We propose and investigate a simple one-dimensional model for a single-channel quantum wire hosting electrons that interact repulsively and are subject to a significant spin-orbit interaction. We show that an external Zeeman magnetic field, applied at the right angle to the Rashba spin-orbit axis, drives the wire into a correlated spin-density wave state with gapped spin and gapless charge excitations. By computing the ground-state degeneracies of the model with either (anti-)periodic or open boundary conditions, we conclude that the correlated spin-density state realizes a gapless symmetry-protected topological phase, as the ground state is unique in the ring geometry while it is two-fold degenerate in the wire with open boundaries. Microscopically the two-fold degeneracy is found to be protected by the conservation of the magnetization parity. Open boundaries induce localized zero-energy (midgap) states which are described, at the special Luther-Emery point of the model, by Majorana fermions. We find that spin densities at the open ends of the wire exhibit unusual long-ranged correlations despite the fact that all correlations in the bulk of the wire decay in a power-law or exponential fashion. Our study exposes the crucial importance of the long-ranged string operator needed to implement the correct commutation relations between spin densities at different points in the wire. Along the way we rederive the low-energy theory of Galilean-invariant electron systems in terms of current operators.
I consider a model of two thin superconducting wires interacting through Josephson tunneling and Coulomb interactions. It is shown that there is a parameter range where such a model may have two ground states with different types of quasi-long-range order: one is superconducting and the other is pair density wave. It is further shown that boundaries between these different phases support zero energy Majorana modes and that these modes are robust against disorder.
In this work we investigate Majorana correlations in quantum impurities coupled to a topological superconducting wire. By employing a density matrix renormalization group approach, we have calculated the Majorana correlation functions in the ground state of the system for different positions of the impurities along the wire. We observe that the correlations decreases exponentially with the distance between the impurities and the ends of the wire. Moreover, different electron-electron interactions on the wire and on the impurities were also analyzed, and the results showed a stronger effect as …
Controlling the dynamics of Majorana fermions (MF) subject to time-varying driving fields is of fundamental importance for the practical realization of topological quantum computing. In this work we study how it is possible to dynamically generate and maintain the topological phase in one-dimensional superconducting nanowires after the temporal variation of the Hamiltonian parameters. Remarkably we show that for a sudden quench the system can never relax towards a state exhibiting fully developed MF, independently of the initial and final Hamiltonians. Only for sufficiently slow protocols the …
The signatures of Majorana zero-energy mode leaking into a spin-charge entangled double quantum dot are investigated theoretically in the strong electron correlation regime. The considered setup consists of two capacitively coupled quantum dots attached to external contacts and side-attached to topological superconducting wire hosting Majorana quasiparticles. We show that the presence of Majorana mode gives rise to unique features in the local density of states in the $SU(4)$ Kondo regime. Moreover, it greatly modifies the gate voltage dependence of the linear conductance, leading to fractiona…
One-dimensional lattice with strong spin-orbit interactions (SOI) and Zeeman magnetic field is shown to lead to the formation of a helical charge-density wave (CDW) state near half-filling. Interplay of the magnetic field, SOI constants and the CDW gap seems to support Majorana bound states under appropriate value of the external parameters. Explicit calculation of the quasi-particles' wave functions supports a formation of the localized zero-energy state, bounded to the sample end-points. Symmetry classification of the system is provided. Relative value of the density of states shows a precis…
We focus on inducing topological state from regular, or irregular scattering in (i) p-wave superconducting wires and (ii) Rashba wires proximity coupled to an s-wave superconductor. We find that contrary to common expectations the topological properties of both systems are fundamentally different: In p-wave wires, disorder generally has a detrimental effect on the topological order and the topological state is destroyed beyond a critical disorder strength. In contrast, in Rashba wires, which are relevant for recent experiments, disorder can {\it induce} topological order, reducing the need for…
