Splitting of a Cooper pair by a pair of Majorana bound states

Nonlocal correlations transmitted between quantum dots via short topological superconductor

We study the quasiparticle states and nonlocal correlations of a hybrid structure, comprising two quantum dots interconnected through a short-length topological superconducting nanowire hosting overlaping Majorana modes. We show that the hybridization between different components of this setup gives rise to the emergence of molecular states, which are responsible for nonlocal correlations. We inspect the resulting energy structure, focusing on the inter-dependence between the quasiparticles of individual quantum dots. We predict the existence of nonlocal effects, which could be accessed and probed by crossed Andreev reflection spectroscopy. Our study would be relevant to a recent experimental realization of the minimal Kitaev model [T. Dvir et al., Nature 614, 445 (2023) ], by considering its hybrid structure with side-attached quantum dots.

Dislocation Majorana bound states in iron-based superconductors

We show that lattice dislocations of topological iron-based superconductors such as FeTe1-xSex will intrinsically trap non-Abelian Majorana quasiparticles, in the absence of any external magnetic field. Our theory is motivated by the recent experimental observations of normal-state weak topology and surface magnetism that coexist with superconductivity in FeTe1-xSex, the combination of which naturally achieves an emergent second-order topological superconductivity in a two-dimensional subsystem spanned by screw or edge dislocations. This exemplifies a new embedded higher-order topological phase in class D, where Majorana zero modes appear around the "corners" of a low-dimensional embedded subsystem, instead of those of the full crystal. A nested domain wall theory is developed to understand the origin of these defect Majorana zero modes. When the surface magnetism is absent, we further find that s± pairing symmetry itself is capable of inducing a different type of class-DIII embedded higher-order topology with defect-bound Majorana Kramers pairs. We also provide detailed discussions on the real-world material candidates for our proposals, including FeTe1-xSex, LiFeAs, β-PdBi2, and heterostructures of bismuth, etc. Our work establishes lattice defects as a new venue to achieve high-temperature topological quantum information processing.

Why Shot Noise Does Not Generally Detect Pairing in Mesoscopic Superconducting Tunnel Junctions

The shot noise in tunneling experiments reflects the Poissonian nature of the tunneling process. The shot-noise power is proportional to both the magnitude of the current and the effective charge of the carrier. Shot-noise spectroscopy thus enables us, in principle, to determine the effective charge q of the charge carriers of that tunnel. This can be used to detect electron pairing in superconductors: In the normal state, the noise corresponds to single electron tunneling (q=1e), while in the paired state, the noise corresponds to q=2e. Here, we use a newly developed amplifier to reveal that in typical mesoscopic superconducting junctions, the shot noise does not reflect the signatures of pairing and instead stays at a level corresponding to q=1e. We show that transparency can control the shot noise, and this q=1e is due to the large number of tunneling channels with each having very low transparency. Our results indicate that in typical mesoscopic superconducting junctions, one should expect q=1e noise and lead to design guidelines for junctions that allow the detection of electron pairing.

Full counting statistics, fluctuation relations, and linear response properties in a one-dimensional Kitaev chain

We analytically calculate the cumulant generating function of energy and particle transport in an open one-dimensional Kitaev chain at finite temperature by utilizing the Keldysh technique. The joint distribution of particle and energy currents satisfies different fluctuation relations in different regions of the parameter space as a result of U(1) symmetry breaking and energy conservation. Furthermore, we investigate the linear response behavior of the Kitaev chain within the framework of three-terminal systems, deriving the expressions for the Seebeck coefficient and thermal conductance. Notably, we observe a pronounced peak in the thermal conductance near the phase transition point, in agreement with previous predictions. Additionally, we prove that the peak value saturates at half of the thermal conductance quantum for finite-length chains at the zero temperature limit.

Quantum Spin Hall Effect in Two-Monolayer-Thick InN/InGaN Coupled Multiple Quantum Wells

In this study, we present a theoretical study of the quantum spin Hall effect in InN/InGaN coupled multiple quantum wells with the individual well widths equal to two atomic monolayers. We consider triple and quadruple quantum wells in which the In content in the interwell barriers is greater than or equal to the In content in the external barriers. To calculate the electronic subbands in these nanostructures, we use the eight-band k∙p Hamiltonian, assuming that the effective spin-orbit interaction in InN is negative, which represents the worst-case scenario for achieving a two-dimensional topological insulator. For triple quantum wells, we find that when the In contents of the external and interwell barriers are the same and the widths of the internal barriers are equal to two monolayers, a topological insulator with a bulk energy gap of 0.25 meV can appear. Increasing the In content in the interwell barriers leads to a significant increase in the bulk energy gap of the topological insulator, reaching about 0.8 meV. In these structures, the topological insulator can be achieved when the In content in the external barriers is about 0.64, causing relatively low strain in quantum wells and making the epitaxial growth of these structures within the range of current technology. Using the effective 2D Hamiltonian, we study the edge states in strip structures containing topological triple quantum wells. We demonstrate that the opening of the gap in the spectrum of the edge states caused by decreasing the width of the strip has an oscillatory character regardless of whether the pseudospin-mixing elements of the effective Hamiltonian are omitted or taken into account. The strength of the finite size effect in these structures is several times smaller than that in HgTe/HgCdTe and InAs/GaSb/AlSb topological insulators. Therefore, its influence on the quantum spin Hall effect is negligible in strips with a width larger than 150 nm, unless the temperature at which electron transport is measured is less than 1 mK. In the case of quadruple quantum wells, we find the topological insulator phase only when the In content in the interwell barriers is larger than in the external barriers. We show that in these structures, a topological insulator with a bulk energy gap of 0.038 meV can be achieved when the In content in the external barriers is about 0.75. Since this value of the bulk energy gap is very small, quadruple quantum wells are less useful for realizing a measurable quantum spin Hall system, but they are still attractive for achieving a topological phase transition and a nonlocal topological semimetal phase.

