arXiv subjects

Anton Akhmerov

Publications and source records attributed to Anton Akhmerov.

13 recordsLinked to original sources

arXiv2026

Computational quantum transport: a scattering approach perspective

This review is devoted to the different techniques that have been developed to compute the phase-coherent transport properties of quantum nanoelectronic systems connected to electrodes. Beside a review of the different algorithms proposed in the literature, we provide a comprehensive and pedagogical derivation of the two formalisms on which these techniques are based: the scattering approach and the (nonequilibrium) Green's function approach. We show that the scattering problem can be formulated as a system of linear equations and that different existing algorithms for solving this scattering problem amount to different sequences of Gaussian elimination. We explicitly prove the equivalence of the two formalisms. We discuss the stability and numerical complexity of the existing methods. The review ends with a selection of a few applications where numerical calculations were instrumental in shaping our understanding of the physics.

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arXiv2026

Loopless multiterminal quantum circuits at odd parity

We theoretically investigate loopless multiterminal hybrid superconducting devices at odd fermion parity with time-reversal symmetry. We find that the energy-phase relationship has a double minimum corresponding to opposite windings of the superconducting phases. Spin-orbit coupling adds multi-axial spin splittings, which contrasts with two-terminal devices where spin dependence is uniaxial. Capacitive shunting localizes quantum circuit states in the wells and exponentially suppresses their splitting. For weak spin-orbit strength, the system has a four-dimensional spin-chirality low-energy subspace which can be universally controlled with electric fields only.

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arXiv2026

Strain engineering of Andreev spin qubits in Germanium

Planar germanium heterostructures are promising hosts for hybrid quantum devices due to their compatibility with superconductors, low material disorder, and relaxed fabrication constraints. Also, the potentially low density of nuclear spins and strong spin-orbit interaction make germanium attractive for coherent spin physics. However, recent microwave spectroscopy experiments were unable to resolve a spin-splitting of bound states in germanium Josephson junctions, the prerequisite for defining and controlling Andreev spin qubits. Here, we argue that compressive strain is the key mechanism suppressing spin splitting in current devices. Furthermore, we propose unstrained and tensile-strained heterostructures, fully compatible with state-of-the-art growth technology, that significantly enhance the relevant spin-orbit effect. By numerically simulating ballistic Josephson junctions, we predict spin splittings comfortably in the GHz range, more than 2 orders of magnitude larger than compressively strained cases, and all-electric quantum gates in a hundred nanoseconds. Our results establish strain engineering as a key design principle for realizing Andreev spin qubits in germanium-based devices.

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arXiv2024

Fermionic quantum computation with Cooper pair splitters

We propose a practical implementation of a universal quantum computer that uses local fermionic modes (LFM) rather than qubits. The device layout consists of quantum dots tunnel coupled by a hybrid superconducting island and a tunable capacitive coupling between the dots. We show that coherent control of Cooper pair splitting, elastic cotunneling, and Coulomb interactions allows us to implement the universal set of quantum gates defined by Bravyi and Kitaev. Due to the similarity with charge qubits, we expect charge noise to be the main source of decoherence. For this reason, we also consider an alternative design where the quantum dots have tunable coupling to the superconductor. In this second device design, we show that there is a sweetspot for which the local fermionic modes are charge neutral, making the device insensitive to charge noise effects. Finally, we compare both designs and their experimental limitations and suggest future efforts to overcome them.

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arXiv2023

Bloch-Lorentz magnetoresistance oscillations in delafossites

Recent measurements of the out-of-plane magnetoresistance of delafossites (PdCoO$_2$ and PtCoO$_2$) observed oscillations closely resembling the Aharonov-Bohm effect. Here, we show that the magnetoresistance oscillations are explained by the Bloch-like oscillations of the out-of-plane electron trajectories. We develop a semiclassical theory of these Bloch-Lorentz oscillations and show that they are a consequence of the ballistic motion and quasi-2D dispersion of delafossites. Our model identifies the sample wall scattering to be the most likely factor limiting the visibility of these Bloch-Lorentz oscillations in existing experiments.

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arXiv2023

Aharonov-Bohm magnetism in open Fermi surfaces

Orbital diamagnetism requires closed orbits according to the Liftshiftz-Kosevich theory. Therefore, one might expect that open Fermi surfaces do not have a diamagnetic response. Contrary to this expectation, we show that open orbits in finite systems do contribute a magnetic response which oscillates between diamagnetism and paramagnetism. The oscillations are similar to the Aharonov-Bohm effect, because the oscillation phase is set by the number of flux quanta through the area defined by the width of the sample and the distance between adjacent atomic layers. The magnetic response originates from the closed trajectories formed by counter-propagating open orbits coupled via specular boundary reflections. The phenomenon acts as a probe of the phase coherence of open electron trajectories.

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arXiv2022

Impact of disorder on the distribution of gate coupling strengths in a spin qubit device

A scalable spin-based quantum processor requires a suitable semiconductor heterostructure and a gate design, with multiple alternatives being investigated. Characterizing such devices experimentally is a demanding task, with the full development cycle taking at least months. While numerical simulations are more time-efficient, their predictive power is limited due to unavoidable disorder and device-to-device variation. We develop a spin-qubit device simulation for determining the distribution of the coupling strengths between the electrostatic gate potentials and the effective device Hamiltonian in presence of disorder. By comparing our simulation results with the experimental data, we demonstrate that the coupling of the gate voltages to the dot chemical potential and the interdot tunnel coupling match up to disorder-induced variance. To demonstrate the flexibility of our approach, we also analyze an alternative non-planar geometry inspired by FinFET devices.

