systems. Our results are quantitatively corroborated and exemplified by numerically exact simulations on a microscopic lattice model. The proposed setting provides a conceptually minimal framework for the realization and study of topological NH phases in quantum many-body systems.

Low-temperature transport in CdS disordered quantum wires: dephasing

We study the effect of disorder and dephase in transmission of a CdS quantum wire using the Green’s function technique. Our results show that the transmission decreases with the increasing disorder strength. The resistance of a CdS quantum wire with phase-breaking scattering only increases with increasing dephasing. Obtained results show that the drain current of a CdS quantum wire with inelastic scattering by phonons with energy $$\hbar \omega = 30$$ meV decreases with the increasing disorder strength. Moreover, our theoretical results are independently supported by simulations of CdS disordered quantum wires based on a tight-binding model.

Entanglement between Distant Regions in Disordered Quantum Wires

AbstractThe entanglement negativity for spinless fermions in a strongly disordered 1D Anderson model is studied. For two close regions, the negativity is log‐normally distributed, and is suppressed by repulsive interactions. With increasing distance between the regions, the typical negativity decays, but there remains a peak in the distribution, also at high values, representing highly entangled distant regions. For intermediate distances, in the noninteracting case, two distinct peaks are observed. As a function of interaction strength, the two peaks merge into each other. The abundance and nature of these entangled regions is studied. The relation to resonances between single‐particle eigenstates is demonstrated. Thus, although the system is strongly disordered, it is nevertheless possible to encounter two far‐away regions which are entangled.

Algebraic localization from power-law couplings in disordered quantum wires

We analyze the effects of disorder on the correlation functions of one-dimensional quantum models of fermions and spins with long-range interactions that decay with distance $\ell$ as a power-law $1/\ell^\alpha$. Using a combination of analytical and numerical results, we demonstrate that power-law interactions imply a long-distance algebraic decay of correlations within disordered-localized phases, for all exponents $\alpha$. The exponent of algebraic decay depends only on $\alpha$, and not, e.g., on the strength of disorder. We find a similar algebraic localization for wave-functions. These results are in contrast to expectations from short-range models and are of direct relevance for a variety of quantum mechanical systems in atomic, molecular and solid-state physics.

Heat Transport and Majorana Fermions in a Superconducting Dot-Wire System: An Exact Solution

We obtain exact expressions for the first three moments of the heat conductance of a quantum chain that crosses over from a superconducting quantum dot to a superconducting disordered quantum wire. Our analytic solution provides exact detailed descriptions of all crossovers that can be observed in the system as a function of its length, which include ballistic-metallic and metallic-insulating crossovers. The two Bogoliubov-de Gennes (BdG) symmetry classes with time-reversal symmetry are accounted for. The striking effect of total suppression of the insulating regime in systems with broken spin-rotation invariance is observed at large length scales. For a single channel system, this anomalous effect can be interpreted as a signature of the presence of the elusive Majorana fermion in a condensed matter system.

Magnetotransport measurements on Bi2Te3 nanowires electrodeposited in etched ion-track membranes

We report on the magneto-transport properties of individual Bi2Te3 nanowires with diameters ranging from 25 nm to 120 nm fabricated by electrodeposition in etched ion-track membranes. The metallic behavior of all nanowires is typical for highly-degenerate semiconductors and the weak temperature dependence of the resistivity suggests a weak electron-phonon coupling, as expected for topological surface states with quantum confinement. The diameter dependence of the resistivity further confirms the quasi-ballistic nature of charge carriers, in agreement with the reduction of the number of surface conductance channels in disordered quantum wires with a stronger quantum confinement. Although the bulk conductance is not negligible, both the transport length of bulk carriers and their electrostatic screening length remain shorter than the nanowire diameter, probably leading to a small contribution to the resistivity change. Quantum transport measurements give further evidence of finite-size effects, as shown by the weak anti-localization correction to the conductance, below 15K, and reveal the coexistence of surface Aharonov-Bohm oscillations and bulk universal conductance fluctuations, below 5K.

Localization length versus level repulsion in one-dimensional driven disordered quantum wires

We study the level repulsion and its relationship with the localization length in a disordered one-dimensional quantum wire excited with monochromatic linearly polarized light and described by the Anderson-Floquet model. In the high frequency regime, the linear scaling between the localization length divided by the length of the system and the spectral repulsion is the same as in the one-dimensional Anderson model without driving, although both quantities depend on the parameters of the external field. In the low frequency regime the level repulsion depends mainly on the value of the amplitude of the field and the proportionality between level repulsion and localization length is lost.