Quantized Spin Pumping in Topological Ferromagnetic-Superconducting Nanowires

Semiconducting nanowires with strong spin-orbit coupling in the presence of induced superconductivity and ferromagnetism can support Majorana zero modes. We study the pumping due to the precession of the magnetization in single-subband nanowires and show that spin pumping is robustly quantized when the hybrid nanowire is in the topologically nontrivial phase, whereas charge pumping is not quantized. Moreover, there exists one-to-one correspondence between the quantized conductance, entropy change and spin pumping in long topologically nontrivial nanowires but these observables are uncorrelated in the case of accidental zero-energy Andreev bound states in the trivial phase. Thus, we conclude that observation of correlated and quantized peaks in the conductance, entropy change and spin pumping would provide strong evidence of Majorana zero modes, and we elaborate how topological Majorana zero modes can be distinguished from quasi-Majorana modes potentially created by a smooth tunnel barrier at the lead-nanowire interface. Finally, we discuss peculiar interference effects affecting the spin pumping in short nanowires at very low energies.

Statistical Majorana Bound State Spectroscopy

Tunnel spectroscopy data for the detection of Majorana bound states (MBS) is often criticized for its proneness to misinterpretation of genuine MBS with low-lying Andreev bound states. Here, we suggest a protocol removing this ambiguity by extending single shot measurements to sequences performed at varying system parameters. We demonstrate how such sampling, which we argue requires only moderate effort for current experimental platforms, resolves the statistics of Andreev side lobes, thus providing compelling evidence for the presence or absence of a Majorana center peak.

Readout of Parafermionic States by Transport Measurements

Recent experiments have demonstrated the possibility of inducing superconducting pairing into counterpropagating fractional quantum Hall edge modes. This paves the way for the realization of localized parafermionic modes, non-Abelian anyons that share fractional charges in a nonlocal way. We show that, for a pair of isolated parafermions, this joint degree of freedom can be read by conductance measurements across standard metallic electrodes. We propose two complementary setups. We investigate first the transport through a grounded superconductor hosting two interacting parafermions. In the low-energy limit, its conductance peaks reveal their shared fractional charge yielding a three-state telegraph noise for weak quasiparticle poisoning. We then examine the two-terminal electron conductance of a blockaded fractional topological superconductor, which displays a characteristic e/3 periodicity of its zero-bias peaks in the deep topological regime, thus signaling the presence of parafermionic modes.

On-demand quantum spin Hall insulators controlled by two-dimensional ferroelectricity

We propose a new class of quantum materials, type-II two-dimensional ferroelectric topological insulators (2DFETIs), which allow non-volatility and an on-off switch of quantum spin Hall states. A general strategy is developed to realize type-II 2DFETIs using only topologically trivial 2D ferroelectrics. The built-in electric field arising from the out-of-plane polarization across the bilayer heterostrucuture of 2D ferroelectrics enables robust control of the band gap size and band inversion strength, which can be utilized to manipulate the topological phase transitions on-demand. Using first-principles calculations with hybrid density functionals, we demonstrate that a series of bilayer heterostructures are type-II 2DFETIs characterized with a direct coupling between the band topology and polarization state. We propose a few 2DFETI-based quantum electronics, including domain-wall quantum circuits and topological memristors.

Electrically Controlled Crossed Andreev Reflection in Two-Dimensional Antiferromagnets

We report generic and tunable crossed Andreev reflection (CAR) in a superconductor sandwiched between two antiferromagnetic layers. We consider recent examples of two-dimensional magnets with hexagonal lattices, where gate voltages control the carrier type and density, and predict a robust signature of perfect CAR in the nonlocal differential conductance with one electron-doped and one hole-doped antiferromagnetic lead. The magnetic field-free and spin-degenerate CAR signal is electrically controlled and visible over a large voltage range, showing promise for solid-state quantum entanglement applications.

Interference effect on the Andreev reflections induced by Majorana bound states

We investigate the effect of quantum interference on the Andreev reflections (ARs) induced by Majorana bound states (MBSs), by considering their additional coupling via a quantum-dot molecule. It is found that due to the direct and indirect couplings of MBSs, a quantum ring is constructed in this system. Consequently, the interference effect makes important contribution to the ARs, especially in the presence of the local magnetic flux. All the results are manifested as the tight dependence of the differential conductance and Fano factors on the magnetic flux phase factor, dot-MBS couplings, and the dot level, respectively. Moreover, at the zero-bias limit, the magnitudes of the Fano factors and their relation can be efficiently altered by the interference properties. We believe that quantum interference is important for manipulating the Andreev reflection behaviors of the MBSs.