We explore a scheme for engineering a one-dimensional spinless p-wave superconductor hosting unpaired Majorana zero-energy modes, using an all-electric setup with a spin-orbit coupled quantum wire in proximity to an s-wave superconductor. The required crossing of the Fermi level by a single spin-split energy band is ensured by employing a periodically modulated Rashba interaction, which, assisted by electron-electron interactions and a uniform Dresselhaus interaction, opens a gap at two of the spin-orbit shifted Fermi points. While an implementation in a hybrid superconductor-semiconductor dev…
Among the broad spectrum of systems predicted to exhibit topological superconductivity and Majorana fermions, one-dimensional wires with strong spin-orbit coupling provide one of the most promising experimental candidates. Here we investigate the fate of the topological superconducting phase in such wires when repulsive interactions are present. Using a combination of Density Matrix Renormalization Group, bosonization, and Hartree-Fock techniques, we demonstrate that while interactions degrade the bulk gap -consistent with recent results of Gangadharaiah et al.- they also greatly expand the pa…
We study the interplay between disorder and interaction in one-dimensional topological superconductors which carry localized Majorana zero-energy states. Using Abelian bosonization and the perturbative renormalization group (RG) approach, we obtain the RG-flow and the associated scaling dimensions of the parameters and identify the critical points of the low-energy theory. We predict a quantum phase transition from a topological superconducting phase to a non-topological localized phase, and obtain the phase boundary between these two phases as a function of the electron-electron interaction a…
The transport behavior of a double quantum dot side-attached to a topological superconducting wire hosting Majorana zero-energy modes is studied theoretically in the strong correlation regime. It is shown that Majorana modes can leak to the whole nanostructure, giving rise to a subtle interplay between the two-stage Kondo screening and the half-fermionic nature of Majorana quasiparticles. In particular, the coupling to the topological wire is found to reduce the effective exchange interaction between the two quantum dots in the absence of normal leads. Interestingly, it also results in an enha…
We develop a Gaussian variational approach in replica space to investigate the phase diagram of a one-dimensional interacting disordered topological superconducting wire in the strong coupling regime. This method allows for a non-perturbative treatment in the disorder strength, electron- electron interactions and the superconducting pairing amplitude. We find only two stable phases: a topological superconducting phase, and a glassy, non-topological localized phase, characterized by replica symmetry breaking.
In this work we study interacting spinless fermions on a two-chain ladder with inter-chain pair tunneling while single-particle tunneling is suppressed at low energy. The model embodies a $\mathbb{Z}_2$ symmetry associated with the fermion parity on each chain. We find that when the system is driven to the strong-coupling phase by the pair tunneling, Majorana excitations appear on the boundary. Such Majorana edge states correspond to two-fold degeneracy of ground states distinguished by different fermion parity on each chain, thus representing a generalization of one-dimensional topological su…
We investigate theoretically the features of the Majorana hallmark in the presence of Coulomb repulsion between two quantum dots describing a spinless Aharonov-Bohm-like interferometer, where one of the dots is strongly coupled to a Kitaev wire within the topological phase. Such a system has been originally proposed without Coulomb interaction in J. of Appl. Phys. 116, 173701 (2014). Our findings reveal that for dots in resonance, the ratio between the strength of Coulomb repulsion and the dot-wire coupling changes the width of the Majorana zero-bias peak for both Fano regimes studied, indicat…
Time reversal symmetric topological superconductors in three spatial dimensions carry gapless surface Majorana fermions. They are robust against any time reversal symmetric single-body perturbation weaker than the bulk energy gap. We mimic the massless surface Majorana's by coupled wire models in two spatial dimensions. We introduce explicit many-body interwire interactions that preserve time reversal symmetry and give energy gaps to all low energy degrees of freedom. We show the gapped models generically carry non-trivial topological order and support anyonic excitations.
