Majorana States Research Articles

Propagation, dissipation, and breakdown in quantum anomalous Hall edge states probed by microwave edge plasmons

The quantum anomalous Hall (QAH) effect, with its single chiral, topologically protected edge state, offers a platform for flying Majorana states as well as nonreciprocal microwave devices. While recent research showed the nonreciprocity of edge plasmons in Cr-doped (BixSb1−x)2Te3, the understanding of their dissipation remains incomplete. Our study explores edge plasmon dissipation in V-doped (BixSb1−x)2Te3 films, analyzing microwave transmission across various conditions. We identify interactions with charge puddles as a primary source, providing insights critical for developing improved QAH-based technologies. Published by the American Physical Society 2024

Authentic Majorana versus singlet Dirac neutrino contributions to μ+μ+→ℓ+ℓ+ (ℓ=e,τ) transitions

We revisited the computation of the cross section for the μ+μ+→ℓ+ℓ+ (ℓ+=τ+,e+) transitions in the presence of new heavy Majorana neutrinos. We focus on scenarios where the masses of the new states are around some few TeV, the so-called low-scale seesaw models. Our analysis is set in a simple model with only two new heavy Majorana neutrinos considering the current limits on the heavy-light mixings. Our results illustrate the difference between the genuine effects of two nondegenerate heavy Majorana states and the degenerate case where they form a Dirac singlet field. Published by the American Physical Society 2024

Robust poor man’s Majorana zero modes using Yu-Shiba-Rusinov states

Kitaev chains in quantum dot-superconductor arrays are a promising platform for the realization of topological superconductivity. As recently demonstrated, even a two-site chain can host Majorana zero modes known as “poor man’s Majorana”. Harnessing the potential of these states for quantum information processing, however, requires increasing their robustness to external perturbations. Here, we form a two-site Kitaev chain using Yu-Shiba-Rusinov states in proximitized quantum dots. By deterministically tuning the hybridization between the quantum dots and the superconductor, we observe poor man’s Majorana states with a gap larger than 70 μeV. The sensitivity to charge fluctuations is also greatly reduced compared to Kitaev chains made with non-proximitized dots. The systematic control and improved energy scales of poor man’s Majorana states realized with Yu-Shiba-Rusinov states will benefit the realization of longer Kitaev chains, parity qubits, and the demonstration of non-Abelian physics.

Influence of disorder on antidot vortex Majorana states in three-dimensional topological insulators

Influence of disorder on antidot vortex Majorana states in three-dimensional topological insulators

Phase jumps in Josephson junctions with time-dependent spin–orbit coupling

Planar Josephson junctions (JJs), based on common superconductors and III–V semiconductors, are sought for Majorana states and fault-tolerant quantum computing. However, with gate-tunable spin–orbit coupling (SOC), we show that the range of potential applications of such JJs becomes much broader. The time-dependent SOC offers unexplored mechanisms for switching JJs, accompanied by the 2π-phase jumps and the voltage pulses corresponding to the single-flux-quantum transitions, key to high-speed and low-power superconducting electronics. In a constant applied magnetic field, with Rashba and Dresselhaus SOC, anharmonic current-phase relations, calculated microscopically in these JJs, yield a nonreciprocal transport and superconducting diode effect. Together with the time-dependent SOC, this allows us to identify a switching mechanism at no applied current bias, which supports fractional-flux-quantum superconducting circuits and neuromorphic computing.

Topological Phase Diagram of an Interacting Kitaev Chain: Mean Field versus DMRG Study

In this work, we study the topological phase transitions of a Kitaev chain generalized by the addition of nearest-neighbor Coulomb interaction. We show the presence of a robust topological phase as a function of the interaction strength and of the on-site energy with associated non-zero energy Majorana states localized at the chain edges. We provide an effective mean-field model that allows for the self-consistent computation of the mean value of the local particle number operator, and we also perform Density Matrix Renormalization Group numerical simulations based on a tensor network approach. We find that the two methods show a good agreement in reporting the phase transition between trivial and topological superconductivity. Temperature robustness within a physically relevant threshold has also been demonstrated. These findings shed light on an entire class of topological interacting one-dimensional systems in which the effects of residual Coulomb interactions play a relevant role.