Full counting statistics of the particle currents through a Kitaev chain and the exchange fluctuation theorem

Exchange fluctuation theorems (XFTs) describe a fundamental symmetry relation for particle and energy exchange between several systems. Here we study the XFTs of a Kitaev chain connected to two reservoirs at the same temperature but different bias. By varying the parameters in the Kitaev chain model, we calculate analytically the full counting statistics of the transport current and formulate the corresponding XFTs for multiple current components. We also demonstrate the XFTs with numerical results. We find that due to the presence of the U(1) symmetry breaking terms in the Hamiltonian of the Kitaev chain, various forms of the XFTs emerge, and they can be interpreted in terms of various well-known transport processes.

Spin-Orbit-Parity-Coupled Superconductivity in Topological Monolayer WTe_{2}

Recent experiments reported gate-induced superconductivity in the monolayer 1T^{'}-WTe_{2} which is a two-dimensional topological insulator in its normal state. The in-plane upper critical field B_{c2} is found to exceed the conventional Pauli paramagnetic limit B_{p} by one to three times. The enhancement cannot be explained by conventional spin-orbit coupling which vanishes due to inversion symmetry. In this Letter, we unveil some distinctive superconducting properties of centrosymmetric 1T^{'}-WTe_{2} which arise from the coupling of spin, momentum and band parity degrees of freedom. As a result of this spin-orbit-parity coupling (SOPC): (i) there is a first-order superconductor-metal transition at B_{c2} that is much higher than the Pauli paramagnetic limit B_{p}, (ii) spin-susceptibility is anisotropic with respect to in-plane directions and can result in possible anisotropic B_{c2}, and (iii) the B_{c2} exhibits a strong gate dependence as the spin-orbit-parity coupling is significant only near the topological band crossing points. The importance of SOPC on the topologically nontrivial inter-orbital pairing phase is also discussed. Our theory generally applies to centrosymmetric materials with topological band inversions.

Double-frequency Aharonov-Bohm effect and non-Abelian braiding properties of Jackiw-Rebbi zero-mode

Ever since its first proposal in 1976, Jackiw-Rebbi zero-mode has been drawing extensive attention for its charming properties including charge fractionalization, topologically protected zero-energy and possible non-Abelian statistics. We investigate these properties through the Jackiw-Rebbi zero-modes in quantum spin Hall insulators. Though charge fractionalization is not manifested, Jackiw-Rebbi zero-mode's zero-energy nature leads to a double-frequency Aharonov-Bohm effect, implying that it can be viewed as a special case of Majorana zero-mode without particle-hole symmetry. Such relation is strengthened for Jackiw-Rebbi zero-modes also exhibiting non-Abelian properties in the absence of superconductivity. Furthermore, in the condition that the degeneracy of Jackiw-Rebbi zero-modes is lifted, we demonstrate a novel non-Abelian braiding with continuously tunable fusion rule, which is a generalization of Majorana zero-modes' braiding properties.

Transconductance as a probe of nonlocality of Majorana fermions

Each end of a Kitaev chain in topological phase hosts a Majorana fermion. Zero bias conductance peak is an evidence of Majorana fermion when the two Majorana fermions are decoupled. These two Majorana fermions are separated in space and this nonlocal aspect can be probed when the two are coupled. Crossed Andreev reflection is the evidence of the nonlocality of Majorana fermions. Nonlocality of Majorana fermions has been proposed to be probed by noise measurements since simple conductance measurements cannot probe it due to the almost cancellation of currents from electron tunneling and crossed Andreev reflection. Kitaev ladders on the other hand host subgap Andreev states which can be used to control the relative currents due to crossed Andreev reflection and electron tunneling. We propose to employ Kitaev ladder in series with Kitaev chain and show that the transconductance in this setup can be used as a probe of nonlocality of Majorana fermions by enhancing crossed Andreev reflection over electron tunneling.

Enhancement of crossed Andreev reflection in a Kitaev ladder connected to normal metal leads

We study nonlocal transport in a two-leg Kitaev ladder connected to two normal metals. The coupling between the two legs of the ladder when the legs are maintained at a (large) superconducting phase difference, results in the creation of subgap Andreev states. These states in turn are responsible for the enhancement of crossed Andreev reflection (CAR). We find that tuning the different parameters of the system suitably leads to enhancement of CAR signalled by transconductance acquiring the most negative value possible. Furthermore, subgap states cause oscillations of the transconductance as a function of various system parameters such as chemical potential and ladder length, which are seen to be a consequence of Fabry-Pérot resonance.

Perfect Crossed Andreev Reflection in Dirac Hybrid Junctions in the Quantum Hall Regime

Perfect crossed Andreev reflection (CAR) is striking for high-efficiency Cooper pair splitting, which bears promising applications in quantum communication. Recent experimental advances have disclosed the way to explore CAR in Dirac fermion systems under ultrastrong magnetic fields. We develop a scattering approach to study quantum-Hall-superconductor-quantum-Hall junctions formed by a two-dimensional time-reversal symmetric Dirac semimetal. We propose two different setups of the hybrid junction in the quantum limit, where only zeroth Landau levels are involved in transport to exploit perfect CAR. In both setups, the CAR probability can reach unity without applying bias voltage and is controllable by the magnetic field strength, the junction width, the length, and the doping of the superconductor. CAR dominates the nonlocal transport and is directly measurable by the differential conductances. We also identify a quantized spin injection per CAR event in one of the two setups. Our proposal is experimentally feasible and will be helpful for exploring high-efficiency Cooper pair splitting and spin injection in Dirac materials.