We study the collective states of interacting non-Abelian anyons that emerge in Kitaev's honeycomb lattice model. Vortex-vortex interactions are shown to lead to the lifting of the topological degeneracy and the energy is discovered to exhibit oscillations that are consistent with Majorana fermions being localized at vortex cores. We show how to construct states corresponding to the fusion channel degrees of freedom and obtain the energy gaps characterizing the stability of the topological low energy spectrum. To study the collective behavior of many vortices, we introduce an effective lattice…
Twisted bilayer graphene (TBG) realizes a highly tunable, strongly interacting system featuring superconductivity and various correlated insulating states. We establish gate-defined wires in TBG with proximity-induced spin-orbit coupling as $(i)$ a tool for revealing the nature of correlated insulators and $(ii)$ a platform for Majorana-based topological qubits. In particular, we show that the band structure of a gate-defined wire immersed in an `inter-valley coherent' correlated insulator inherits electrically detectable fingerprints of symmetry breaking native to the latter. Surrounding the …
Topological superconductors in one spatial dimension exhibiting a single Majorana bound state at each end are distinguished from trivial gapped systems by a Z_2 topological invariant. Originally, this invariant was calculated by Kitaev in terms of the Pfaffian of the Majorana representation of the Hamiltonian: The sign of this Pfaffian divides the set of all gapped quadratic forms of Majorana fermions into two inequivalent classes. In the more familiar Bogoliubov de Gennes mean field description of superconductivity, an emergent particle hole symmetry gives rise to a quantized Zak-Berry phase …
We propose a method to detect a signature of non-abelian statistics in a 1D superconducting wire by tuning the effective coupling between a pair of Majorana particles. Our experiment requires a single wire with two segments in the topological superconducting phase, and a total of 4 Majorana particles. We show that an appropriately timed "pulse" in the coupling between the two middle Majoranas leads to a coherent rotation of the two q-bits associated with the pairs of Majoranas in the two TSC segments, in much the same way that an appropriate-length pulse of a transverse magnetic field can be u…
Majorana zero modes are a promising platform for topologically protected quantum information processing. Their non-Abelian nature, which is key for performing quantum gates, is most prominently exhibited through braiding. While originally formulated for two-dimensional (2d) systems, it has been shown that braiding can also be realized using one-dimensional (1d) wires by forming an essentially two-dimensional network. Here, we show that in driven systems far from equilibrium, one can do away with the second spatial dimension altogether by instead using quasienergy as the second dimension. To re…
We study a one-dimensional (1D) chain of $2N$ Majorana bound states, which interact through a local quartic interaction. This model describes for example the edge physics of a quasi 1D stack of $2N$ Kitaev chains with modified time-reversal symmetry $Tγ_iT^{-1}=γ_i$, which precludes the presence of quadratic coupling. The ground state of our 1D Majorana chain displays a four-fold periodicity in $N$, corresponding to the four distinct topological classes of the stacked Kitaev chains. We analyze the transport properties of the 1D Majorana chain, when probed by local conductors located at its end…
In this study, the problem of strong Coulomb interactions in topological superconducting wire is analyzed by means of the density-matrix-renormalization-group (DMRG) approach. To analyze properties of edge states in the BDI-class structure a quantity called Majorana polarization is used. From its dependence on wire length and an entanglement-spectrum degeneracy topological phase diagrams are obtained. The DMRG calculations for the Shubin-Vonsovsky-type model of the wire show the transformation of phases with Majorana single and double modes (MSMs and MDMs, respectively) under the increase of o…
The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes. We propose a solid-state implementation based on a quantum dot coupled to an array of topological superconducting wires hosting Majorana zero modes. Interactions and disorder intrinsic to the dot mediate the desired random Majorana couplings, while an approximate symmetry suppresses additional unwanted terms. We use random matrix theory and numerics to show that our setup emulates the SYK model (up to corrections that we quantif…
A time-reversal invariant topological superconductivity is suggested to be realized in a quasi-one dimensional structure on a plane, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin-orbit interactions when intra-wire s-wave and inter-wire d-wave pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. We analyze effects of Zeeman magnetic field on Majorana zero-energy states. …
We propose a platform for engineering helical fermions in a hybridized double-quantum-wire setup. When our setup is proximity coupled to an $s$-wave superconductor it can become a class $D$ topological superconductor exhibiting Majorana zero modes. The goal of this proposal is to expand the group of available Hamiltonians to those without strong Rashba spin-orbit interactions which are essential to many other approaches. Furthermore, we show that there exist electron-electron interactions that stabilize fractional excitations which obey $\mathbb{Z}^{\,}_{3}$ parafermionic algebra.
We discuss a network of Kitaev wires coupled to several individually-tunable quantum dots as an extension of the recent experiments on a quantum dot coupled to a nanowire hosting Majorana zero modes [Deng et al. Science 354 1557 (2016) and Deng et al. arXiv:1712.03536 (2017)]. The setup features localized Majorana modes with exact zero energy and we show that they can be manipulated by solely acting on the quantum dots. A braiding process can be obtained by arranging three wires as a trijunction and a charge readout of the quantum dots can be used to reveal the non-Abelian statistics of Majora…
We study the p-wave superconducting wire with a periodically modulated chemical potential and show that the Majorana edge states are robust against the periodic modulation. We find that the critical amplitude of modulated potential, at which the Majorana edge fermions and topological phase disappear, strongly depends on the phase shifts. For some specific values of the phase shift, the critical amplitude tends to infinity. The existence of Majorana edge fermions in the open chain can be characterized by a topological $Z_2$ invariant of the bulk system, which can be applied to determine the pha…
We show that long-ranged superconducting order is not necessary to guarantee the existence of Majorana fermion zero modes at the ends of a quantum wire. We formulate a concrete model which applies, for instance, to a semiconducting quantum wire with strong spin-orbit coupling and Zeeman splitting coupled to a wire with algebraically-decaying superconducting fluctuations. We solve this model by bosonization and show that it supports Majorana fermion zero modes. We argue that a large class of models will also show the same phenomenon. We discuss the implications for experiments on spin-orbit cou…
An array of superconducting islands with semiconducting nanowires in the right regime provides a macroscopic implementation of Kitaev's toy model for Majorana wires. We show that a capacitive coupling between adjacent islands leads to an effective interaction between the Majorana modes. We demonstrate that even though strong repulsive interaction eventually drive the system into a Mott insulating state the competition between the (trivial) band-insulator and the (trivial) Mott insulator leads to an interjacent topological insulating state for arbitrary strong interactions.