Nonlocality of Majorana bound states revealed by electron waiting times in a topological Andreev interferometer

The analysis of waiting times of electron transfers has recently become experimentally accessible owing to advances in noninvasive probes working in the short-time regime. We study electron waiting times in a topological Andreev interferometer: a superconducting loop with controllable phase difference connected to a quantum spin Hall edge, where the edge state helicity enables the transfer of electrons and holes into separate leads, with transmission controlled by the loop's phase difference ϕ. This setup features gapless Majorana bound states at ϕ=π. The waiting times for electron transfers across the junction are sensitive to the presence of the gapless states, but are uncorrelated for all ϕ. By contrast, at ϕ=π the waiting times of Andreev-scattered holes show a strong correlation and the crossed (hole-electron) distributions feature a unique behavior. Both effects exclusively result from the nonlocal properties of Majorana bound states. Consequently, electron waiting times and their correlations could circumvent some of the challenges for detecting topological superconductivity and Majorana states beyond conductance signatures. Published by the American Physical Society 2024

Design of a Majorana trijunction

Braiding of Majorana states demonstrates their non-Abelian exchange statistics. One implementation of braiding requires control of the pairwise couplings between all Majorana states in a trijunction device. To have adiabaticity, a trijunction device requires the desired pair coupling to be sufficiently large and the undesired couplings to vanish. In this work, we design and simulate a trijunction device in a two-dimensional electron gas with a focus on the normal region that connects three Majorana states. We use an optimisation approach to find the operational regime of the device in a multi-dimensional voltage space. Using the optimization results, we simulate a braiding experiment by adiabatically coupling different pairs of Majorana states without closing the topological gap. We then evaluate the feasibility of braiding in a trijunction device for different shapes and disorder strengths.

Multipoles from Majorana constellations

Majorana stars, the 2S spin coherent states that are orthogonal to a spin-S state, offer an elegant method to visualize quantum states, disclosing their intrinsic symmetries. These states are naturally described by the corresponding multipoles. These quantities can be experimentally determined and allow for an SU(2)-invariant analysis. We investigate the relationship between Majorana constellations and state multipoles, thus providing insights into the underlying symmetries of the system. We illustrate our approach with some relevant and informative examples. Published by the American Physical Society 2024

Phase-tunable multiple Andreev reflections in a quantum spin Hall strip

A quantum spin Hall strip where different edges are contacted by s-wave superconductors with a phase difference φ supports Majorana bound states protected by time-reversal symmetry. We study signatures of these states in a four-terminal setup where two Josephson junctions are built on opposite edges of the strip and the phase difference between superconductors can be controlled by an external flux. Applying a voltage bias across the quantum spin Hall strip results in a sequence of conductance peaks from multiple Andreev reflections (MARs). We find that this so-called subharmonic gap structure is very sensitive to the phase difference and displays a phase-controlled even–odd effect, where all odd spikes disappear when the Majorana states are formed for . Moreover, the remaining even spikes split when the superconductors forming the junction have different gap size. We explain these features by showing that any midgap bound states enhance the transmission of the even order MARs, while the reduced density of states at the gap edges suppresses the odd order ones.

Discrete global symmetries and dynamics of emergent fermions

Global symmetries that define the number of low-energy degrees of freedom have profound consequences on universal properties near topological quantum critical points and in other gapless or nearly gapless states of emergent fermions. We take a ${Z}_{2}$ global symmetry (such as time-reversal) as an example to study its effect on thermodynamic and transport properties. Although the thermal entropy density of ${Z}_{2}$ symmetric systems is simply twice that of their counterparts without any global symmetries or the ${Z}_{1}$ class, the temperature dependence of thermal conductivity $\ensuremath{\kappa}$ is distinctly and drastically different for different symmetries. For systems with dynamic exponent $z=1$, in the ${Z}_{2}$ symmetric class, we have $\ensuremath{\kappa}\ensuremath{\propto}{T}^{\ensuremath{-}(d\ensuremath{-}1)}$ in the quantum critical regime near weakly interacting fixed points, while for systems with no global symmetries (i.e., the ${Z}_{1}$ class), we have $\ensuremath{\kappa}\ensuremath{\propto}{T}^{\ensuremath{-}(d+3)}$, with $d$ being the spatial dimension. Only near strong-coupling fixed points, both cases with or without ${Z}_{2}$ global symmetries follow the same scaling function, $\ensuremath{\kappa}\ensuremath{\propto}{T}^{d\ensuremath{-}1}$. These distinct scalings of thermal conductivity can also appear in gapless surface Majorana states.