Giant Shot Noise from Majorana Zero Modes in Topological Trijunctions

The clear-cut experimental identification of Majorana bound states in transport measurements still poses experimental challenges. We here show that the zero-energy Majorana state formed at a junction of three topological superconductor wires is directly responsible for giant shot noise amplitudes, in particular at low voltages and for small contact transparency. The only intrinsic noise limitation comes from the current-induced dephasing rate due to multiple Andreev reflection processes.

Measuring the nonlocality of different types of Majorana bound states in a topological superconducting wire

According to the degree of topological protection, Majorana bound states (MBSs) can be divided into three types: ideal zero-energy MBSs (IZMs), finite-energy MBSs (FEMs) and zero-energy MBSs at parity crossing points (PZMs). Herein, we investigate the nonlocality of these three types of MBSs by comparing the conductance spectra of a normal lead-topological superconducting wire-normal lead (NSN) junction and an NS junction. We find that for the FEM-related tunnelling process, the decrease in the nonlocal processes is trivially accompanied by an increase in the local processes, whereas for the IZM-related tunnelling process, the left and right tunnelling processes are completely independent. Remarkably, PZMs induce a nonlocal electron-blocking effect in which incoming electrons from the left lead cannot participate in local Andreev reflection unless the right lead is present, even though no nonlocal tunnelling processes occur in the right lead of an NSN junction. We show that this PZM-mediated nonlocal electron-blocking effect is due to the nonlocal coupling of the left lead to the more distant PZM and that the phase difference between the two end PZMs is [Formula: see text]. Our findings provide an experimentally accessible method for characterizing MBSs by probing their different nonlocal signatures.

Spin dependence of crossed Andreev reflection and electron tunneling induced by Majorana fermions

We investigate spin dependence of the nonlocal transport induced by Majorana fermions in a one-dimensional ferromagnet-ferromagnetic-insulator-superconductor-ferromagnetic-insulator-ferromagnet junction on the edge of a two-dimensional topological insulator. The results show that coupled Majorana fermions lead to the nonlocal transport processes including electron tunneling and crossed Andreev reflection, which can be tuned by adjusting the spin polarizations of the Majorana fermions. By manipulating the bands in the two ferromagnets, the nonlocal transport can be selected as either pure electron tunneling or pure crossed Andreev reflection, the transmission probability of which could be 100%. Furthermore, the pure electron tunneling and the pure crossed Andreev reflection are well controlled by the spin directions of the electron states in the two ferromagnets.

High-Temperature Majorana Corner States

Majorana bound states often occur at the end of a 1D topological superconductor. Validated by a new bulk invariant and an intuitive edge argument, we show the emergence of one Majorana Kramers pair at each corner of a square-shaped 2D topological insulator proximitized by an s_{±}-wave (e.g., Fe-based) superconductor. We obtain a phase diagram that addresses the relaxation of crystal symmetry and edge orientation. We propose two experimental realizations in candidate materials. Our scheme offers a higher-order and higher-temperature route for exploring non-Abelian quasiparticles.

Interplay between correlations and Majorana mode in proximitized quantum dot

We study the low energy spectrum and transport properties of a correlated quantum dot coupled between normal and superconducting reservoirs and additionally hybridized with a topological superconducting nanowire, hosting the Majorana end-modes. In this setup the Majorana quasiparticle leaking into the quantum dot can be confronted simultaneously with the on-dot pairing and correlations. We study this interplay, focusing on the quantum phase transition from the spinless (BCS-type) to the spinful (singly occupied) configuration, where the subgap Kondo effect may arise. Using the selfconsistent perturbative treatment for correlations and the unbiased numerical renormalization group calculations we find that the Majorana mode has either constructive or destructive effect on the low-energy transport behavior of the quantum dot, depending on its spin. This spin-selective influence could be verified by means of the polarized STM spectroscopy.

Manifestation of topological transitions in a multi-terminal Josephson junction

We study nonequilibrium (NE) transport in four-terminal (three-terminal) topological superconductor (SC)-quantum dot (QD) topological superconductor junctions, where the QD is connected via tunneling barriers to the two TS leads and two (one) normal leads (N), respectively. For the four-terminal junction, we find that when increasing the Zeeman field from 0 to a critical value, the supercurrent profile evolves from a typical s-wave pattern to a pure p-wave pattern. In addition, by analyzing the zero-phase difference supercurrent as a function of voltage [Formula: see text] applied to the normal leads and the Zeeman field h applied to the SC, the low-momentum gap [Formula: see text] can be inferred by utilizing the fact that the emergence of a tunneling-induced current should be satisfied under the condition [Formula: see text]. For the three-terminal junction, the NE supercurrent can reveal the quasi-Andreev bound state by exploiting the Andreev reflection process-induced current occurring between the N and SC. Our findings provide an arguably easier route for manifesting the topological phase transition by observing the gap collapse and then reopening as the Zeeman field increases through multi-terminal NE transport.