Signatures of subband quantization in the Coulomb blockade regime of a disordered quantum wire

Abstract We report experiments on the two-terminal conductance of a long disordered quantum wire in a perpendicular magnetic field. Pronouncedly enhanced magnetoconductance in magnetic fields of intermediate strength is observed in the Coulomb blockade regime, which is well explained using the boundary roughness scattering and the subband quantization of the quantum wire, by modeling the disordered quantum wire as that of a quantum dot defined in a quantum wire. Assuming a parabolic constriction in the disordered quantum wire, we further obtained the magnetic field dependence of high energy levels in the quantum dot and the gate voltage dependence of the effective width of the quantum wire. Our results may provide useful information for further studies on integrated structures in on-chip laboratories.

Anderson localization of a Majorana fermion

Isolated Majorana fermion states can be produced at the boundary of a topological superconductor in a quasi–one-dimensional geometry. If such a superconductor is connected to a disordered quantum wire, the Majorana fermion is spread into the wire, subject to Anderson localization. We study this effect in the limit of a thick wire with broken time-reversal and spin-rotational symmetries. With the use of a supersymmetric nonlinear sigma model, we calculate the average local density of states in the wire as a function of energy and of the distance from the interface with the superconductor. Our results may be qualitatively explained by the repulsion of states from the Majorana level and by Mott hybridization of localized states.

Orbital entanglement and electron localization in quantum wires

We study the signatures of disorder in the production of orbital electron entanglement in quantum wires. Disordered entanglers suffer the effects of localization of the electron wave function and random fluctuations in the entanglement production. This manifests in the statistics of the concurrence, a measure of the produced two-qubit entanglement. We calculate the concurrence distribution as a function of the disorder strength within a random-matrix approach. We also identify significant constraints on the entanglement production as a consequence of the breaking/preservation of time-reversal invariance. Additionally, our theoretical results are independently supported by simulations of disordered quantum wires based on a tight-binding model.

Quasiclassical theory of disordered multi-channel Majorana quantum wires

Multi-channel spin–orbit quantum wires, when subjected to a magnetic field and proximity coupled to an s-wave superconductor, may support Majorana states. We study what happens to these systems in the presence of disorder. Inspired by the widely established theoretical methods of mesoscopic superconductivity, we develop á la Eilenberger a quasiclassical approach to topological nanowires valid in the limit of strong spin–orbit coupling. We find that the ‘Majorana number’ , distinguishing between the state with Majorana fermions (symmetry class B) and no Majorana fermions (class D), is given by the product of two Pfaffians of gapped quasiclassical Green's functions fixed by the right and left terminals connected to the wire. A numerical solution of the Eilenberger equations reveals that the class D disordered quantum wires are prone to the formation of the zero-energy anomaly (class D impurity spectral peak) in the local density of states that shares the key features of the Majorana peak. In this way, we confirm the robustness of our previous conclusions (Bagrets and Altland 2012 Phys. Rev. Lett.109 227005) on a more restrictive system setup. Generally speaking, we find that the quasiclassical approach provides a highly efficient means to address disordered class D superconductors both in the presence and in the absence of topological structures.

Localization length in the quasi one-dimensional disordered system revisited

We have provided a complete description of the electron localization length (LL) in quasi-one dimensional (Q1D) disordered quantum wire with hard wall and periodic boundary conditions. Presented analytical expressions for LL are in excellent agreement with numerical calculations, exact up to order W2 (W being the disorder strength), and valid for an arbitrary number of propagating and evanescent channels. We have calculated the average conductance in Q1D systems, establish relationship between various lengths and show that it basically differs from 1D case.

Disordered Quantum Wires: Microscopic Origins of the DMPK Theory and Ohm’s Law

We study the electronic transport properties of the Anderson model on a strip, modeling a quasi one-dimensional disordered quantum wire. In the literature, the standard description of such wires is via random matrix theory (RMT). Our objective is to firmly relate this theory to a microscopic model. We correct and extend previous work (arXiv:0912.1574) on the same topic. In particular, we obtain through a physically motivated scaling limit an ensemble of random matrices that is close to, but not identical to the standard transfer matrix ensembles (sometimes called TOE, TUE), corresponding to the Dyson symmetry classes \beta=1,2. In the \beta=2 class, the resulting conductance is the same as the one from the ideal ensemble, i.e.\ from TUE. In the \beta=1 class, we find a deviation from TOE. It remains to be seen whether or not this deviation vanishes in a thick-wire limit, which is the experimentally relevant regime. For the ideal ensembles, we also prove Ohm's law for all symmetry classes, making mathematically precise a moment expansion by Mello and Stone. This proof bypasses the explicit but intricate solution methods that underlie most previous results.