Zero modes of fermions trapped by giant vortices

Zero-energy solutions of the Dirac equation for the fermions bound to giant vortices of large winding number n are studied in the abelian Higgs and Chern-Simons Higgs models. The case of Jackiw-Rossi theory of the Majorana states in topological superconductors is discussed in detail. By expanding in inverse powers of n we find an analytic result for asymptotically all n solutions required by the index theorem. In the abelian Higgs model the zero modes fill the vortex core and reveal a universal structure independent of fine details of the gauge and scalar field interactions which, in particular, determines the general properties of the large-n superconducting cosmic strings. On the contrary, for the Chern-Simons Higgs vortices the zero modes are localized on the core boundary and the explicit solution is obtained for the supersymmetric couplings in a self-dual background.

Hallmarks of orbital-flavored Majorana states in Josephson junctions based on oxide nanochannels

We investigate the topological properties of a Josephson junction obtained by constraining a two-dimensional electron gas at oxide interface to form a quasi-1D conductor. We reveal an anomalous critical current behaviour with a magnetic field applied perpendicular to the Rashba spin-orbit one. We relate the observed critical current enhancement at small magnetic fields with a non-trivial topology, accompanied by Majorana bound states (MBSs) pinned at the edges of the superconducting leads. Signatures of MBSs also include a sawtooth profile in the current-phase relation. Our findings allow to recognize fingerprints of topological superconductivity in non-centrosymmetric materials and confined systems with Rashba spin-orbit interaction, and to explain recent experimental observations for which a microscopic description is still lacking.

Microwave detection of gliding Majorana zero modes in nanowires

We study a topological superconducting nanowire that hosts gliding Majorana zero modes in the presence of a microwave cavity field. We show that the cavity decay rate depends on both the parity encoded by the Majorana zero modes and their motion, in the absence of any direct overlap of their wave functions. That is because the extended bulk states that overlap with both Majorana states facilitate their momentum-resolved microwave spectroscopy, with the gliding acting to modify the interference pattern via a momentum boost. Moreover, we demonstrate that these nonlocal effects are robust against moderate disorder in the chemical potential, and we confirm the numerical calculations with an analytical low-energy model. Our approach offers an alternative to tunneling spectroscopy to probe nonlocal features associated with the Majorana zero modes in nanowires.

Evolution of 4π-Periodic Supercurrent in the Presence of an In-Plane Magnetic Field.

In the presence of a 4π-periodic contribution to the current phase relation, for example in topological Josephson junctions, odd Shapiro steps are expected to be missing. While missing odd Shapiro steps have been observed in several material systems and interpreted in the context of topological superconductivity, they have also been observed in topologically trivial junctions. Here, we study the evolution of such trivial missing odd Shapiro steps in Al-InAs junctions in the presence of an in-plane magnetic field Bθ. We find that the odd steps reappear at a crossover Bθ value, exhibiting an in-plane field angle anisotropy that depends on spin-orbit coupling effects. We interpret this behavior by theoretically analyzing the Andreev bound state spectrum and the transitions induced by the nonadiabatic dynamics of the junction and attribute the observed anisotropy to mode-to-mode coupling. Our results highlight the complex phenomenology of missing Shapiro steps and the underlying current phase relations in planar Josephson junctions designed to realize Majorana states.

Realization of a minimal Kitaev chain in coupled quantum dots.