Thermoelectric Efficiency of a Topological Nano-Junction

We studied the non-equilibrium current, transport coefficients and thermoelectric performance of a nano-junction, composed by a quantum dot connected to a normal superconductor and a topological superconductor leads, respectively. We considered a one-dimensional topological superconductor, which hosts two Majorana fermion states at its edges. Our results show that the electric and thermal currents across the junction are highly mediated by multiple Andreev reflections between the quantum dot and the leads, thus leading to a strong nonlinear dependence of the current on the applied bias voltage. Remarkably, we find that our system reaches a sharp maximum of its thermoelectric efficiency at a finite bias, when an external magnetic field is imposed upon the junction. We propose that this feature can be used for accurate temperature sensing at the nanoscale.

Quantum spin Hall insulator with a large bandgap, Dirac fermions, and bilayer graphene analog

The search for room temperature quantum spin Hall insulators (QSHIs) based on widely available materials and a controlled manufacturing process is one of the major challenges of today's topological physics. We propose a new class of semiconductor systems based on multilayer broken-gap quantum wells, in which the QSHI gap reaches 60 meV and remains insensitive to temperature. Depending on their layer thicknesses and geometry, these novel structures also host a graphene-like phase and a bilayer graphene analog. Our theoretical results significantly extend the application potential of topological materials based on III-V semiconductors.

Revealing the interference effect of Majorana fermions in a topological Josephson junction

We study theoretically the local density of states (DOS) in a topological Josephson junction. We show that the well-known 4π Josephson effect originates from the interference effect between two Majorana fermions (MFs) that are localized at the Josephson junction. In addition, the DOS for electrons (holes) shows the 4π interference information along each parity conserved energy spectrum. The DOS displays a 2π period oscillation when two trivial states interfere with each other. This means that the DOS information may be used to distinguish the MFs from trivial localized states. We suggest that the interference effect and the DOS can be detected by using two STM leads or two normal leads. A single side lead can only detect the Andreev reflection tunneling process in the junction, which cannot reveal information about the interference effect in general. However, using two side leads, we can reveal information about the interference effect of the MFs as well as the DOS by combining Andreev reflection with the electron transmission process.

Creation of Spin-Triplet Cooper Pairs in the Absence of Magnetic Ordering

In superconducting spintronics, it is essential to generate spin-triplet Cooper pairs on demand. Up to now, proposals to do so concentrate on hybrid structures in which a superconductor (SC) is combined with a magnetically ordered material (or an external magnetic field). We, instead, identify a novel way to create and isolate spin-triplet Cooper pairs in the absence of any magnetic ordering. This achievement is only possible because we drive a system with strong spin-orbit interaction-the Dirac surface states of a strong topological insulator (TI)-out of equilibrium. In particular, we consider a bipolar TI-SC-TI junction, where the electrochemical potentials in the outer leads differ in their overall sign. As a result, we find that nonlocal singlet pairing across the junction is completely suppressed for any excitation energy. Hence, this junction acts as a perfect spin-triplet filter across the SC, generating equal-spin Cooper pairs via crossed Andreev reflection.

Topological Majorana Two-Channel Kondo Effect

A one-dimensional time-reversal-invariant topological superconductor hosts a Majorana Kramers pair at each end, where time-reversal symmetry acts as a supersymmetry that flips local fermion parity. We examine the transport anomaly of such a superconductor, floating and tunnel-coupled to normal leads at its two ends. We demonstrate the realization of a topologically protected, channel-symmetric, two-channel Kondo effect without fine-tuning. Whereas the nonlocal teleportation vanishes, a lead present at one end telecontrols the universal transport through the other end.

Creating single Majorana type topological zero mode in superfluids of cold fermionic atoms

We explore the topological phase, which involves Majorana type topological zero mode fermions (MTZFs) at the edge, using d–wave superfluid with Rashba spin-orbit coupling (SOC) interactions. The self-Hermitian of this MTZF(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\gamma }}}^{{\boldsymbol{\dagger }}}{\boldsymbol{(}}{\bf{k}}{\boldsymbol{)}}{\boldsymbol{=}}{\boldsymbol{\gamma }}{\boldsymbol{(}}{\bf{k}}{\boldsymbol{)}}$$\end{document}γ†(k)=γ(k)) is similar to that of the Majorana fermions (MFs) (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\gamma }}}^{{\boldsymbol{\dagger }}}={\boldsymbol{\gamma }}$$\end{document}γ†=γ). We show that, to realize a single MTZF at each edge in superfluid with d–wave pairing in a Majorana type Kramers Doublet (MTKD) state, it is important to lift both the spin and the Dirac Cones degeneracies. These non-Abelian anyons obey the non-Abelian statistics which may be useful to realize topological quantum computation. We suggest that the topological feature could be tested experimentally in superfluids of cold fermionic atoms with laser field induced spin orbit interactions. These studies give a new possible way to investigate the MTZFs in a two-dimensional (2D) system as compared to MFs in the one-dimensional (1D) nano-wire and 2D system, and enrich the theoretical research on finding non-Abelian anyons in topological system.