We study the decoherence of Majorana modes of a fermion chain, where the fermions interact with their nearest neighbours. We investigate the effect of dissipation and dephasing on the Majorana modes of a fermionic chain. The dissipative and dephasing noises induce the non-parity- and parity-preserving transitions between the eigenstates of the system, respectively. Therefore, these two types of noises lead to the different decoherence mechanisms. In each type of noise, we discuss the low- and high-frequency regimes to describe the different environments. We numerically calculate the dissipatio…
We show that one-dimensional electron systems in proximity of a superconductor that support Majorana edge states are extremely susceptible to electron-electron interactions. Strong interactions generically destroy the induced superconducting gap that stabilizes the Majorana edge states. For weak interactions, the renormalization of the gap is nonuniversal and allows for a regime, in which the Majorana edge states persist. We present strategies how this regime can be reached.
We show that a strongly interacting chain of Majorana zero modes exhibits a supersymmetric quantum critical point corresponding to the $c={7\over 10}$ tricritical Ising model, which separates a critical phase in the Ising universality class from a supersymmetric massive phase. We verify our predictions with numerical density-matrix-renormalization-group computations and determine the consequences for tunnelling experiments.
We construct a supersymmetric model of interacting Majorana fermions on the kagome lattice. In the infinite-coupling limit, the model exhibits an extensively degenerate ground state manifold separated in two topological sectors, in addition to two parity supersectors. An exact solution for thin-torus geometries allows us to analytically construct the entire zero-energy ground state manifold. Upon inclusion of hopping terms with energy scale $g$, the supersymmetry is spontaneously broken with the ground state energy density scaling as $g^4$. We also briefly discuss the non-interacting limit of …
It is shown that the presence of the Majorana fermion edge states along the perimeter of a topological superconductor can be probed using an interacting quantum dot coupled to three terminals: two spin-polarized (ferromagnetic) leads and one lead supporting the Majorana edge states. The hybridization with the Majorana states induces a particular type of the Kondo effect with non-Fermi-liquid properties which can be detected by performing linear conductance measurements between the source and drain normal leads: the temperature dependence of the conductance is characteristically different from …
Majorana fermions were proposed to occur at edges and interfaces of gapped one-dimensional systems where phases with different topological character meet due to an interplay of spin-orbit coupling, proximity-induced superconductivity and external magnetic fields. Here we investigate the effect of strong particle interactions, and show that the helical liquid offers a mechanism that protects the very existence of Majorana edge states: whereas moderate interactions close the proximity gap which supports the edge states, in helical liquids the gap re-opens due to two-particle processes. However, …
Majorana fermions are a fascinating medium for discovering new phases of matter. However, the standard analytical tools are very limited in probing the non-perturbative aspects of interacting Majoranas in more than one dimensions. Here, we employ the holographic correspondence to determine the specific heat of a two-dimensional interacting gapless Majorana system. To perform our analysis we first describe the interactions in terms of a pseudo-scalar torsion field. We then allow fluctuations in the background curvature thus identifying our model with a $(2+1)$-dimensional Anti-de Sitter (AdS) g…
We consider a three-dimensional topological insulator (TI) wire with a non-uniform chemical potential induced by gating across the cross-section. This inhomogeneity in chemical potential lifts the degeneracy between two one-dimensional surface state subbands. A magnetic field applied along the wire, due to orbital effects, breaks time-reversal symmetry and lifts the Kramers degeneracy at zero-momentum. If placed in proximity to an $s$-wave superconductor, the system can be brought into a topological phase at relatively weak magnetic fields. Majorana bound states (MBSs), localized at the ends o…
We investigate the robustness of Majorana edge modes under disorder and interactions. We exploit a recently found mapping of the interacting Kitaev chain in the symmetric region ($μ= 0$, $t = Δ$) to free fermions. Extending the exact solution to the disordered case allows us to calculate analytically the topological phase boundary for all interaction and disorder strengths, which has been thought to be only accessible numerically. We discover a regime in which moderate disorder in the interaction matrix elements enhances topological order well into the strongly interacting regime $U > t$. We a…
In this paper, we formulate and quantitatively examine the effect of dissipation on topological systems. We use a specific model of Kitaev quantum wire with an onsite Ohmic dissipation, and perform a numerically exact quantum Monte Carlo simulation to investigate this interacting open quantum system with a strong system-bath (SB) coupling beyond the scope of Born-Markovian approximation. We concentrate on the effect of dissipation on the topological features of the system (e.g. the Majorana edge mode) at zero temperature, and find that even though the topological phase is robust against weak S…
We study Kitaev model in one-dimension with open boundary condition by using exact analytic methods for non-interacting system at zero chemical potential as well as in the symmetric case of Δ = t, and by using density-matrix-renormalizationgroup method for interacting system with nearest neighbor repulsion interaction. We suggest and examine an edge correlation function of Majorana fermions to characterize the long range order in the topological superconducting states and study the phase diagram of the interating Kitaev chain.