Majorana bound states constitute one of the simplest examples of emergent non-Abelian excitations in condensed matter physics. A toy model proposed by Kitaev shows that such states can arise at the ends of a spinless p-wave superconducting chain1. Practical proposals for its realization2,3 require coupling neighbouring quantum dots (QDs) in a chain through both electron tunnelling and crossed Andreev reflection4. Although both processes have been observed in semiconducting nanowires and carbon nanotubes5-8, crossed-Andreev interaction was neither easily tunable nor strong enough to induce coherent hybridization of dot states. Here we demonstrate the simultaneous presence of all necessary ingredients for an artificial Kitaev chain: two spin-polarized QDs in an InSb nanowire strongly coupled by both elastic co-tunnelling (ECT) and crossed Andreev reflection (CAR). We fine-tune this system to a sweet spot where a pair of poor man's Majorana states is predicted to appear. At this sweet spot, the transport characteristics satisfy the theoretical predictions for such a system, including pairwise correlation, zero charge and stability against local perturbations. Although the simple system presented here can be scaled to simulate a full Kitaev chain with an emergent topological order, it can also be used imminently to explore relevant physics related to non-Abelian anyons.

Majorana Bound States in the Presence of Half-Smeared Potential

The Majorana bound state can be realized in one dimensional chain, in form of two well localized and separated states at both ends of the chain. In this paper, we discuss the case when the potential is smeared at one end of the system. In our investigation, we assume the smearing in form of a quadratic function of position. We show that the smearing potential lead to the emergence of extra in-gap states, and effectively decrease the local gap (around the smeared potential). The Majorana states are still preserved in the system, however, their localization depend on the smearing. Moreover, the symmetric localization of the Majorana states from both side of the system is no longer preserved in the presence of the smearing potential.

Zero-energy states in the Kitaev finite and semi-infinite model

The Kitaev chain models a p -wave superconductor and hosts two Majorana bound states at the ends of the chain in the topological phase, for example if μ = 0 , Δ = t , where μ , Δ and t are chemical potential, superconducting pairing potential, and the next-nearest neighbor hopping amplitude, respectively. We consider finite and semi-infinite chains with close parameters μ = 0 and Δ = t + ɛ where ɛ is small, near the point Δ − t = 0 . Using the Dyson equation and the Green’s function for the infinite Kitaev chain, we analytically study the conditions for the appearance of zero-energy states, as well as their wave functions. We proove that in the finite chain such states exist only if Δ > t and the number of sites is odd. Zero-energy states disappear in the finite chain in the presence of an impurity potential, which indicates their instability. But in the semi-infinite chain, for Δ > t there is a single Majorana state and it is robust against an impurity.Thus the bulk-boundary correspondence may be violated for the Kitaev chain near the singular point. • We study the Kitaev chain with the pair potential close to the hopping amplitude. • Zero-energy states exist only for odd sites number and a large enough pair potential. • For a large pair potential there is Majorana state in the semi-infinite Kitaev chain. • The bulk-boundary correspondence is not always satisfied for the Kitaev chain.

Thermoelectric transport properties of single quantum dot systems in the presence of Majorana states

We present theoretical results for the thermoelectric transport properties in a single quantum dot system side coupled to a Majorana nanowire. The system’s electrical conductivity G , and the fundamental thermoelectric parameters such as the Seebeck coefficient S and thermal conductivity κ are numerically estimated based on a linear response approximation. Our results prove that the Majorana states in the side nanowire play an important role in the system’s thermoelectric response. In particular, a proper choice of the quantum dot — Majorana nanowire tunneling rate ξ and of the Majorana states overlap amplitude ɛ M can provide the appropriate physical environment for the experimental detection of Majorana states via thermoelectrical experimental measurements. • We considered the effects of Majorana states on the thermoelectric response of a single quantum dot system. • We present numerical results for the system electrical conductivity, Seebeck coefficient, thermal conductivity, and figure of merit. • The system thermoelectric response is strongly dependent on the quantum dot — Majorana nanowire tunneling rate ξ and of the Majorana states overlap amplitude ɛ M .

О дираковской массе хаббардовских фермионов в сильно коррелированном топологическом сверхпроводнике высокого порядка

Majorana corner modes have a number of advantages over the classical Majorana states in terms of performing topologically protected quantum computations. However, the problem of the influence of Coulomb repulsion on higher-order phases, which inevitably arises when trying to implement such systems in practice, has been poorly studied. In this article, we analyze the features of a topological invariant describing the nontrivial phase with the corner modes for a two-dimensional two-orbital model of a hybrid structure in the regime of extremely strong electron correlations. For this purpose, approximate wave functions of the edge states with a linear dispersion law and the associated Dirac masses, which arise when superconducting pairing in the system is taken into account, are obtained.