Odd-frequency superconductivity induced in topological insulators with and without hexagonal warping

We study the effect of the Fermi surface anisotropy on the odd-frequency spin-triplet pairing component of the induced pair potential. We consider a superconductor/ ferromagnetic insulator (S/FI) hybrid structure formed on the 3D topological insulator (TI) surface. In this case three ingredients ensure the possibility of the odd-frequency pairing: (1) the topological surface states, (2) the induced pair potential, and (3) the magnetic moment of a nearby ferromagnetic insulator. We take into account the strong anisotropy of the Dirac point in topological insulators when the chemical potential lies well above the Dirac cone and its constant energy contour has a snowflake shape. Within this model, we propose that the S/FI boundary should be properly aligned with respect to the snowflake constant energy contour to have an odd-frequency symmetry of the corresponding pairing component and to insure the Majorana bound state at the S/FI boundary. For arbitrary orientation of the boundary, the Majorana bound state is absent. This provides a selection rule to the realization of Majorana modes in S/FI hybrid structures, formed on the topological insulator surface.

Topological Quantum Phase Transition and Local Topological Order in a Strongly Interacting Light-Matter System

An attempt is made to understand the topological quantum phase transition, emergence of relativistic modes and local topological order of light in a strongly interacting light-matter system. We study this system, in a one dimensional array of nonlinear cavities. Topological quantum phase transition occurs with massless excitation only for the finite detuning process. We present a few results based on the exact analytical calculations along with the physical explanations. We observe the emergence of massive Majorana fermion mode at the topological state, massless Majorana-Weyl fermion mode during the topological quantum phase transition and Dirac fermion mode for the non-topological state. Finally, we study the quantized Berry phase (topological order) and its connection to the topological number (winding number).

Direct Cavity Detection of Majorana Pairs

No experiment could directly test the particle-antiparticle duality of Majorana fermions, so far. However, this property represents a necessary ingredient towards the realization of topological quantum computing schemes. Here, we show how to complete this task by using microwave techniques. The direct coupling between a pair of overlapping Majorana bound states and the electric field from a microwave cavity is extremely difficult to detect due to the self-adjoint character of Majorana fermions which forbids direct energy exchanges with the cavity. We show theoretically how this problem can be circumvented by using photoassisted tunneling to fermionic reservoirs. The absence of a direct microwave transition inside the Majorana pair in spite of the light-Majorana coupling would represent a smoking gun for the Majorana self-adjoint character.

Two-Dimensional Platform for Networks of Majorana Bound States

We model theoretically a two-dimensional electron gas (2DEG) covered by a superconductor and demonstrate that topological superconducting channels are formed when stripes of the superconducting layer are removed. As a consequence, Majorana bound states (MBSs) are created at the ends of the stripes. We calculate the topological invariant and energy gap of a single stripe, using realistic values for an InAs 2DEG proximitized by an epitaxial Al layer. We show that the topological gap is enhanced when the structure is made asymmetric. This can be achieved either by imposing a phase difference (by driving a supercurrent or using a magnetic-flux loop) over the strip or by replacing one superconductor by a metallic gate. Both strategies also enable control over the MBS splitting, thereby facilitating braiding and readout schemes based on controlled fusion of MBSs. Finally, we outline how a network of Majorana stripes can be designed.

Spin-sensitive interference due to Majorana state on the interface between normal and superconducting leads

We investigate the subgap spectrum and transport properties of the quantum dot on the interface between the metallic and superconducting leads and additionally side-coupled to the edge of the topological superconducting (TS) chain, hosting the Majorana quasiparticle. Due to the chiral nature of the Majorana states only one spin component of the quantum dot electrons (say [Formula: see text]) is directly affected, however the proximity induced on-dot pairing transmits its influence on the opposite spin as well. We investigate the unique interferometric patterns driven by the Majorana quasiparticle that are different for each spin component. We also address the spin-sensitive interplay with the Kondo effect manifested at the same zero-energy and we come to the conclusion that quantum interferometry can unambiguously identify the Majorana quasiparticle.

Quantum simulations and many-body physics with light

In this review we discuss the works in the area of quantum simulation and many-body physics with light, from the early proposals on equilibrium models to the more recent works in driven dissipative platforms. We start by describing the founding works on Jaynes-Cummings-Hubbard model and the corresponding photon-blockade induced Mott transitions and continue by discussing the proposals to simulate effective spin models and fractional quantum Hall states in coupled resonator arrays (CRAs). We also analyse the recent efforts to study out-of-equilibrium many-body effects using driven CRAs, including the predictions for photon fermionisation and crystallisation in driven rings of CRAs as well as other dynamical and transient phenomena. We try to summarise some of the relatively recent results predicting exotic phases such as super-solidity and Majorana like modes and then shift our attention to developments involving 1D nonlinear slow light setups. There the simulation of strongly correlated phases characterising Tonks-Girardeau gases, Luttinger liquids, and interacting relativistic fermionic models is described. We review the major theory results and also briefly outline recent developments in ongoing experimental efforts involving different platforms in circuit QED, photonic crystals and nanophotonic fibres interfaced with cold atoms.