We study the effects of Coulomb repulsive interactions on a Majorana Benalcazar-Bernevig-Hughes (MBBH) model. The MBBH model belongs to the class of second--order topological superconductors ($HOTSC_2$), featuring robust Majorana corner modes. We consider an interacting strip of four chains of length $L$ and perform a DMRG numerical analysis based on a tensor--network approach. Study of the nonlocal fermionic correlations and of the degenerate entanglement spectrum indicates that the topological phases are robust in the presence of interactions, even in the strongly interacting regime.
Using a combination of the mean-field Bogoliubov deGennes (BdG) approach and the Density Matrix Renormalization Group (DMRG) method, we discover first order topological transitions between topological superconducting and trivial insulating phases in a sawtooth lattice of inter-site attractive fermions. Topological characterization of different phases is achieved in terms of winding numbers, Majorana edge modes and entanglement spectra. By studying the effect of disorder on the first order topological phase transitions, we establish the disorder-induced topological phase coexistence as a mechan…
We study the effects of Majorana modes and interactions between electrons on transport in a one-dimensional system with a junction of three p-wave superconductors (SCs) which are connected to normal metal leads. For sufficiently long SCs, there are zero energy Majorana modes at the junctions between the SCs and the leads,and, depending on the signs of the p-wave pairings in the three SCs, there can also be one or three Majorana modes at the junction of the three SCs. We show that the various sub-gap conductances have peaks occurring at the energies of all these modes; we therefore get a rich p…
Zero energy Majorana fermion states (Majoranas) can arise at the ends of a semiconducting wire in proximity with a superconductor. A first generation of experiments has detected a zero bias conductance peak in these systems that strongly suggests these Majoranas do exist; however, a definitive demonstration of the long-ranged entanglement that is crucial for potential applications in quantum computing has yet to be carried out. This work discusses two possible measurement schemes to detect this long-ranged entanglement in a wire system with two coupled pairs of Majoranas, by varying the coupli…
Recently, there has been substantial progress in methods of identifying local integrals of motion in interacting integrable models or in systems with many-body localization. We show that one of these approaches can be utilized for constructing local, conserved, Majorana fermions in systems with an arbitrary many-body interaction. As a test case, we first investigate a non-interacting Kitaev model and demonstrate that this approach perfectly reproduces the standard results. Then, we discuss how the many-body interactions influence the spatial structure and the lifetime of the Majorana modes. Fi…
Mechanical strain can generate a pseudo-magnetic field, and hence Landau levels (LL), for low energy excitations of quantum matter in two dimensions. We study the collective state of the fractionalised Majorana fermions arising from residual generic spin interactions in the central LL, where the projected Hamiltonian reflects the spin symmetries in intricate ways: emergent U(1) and particle-hole symmetries forbid any bilinear couplings, leading to an intrinsically strongly interacting system; also, they allow the definition of a filling fraction, which is fixed at 1/2. We argue that the result…
Ken Wilson developed the Numerical Renormalization Group technique which greatly enhanced our understanding of the Kondo effect and other quantum impurity problems. Wilson's NRG also inspired Philippe Nozieres to propose the idea of a large "Kondo screening cloud". While much theoretical evidence has accumulated for this idea it has remained somewhat controversial and has not yet been confirmed experimentally. Recently a new possibility for observing an analogous crossover length scale has emerged, involving a Majorana fermion localized at the interface between a topological superconductor qua…
We numerically explore $\mathbb Z_2$-symmetric random interacting Ising-Majorana chains at high energy. A very rich phase diagram emerges with two topologically distinct many-body localization (MBL) regimes separated by a much broader thermal phase than previously found. This is a striking consequence of the avalanche theory. We further find MBL spin-glass order always associated to a many-body spectral pairing, presumably signaling a strong zero mode operator which opens fascinating perspectives for MBL-protected topological qubits.