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arXiv2019

The influence of lattice termination on the edge states of the quantum spin Hall insulator monolayer $1T'$-WTe$_2$

We study the influence of sample termination on the electronic properties of the novel quantum spin Hall insulator monolayer $1T'$-WTe$_2$. For this purpose, we construct an accurate, minimal 4-orbital tight-binding model with spin-orbit coupling by employing a combination of density-functional theory calculations, symmetry considerations, and fitting to experimental data. Based on this model, we compute energy bands and 2-terminal conductance spectra for various ribbon geometries with different terminations, with and without magnetic field. Because of the strong electron-hole asymmetry we find that the edge Dirac point is buried in the bulk bands for most edge terminations. In the presence of a magnetic field, an in-gap edge Dirac point leads to exponential suppression of conductance as an edge Zeeman gap opens, whereas the conductance stays at the quantized value when the Dirac point is buried in the bulk bands. Finally, we find that disorder in the edge termination drastically changes this picture: the conductance of a sufficiently rough edge is uniformly suppressed for all energies in the bulk gap regardless of the orientation of the edge.

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arXiv2018

Dissipation-enabled fractional Josephson effect

The anomalous $4π$-periodic ac Josephson effect, a hallmark of topological Josephson junctions, was experimentally observed in a quantum spin Hall insulator. This finding is unexpected due to time-reversal symmetry preventing the backscattering of the helical edge states and therefore suppressing the $4π$-periodic component of the Josephson current. Here we analyze the two-particle inelastic scattering as a possible explanation for this experimental finding. We show that a sufficiently strong inelastic scattering restores the $4π$-periodic component of the current beyond the short Josephson junction regime. Its signature is an observable peak in the power spectrum of the junction at half the Josephson frequency. We propose to use the exponential dependence of the peak width on the applied bias and the magnitude of the dc current as means of verifying that the inelastic scattering is indeed the mechanism responsible for the $4π$-periodic signal.

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arXiv2017

Robustness of Majorana bound states in the short junction limit

We study the effects of strong coupling between a superconductor and a semiconductor nanowire on the creation of the Majorana bound states, when the quasiparticle dwell time in the normal part of the nanowire is much shorter than the inverse superconducting gap. This "short junction" limit is relevant for the recent experiments using the epitaxially grown aluminum characterized by a transparent interface with the semiconductor and a small superconducting gap. We find that the small superconducting gap does not have a strong detrimental effect on the Majorana properties. Specifically, both the critical magnetic field required for creating a topological phase and the size of the Majorana bound states are independent of the superconducting gap. The critical magnetic field scales with the wire cross section, while the relative importance of the orbital and Zeeman effects of the magnetic field is controlled by the material parameters only: $g$-factor, effective electron mass, and the semiconductor-superconductor interface transparency.

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arXiv2017

Tailoring supercurrent confinement in graphene bilayer weak links

The Josephson effect is one of the most studied macroscopic quantum phenomena in condensed matter physics and has been an essential part of the quantum technologies development over the last decades. It is already used in many applications such as magnetometry, metrology, quantum computing, detectors or electronic refrigeration. However, developing devices in which the induced superconductivity can be monitored, both spatially and in its magnitude, remains a serious challenge. In this work, we have used local gates to control confinement, amplitude and density profile of the supercurrent induced in one-dimensional nanoscale constrictions, defined in bilayer graphene-hexagonal boron nitride van der Waals heterostructures. The combination of resistance gate maps, out-of-equilibrium transport, magnetic interferometry measurements, analytical and numerical modelling enables us to explore highly tunable superconducting weak links. Our study opens the path way to design more complex superconducting circuits based on this principle such as electronic interferometers or transition-edge sensors.

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arXiv2015

An attractive critical point from weak antilocalization on fractals

We report a new attractive critical point occurring in the Anderson localization scaling flow of symplectic models on fractals. The scaling theory of Anderson localization predicts that in disordered symplectic two-dimensional systems weak antilocalization effects lead to a metal-insulator transition. This transition is characterized by a repulsive critical point above which the system becomes metallic. Fractals possess a non-integer scaling of conductance in the classical limit which can be continuously tuned by changing the fractal structure. We demonstrate that in disordered symplectic Hamiltonians defined on fractals with classical conductance scaling $g \sim L^{-\varepsilon}$, for $0 < \varepsilon < β_\mathrm{max} \approx 0.15$, the metallic phase is replaced by a critical phase with a scale invariant conductance dependent on the fractal dimensionality. Our results show that disordered fractals allow an explicit construction and verification of the $\varepsilon$ expansion.

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arXiv2015

Spatially resolved edge currents and guided-wave electronic states in graphene

A far-reaching goal of graphene research is exploiting the unique properties of carriers to realize extreme nonclassical electronic transport. Of particular interest is harnessing wavelike carriers to guide and direct them on submicron scales, similar to light in optical fibers. Such modes, while long anticipated, have never been demonstrated experimentally. In order to explore this behavior, we employ superconducting interferometry in a graphene Josephson junction to reconstruct the real-space supercurrent density using Fourier methods. Our measurements reveal charge flow guided along crystal boundaries close to charge neutrality. We interpret the observed edge currents in terms of guided-wave states, confined to the edge by band bending and transmitted as plane waves. As a direct analog of refraction-based confinement of light in optical fibers, such nonclassical states afford new means for information transduction and processing at the nanoscale.

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