Detection of Majorana Kramers Pairs Using a Quantum Point Contact

We propose a setup that integrates a quantum point contact (QPC) and a Josephson junction on a quantum spin Hall sample, experimentally realizable in InAs/GaSb quantum wells. The confinement due to both the QPC and the superconductor results in a Kramers pair of Majorana zero-energy bound states when the superconducting phases in the two arms differ by an odd multiple of π across the Josephson junction. We investigate the detection of these Majorana pairs with the integrated QPC, and find a robust switching from normal to Andreev scattering across the edges due to the presence of Majorana Kramers pairs. Such a switching of the current represents a qualitative signature where multiterminal differential conductances oscillate with alternating signs when the external magnetic field is tuned. We show that this qualitative signature is also present in current cross-correlations. Thus, the change of the backscattering current nature affects both conductance and shot noise, the measurement of which offers a significant advantage over quantitative signatures such as conductance quantization in realistic measurements.

Spontaneous Formation of a Superconductor-Topological Insulator-Normal Metal Layered Heterostructure

2D materials with heterolayered structures beyond graphene are explored. A theoretically predicted superconductor-topological insulator-normal metal heterolayered structure is realized experimentally. The generated hybrid structure HfTe3 /HfTe5 /Hf has potential applications in both quantum-spin Hall effect-based and Majorana-based devices.

Fingerprints of Majorana Bound States in Aharonov-Bohm Geometry

We study a ring geometry, coupled to two normal metallic leads, which has a Majorana bound state (MBS) embedded in one of its arms and is threaded by Aharonov-Bohm (AB) flux ϕ. We show that by varying the AB flux, the two leads go through resonance in an anticorrelated fashion while the resonance conductance is quantized to 2e^{2}/h. We further show that such anticorrelation is completely absent when the MBS is replaced by an Andreev bound state (ABS). Hence this anti-correlation in conductance when studied as a function of ϕ provides a unique signature of the MBS which cannot be faked by an ABS. We contrast the phase sensitivity of the MBS and ABS in terms of tunneling conductances. We argue that the relative phase between the tunneling amplitude of the electrons and holes from either lead to the level (MBS or ABS), which is constrained to 0,π for the MBS and unconstrained for the ABS, is responsible for this interesting contrast in the AB effect between the MBS and ABS.

Magnetic Field Tuning and Quantum Interference in a Cooper Pair Splitter

Cooper pair splitting (CPS) is a process in which the electrons of the naturally occurring spin-singlet pairs in a superconductor are spatially separated using two quantum dots. Here, we investigate the evolution of the conductance correlations in an InAs CPS device in the presence of an external magnetic field. In our experiments the gate dependence of the signal that depends on both quantum dots continuously evolves from a slightly asymmetric Lorentzian to a strongly asymmetric Fano-type resonance with increasing field. These experiments can be understood in a simple three-site model, which shows that the nonlocal CPS leads to symmetric line shapes, while the local transport processes can exhibit an asymmetric shape due to quantum interference. These findings demonstrate that the electrons from a Cooper pair splitter can propagate coherently after their emission from the superconductor and how a magnetic field can be used to optimize the performance of a CPS device. In addition, the model calculations suggest that the estimate of the CPS efficiency in the experiments is a lower bound for the actual efficiency.

Catalyst-free vapour-solid technique for deposition of Bi2Te3 and Bi2Se3 nanowires/nanobelts with topological insulator properties

We present a simple two-stage vapour-solid synthesis method for the growth of bismuth chalcogenide (Bi2Te3, Bi2Se3) topological insulator nanowires/nanobelts by using Bi2Se3 or Bi2Te3 powders as source materials. During the first stage of the synthesis process nanoplateteles, serving as "catalysts" for further nanowire/nanobelt growth, are formed. At a second stage of the synthesis, the introduction of a N2 flow at 35 Torr pressure in the chamber induces the formation of free standing nanowires/nanobelts. The synthesised nanostructures demonstrate a layered single-crystalline structure and Bi : Se and Bi : Te ratios 40 : 60 at% for both Bi2Se3 and Bi2Te3 nanowires/nanobelts. The presence of Shubnikov de Haas oscillations in the longitudinal magneto-resistance of the nanowires/nanobelts and their specific angular dependence confirms the existence of 2D topological surface states in the synthesised nanostructures.

Probing Majorana bound states via counting statistics of a single electron transistor

We propose an approach for probing Majorana bound states (MBSs) in a nanowire via counting statistics of a nearby charge detector in the form of a single-electron transistor (SET). We consider the impacts on the counting statistics by both the local coupling between the detector and an adjacent MBS at one end of a nanowire and the nonlocal coupling to the MBS at the other end. We show that the Fano factor and the skewness of the SET current are minimized for a symmetric SET configuration in the absence of the MBSs or when coupled to a fermionic state. However, the minimum points of operation are shifted appreciably in the presence of the MBSs to asymmetric SET configurations with a higher tunnel rate at the drain than at the source. This feature persists even when varying the nonlocal coupling and the pairing energy between the two MBSs. We expect that these MBS-induced shifts can be measured experimentally with available technologies and can serve as important signatures of the MBSs.