We consider a helical spin liquid system which shows majorana fermion modes at the edge. The interaction between the quasiparticles in this system induces phase transition, Majorana-Ising transition. We comply the density matrix renormalization group method to study this phase transition for the entire regime of the parameter space. We observe the presence of topological quantum phase transition for repulsive interaction, however this phase is more stable for the attractive interaction. The length scale dependent study shows many new and important results and we show explicitly that the major …
We devise a number-conserving scheme for the realization of Majorana Zero Modes in an interacting fermionic ladder coupled by Aharonov-Bohm cages. The latter provide an efficient mechanism to cancel single-particle hopping by destructive interference. The crucial parity symmetry in each wire is thus encoded in the geometry of the setup, in particular, its translation invariance. A generic nearest-neighbor interaction generates the desired correlated hopping of pairs. We exhibit the presence of an extended topological region in parameter space, first in a simplified effective model via bosoniza…
Landau levels (LL) have been predicted to emerge in systems with Dirac nodal points under applied non-uniform strain. We consider 2D, $d_{xy}$ singlet (2D-S) and 3D $p \pm i p$ equal-spin triplet (3D-T) superconductors (SCs). We demonstrate the spinful Majorana nature of the bulk gapless zeroth-LLs. Strain along certain directions can induce two topologically distinct phases in the bulk, with zeroth LLs localized at the the interface. These modes are unstable toward ferromagnetism for 2D-S cases. Emergent real-space Majorana fermions in 3D-T allow for more exotic possibilities.
A fundamental open issue in physics is whether and how the fermion sign problem in quantum Monte Carlo (QMC) simulations can be solved generically. Here, we show that Majorana-time-reversal (MTR) symmetries can provide a unifying principle to solve the fermion sign problem in interacting fermionic models. By systematically classifying Majorana-bilinear operators according to the anti-commuting MTR symmetries they respect, we rigorously proved that there are two and only two fundamental symmetry classes which are sign-problem-free and which we call the "Majorana class" and "Kramers class", resp…
We demonstrate that a thermal metal of Majorana fermions forms in a two-dimensional system of interacting non-Abelian (Ising) anyons in the presence of moderate disorder. This bulk metallic phase arises in the $ν=5/2$ quantum Hall state when disorder pins the anyonic quasiparticles. More generally, it naturally occurs for various proposed systems supporting Majorana fermion zero modes when disorder induces the random pinning of a finite density of vortices. This includes all two-dimensional topological superconductors in so-called symmetry class D. A distinct experimental signature of the ther…
We theoretically explore quench dynamics in a finite-sized topological fermionic p-wave superconducting wire with the goal of demonstrating that topological order can have marked effects on such non-equilibrium dynamics. In the case studied here, topological order is reflected in the presence of two (nearly) isolated Majorana fermionic end bound modes together forming an electronic state that can be occupied or not, leading to two (nearly) degenerate ground states characterized by fermion parity. Our study begins with a characterization of the static properties of the finite-sized wire, includ…
I consider a class of one-dimensional models where Majorana fermions interact with bosonic fields. Contrary to a more familiar situation where bosonic degrees of freedom are phonons and as such form a slow subsystem, I consider fast bosons. Such situation exists when the bosonic modes appear as collective excitations of interacting electrons as, for instance, in superconductors or carbon nanotubes. It is shown that an entire new class of excitations emerge, namely bound states of solitons and Majorana fermions. The latter bound states are not topological and their existence and number depend o…
Interesting phases of quantum matter often arise when the constituent particles -- electrons in solids -- interact strongly. Such strongly interacting systems are however quite rare and occur only in extreme environments of low spatial dimension, low temperatures or intense magnetic fields. Here we introduce a new system in which the fundamental electrons interact only weakly but the low energy effective theory is described by strongly interacting Majorana fermions. The system consists of an Abrikosov vortex lattice in the surface of a strong topological insulator and is accessible experimenta…