Topological superconducting phases in disordered quantum wires with strong spin-orbit coupling

Zeeman fields can drive semiconductor quantum wires with strong spin-orbit coupling and in proximity to $s$-wave superconductors into a topological phase which supports end Majorana fermions and offers an attractive platform for realizing topological quantum information processing. Here, we investigate how potential disorder affects the topological phase by a combination of analytical and numerical approaches. Most prominently, we find that the robustness of the topological phase against disorder depends sensitively and nonmonotonously on the Zeeman field applied to the wire.

Random Lie group actions on compact manifolds: A perturbative analysis

A random Lie group action on a compact manifold generates a discrete time Markov process. The main object of this paper is the evaluation of associated Birkhoff sums in a regime of weak, but sufficiently effective coupling of the randomness. This effectiveness is expressed in terms of random Lie algebra elements and replaces the transience or Furstenberg’s irreducibility hypothesis in related problems. The Birkhoff sum of any given smooth function then turns out to be equal to its integral w.r.t. a unique smooth measure on the manifold up to errors of the order of the coupling constant. Applications to the theory of products of random matrices and a model of a disordered quantum wire are presented.

Nonuniversal Shot Noise in Disordered Quantum Wires with Channel-Number Imbalance

The number of conducting channels for one propagating direction is equal to that for the other direction in ordinary quantum wires. However, they can be imbalanced in graphene nanoribbons with zigzag edges. Employing the model system in which a degree of channel-number imbalance can be controlled, we calculate the shot-noise power at zero frequency by using the Boltzmann-Langevin approach. The shot-noise power in an ordinary diffusive conductor is one-third of the Poisson value. We show that with increasing the degree of channel-number imbalance, the universal one-third suppression breaks down and a highly nonuniversal behavior of shot noise appears.

From the Anderson Model on a Strip to the DMPK Equation and Random Matrix Theory

We study weakly disordered quantum wires whose width is large compared to the Fermi wavelength. It is conjectured that such wires diplay universal metallic behaviour as long as their length is shorter than the localization length (which increases with the width). The random matrix theory that accounts for this behaviour - the DMPK theory- rests on assumptions that are in general not satisfied by realistic microscopic models. Starting from the Anderson model on a strip, we show that a twofold scaling limit nevertheless allows to recover rigorously the fundaments of DMPK theory, thus opening a way to settle some conjectures on universal metallic behaviour.

Dimensional dependence of weak localization corrections and spin relaxation in quantum wires with Rashba spin-orbit coupling

The quantum correction to the conductivity in disordered quantum wires with linear Rashba spin-orbit coupling is obtained. For quantum wires with spin-conserving boundary conditions, we find a crossover from weak anti- to weak localization as the wire width W is reduced using exact diagonalization of the Cooperon equation. This crossover is due to the dimensional dependence of the spin relaxation rate of conduction electrons, which becomes diminished, when the wire width is smaller than the bulk spin precession length $L_{SO}$. We thus confirm previous results for small wire width, $W/L_{SO}<= 1$ [PRL98,176808(2007)], where only the transverse 0-modes of the Cooperon equation had been taken into account. We find that spin helix solutions become stable for arbitrary ratios of linear Rashba and Dresselhaus coupling in narrow wires. For wider wires, the spin relaxation rate is found to be not monotonous as function of wire width: it becomes first enhanced for W on the order of the bulk $L_{SO}$ before it becomes diminished for smaller wire widths. In addition, we find that the spin relaxation is smallest at the edge of the wire for wide wires. The effect of the Zeeman coupling to the magnetic field perpendicular to the 2D electron system is studied and found that it shifts the crossover from weak anti- to weak localization to larger wire widths $W_c$. When the transverse confinement potential of the quantum wire is smooth (adiabatic), the spin relaxation rate is found to be enhanced as W is reduced. We find that only a spin polarized state retains a finite spin relaxation rate in such narrow wires. Thus, we conclude that the injection of polarized spins into nonmagnetic quantum wires should be favorable in wires with smooth confinement potential. Finally, in wires with tubular shape, corresponding to transverse periodic boundary conditions, we find no reduction of the spin relaxation rate.

Average and Second Moment of the Conductance of Randomly Coupled Chiral Channels

We study the conductance of a spinless non-interacting electron system consisting of randomly coupled N R right-moving channels and N L left-moving channels. This system serves as a model of disordered quantum wires with unitary symmetry. We focus on the case of N R = 1 with an arbitrary N L . In this case, the dimensionless conductance g for the left-moving channels is by m ≡ N L -1 greater than the dimensionless conductance g ' for the right-moving channels due to the presence of m perfectly conducting channels. That is, g = g '+ m . Using a superspin approach, we obtain the average and second moment of g ' as a function of wire length L . The resulting asymptotic forms in the long- L regime are consistent with those obtained from the existing scaling theory.