Detection of Majorana fermions by Fano resonance in hybrid nanostructures

The realization and detection of Majorana fermions in condensed matter systems are of considerable importance and interest. We propose a scheme to detect the Majorana fermions by Fano resonance in hybrid nanostructures made of semiconductor quantum dots and quantum wire in proximity to superconductor. Through detailed theoretical studies of the transport properties of our hybrid nanostructures based on the non-equilibrium Green's function technique and the equation of motion approach, it is found that the Fano resonance in the current response due to the interference among different transmission paths may give clear signature of the existence of Majorana modes. Moreover, we have found a peculiar relationship between the Fano factor q and the Majorana bound state coupling strength/the length of nanowire, which can be used for a design of an electronic nanoruler. Our method of detection of Majorana fermions based on Fano resonance is related to the global conductance profile, thus is robust to perturbations.

Signatures of majorana zero modes in spin-resolved current correlations

We consider a normal lead coupled to a Majorana bound state. We show that the spin-resolved current correlations exhibit unique features which distinguish Majorana bound states from other low-energy resonances. In particular, the spin-up and spin-down currents from a Majorana bound state are anticorrelated at low bias voltages, and become uncorrelated at higher voltages. This behavior is independent of the exact form of coupling to the lead, and of the direction of the spin polarization. In contrast, an ordinary low-energy Andreev bound state gives rise to a positive correlation between the spin-up and spin-down currents, and this spin-resolved current-current correlation approaches a nonzero constant at high bias voltages. We discuss experimental setups in which this effect can be measured.

Correlated spin currents generated by resonant-crossed Andreev reflections in topological superconductors

Topological superconductors, which support Majorana fermion excitations, have been the subject of intense studies due to their novel transport properties and their potential applications in fault-tolerant quantum computations. Here we propose a new type of topological superconductors that can be used as a novel source of correlated spin currents. We show that inducing superconductivity on a AIII class topological insulator wire, which respects a chiral symmetry and supports protected fermionic end states, will result in a topological superconductor. This topological superconductor supports two topological phases with one or two Majorana fermion end states, respectively. In the phase with two Majorana fermions, the superconductor can split Cooper pairs efficiently into electrons in two spatially separated leads due to Majorana-induced resonant-crossed Andreev reflections. The resulting currents in the leads are correlated and spin-polarized. Importantly, the proposed topological superconductors can be realized using quantum anomalous Hall insulators in proximity to superconductors.

Materials that exhibit topologically protected electronic structures are expected to enable the development of more efficient spintronic devices. He et al. suggest that combining a quantum anomalous Hall insulator with a superconductor could be used to generate correlated spin currents.

Long-range Cooper pair splitter with high entanglement production rate

Cooper pairs in the superconductor are a natural source of spin entanglement. The existing proposals of the Cooper pair splitter can only realize a low efficiency of entanglement production, and its size is constrained by the superconducting coherence length. Here we show that a long-range Cooper pair splitter can be implemented in a normal metal-superconductor-normal metal (NSN) junction by driving a supercurrent in the S. The supercurrent results in a band gap modification of the S, which significantly enhances the crossed Andreev reflection (CAR) of the NSN junction and simultaneously quenches its elastic cotunneling. Therefore, a high entanglement production rate close to its saturation value can be achieved by the inverse CAR. Interestingly, in addition to the conventional entangled electron states between opposite energy levels, novel entangled states with equal energy can also be induced in our proposal.

Electrical transport through a quantum dot side-coupled to a topological superconductor

We propose to measure the differential conductance G as a function of the bias V for a quantum dot side-coupled to a topological superconductor to detect the existence of the chiral Majorana edge states. It turns out that G for the spinless dot is an oscillatory (but not periodic) function of eV due to the coupling to the chiral Majorana edge states, where -e is the charge carried by the electron. The behaviour of G versus eV is distinguished from that of a multi-level dot in three respects. First of all, due to the coupling to the topological superconductor, the value of G will shift upon adding or removing a vortex in the topological superconductor. Next, for an off-resonance dot, the conductance peak in the present case takes a universal value e(2)/(2h) when the two leads are symmetrically coupled to the dot. Finally, for a symmetric setup and an on-resonance dot, the conductance peak will approach the same universal value e(2)/(2h) at a large bias.

Majorana modes in a topological insulator/s-wave superconductor heterostructure

In a recent experiment, signatures of Majorana fermion (MF) were found in the vortex core threading a heterostructure composed of n layers of topological insulator (TI) deposited on a bulk s-wave superconductor. Here we provide strong theoretical support to the experiment. First, we demonstrate that MF modes appear on both top and bottom layers of TI, and are well separated for n ~ 6. The top MF becomes more extended with increasing n, in agrement with the experiment. Second, we show both analytically and numerically that right at the vortex core the MF mode is always accompanied by another low energy bound state, leading to a zero-bias peak plus a side peak in the local density of states (LDOS) therein. However, a local scalar impurity at the core can wipe out the accompanying side-peak state while leaving the zero-energy MF mode intact. Consequently the LDOS becomes symmetric about the fermi level, and the peak does not branch near the vortex core, in agreement with the experiment. Finally but unfortunately, while the MF is extremely stable against a single local impurity, the stability in terms of the critical impurity strength is reduced drastically for a moderate concentration (e.g., 10%) of impurities.