Experimental evidence for topological phases in the magnetoconductance of 2DEG-based hybrid junctions
Kaveh Delfanazari, Llorenc Serra, Pengcheng Ma, Reuben K. Puddy, Teng Yi, Moda Cao, Yilmaz Gul, Ian Farrer, David A. Ritchie, Hannah J. Joyce, Michael J. Kelly, Charles G. Smith
While the application of out-of-plane magnetic fields was, so far, believed to be detrimental for the formation of Majorana phases in artificially engineered hybrid superconducting-semiconducting junctions, several recent theoretical studies have found it indeed useful in establishing such topological phases 1-5. Majorana phases emerge as quantized plateaus in the magnetoconductance of the hybrid junctions based on two-dimensional electron gases (2DEG) under fully out-of-plane magnetic fields. The large transverse Rashba spin-orbit interaction in 2DEG, together with a strong magneto-orbital effect, yield topological phase transitions to nontrivial phases hosting Majorana modes. Such Majorana modes are formed at the ends of 2DEG-based wires with a hybrid superconductor-semiconductor integrity. Here, we report on the experimental observation of such topological phases in Josephson junctions, based on In0.75Ga0.25As 2DEG, by sweeping out-of-plane magnetic fields of as small as 0 < B(mT) < 100 and probing the conductance to highlight the characteristic quantized magnetoconductance plateaus. Our approaches towards (i) creation and detection of topological phases in small out-of-plane magnetic fields, and (ii) integration of an array of topological Josephson junctions on a single chip pave the ways for the development of scalable quantum integrated circuits for their potential applications in fault-tolerant quantum processing and computing.
The magnetoconductance of p-n junctions formed in clean single wall carbon nanotubes is studied in the noninteracting electron approximation and perturbatively in electron-electron interaction, in the geometry where a magnetic field is along the tube axis. For long junctions the low temperature magnetoconductance is anomalously large: the relative change in the conductance becomes of order unity even when the flux through the tube is much smaller than the flux quantum. The magnetoconductance is negative for metallic tubes. For semiconducting and small gap tubes the magnetoconductance is nonmon…
The mechanism of the magnetoconductance oscillations in junctions of a ballistic semiconductor and a superconductor is discussed. The oscillations appear when both the normal and the Andreev reflection occur at the interface. The interplay between the classical cyclotron motion of a quasiparticle and the phase shift caused by the magnetic field is the origin of the conductance oscillations.
We show that the magnetoconductance oscillations of laterally-confined 2D NS junctions are completely suppressed when the superconductor side enters a topological phase. This suppression can be attributed to the modification of the vortex structure of local currents at the junction caused by the topological transition of the superconductor. The two regimes (with and without oscillations) could be seen in a semiconductor 2D junction with a cleaved-edge geometry, one of the junction arms having proximitized superconductivity. We predict similar oscillations and suppression as a function of the R…
We study the zero temperature conductance and magnetoconductance of ballistic \textit{p-n} junctions in Weyl semimetals. Electron transport is mediated by Klein tunneling between \textit{n}- and \textit{p}- regions. The chiral anomaly that is realized in Weyl semimetals plays a crucial role in the magnetoconductance of the junction. With the exception of field orientations where the angle between $\mathbf{B}$ and the junction plane is small, magnetoconductance is positive and linear in $B$ at both weak and strong magnetic fields. In contrast, magnetoconductance in conventional \textit{p-n} jun…
We study Landau levels (LLs) of Weyl semimetal (WSM) with two adjacent Weyl nodes. We consider different orientations $η=\angle(\mathbf{B},\mathbf{k}_0)$ of magnetic field $\mathbf{B}$ with respect to $\mathbf{k}_0$, the vector of Weyl nodes splitting. Magnetic field facilitates the tunneling between the nodes giving rise to a gap in the transverse energy of the zeroth LL. We show how the spectrum is rearranged at different $η$ and how this manifests itself in the change of behavior of differential magnetoconductance $dG(B)/dB$ of a ballistic $p$-$n$ junction. Unlike the single-cone model wher…
We report the first low temperature magnetotransport measurements on electrochemically fabricated atomic scale gold nanojunctions. As $T \to 0$, the junctions exhibit nonperturbatively large zero bias anomalies (ZBAs) in their differential conductance. We consider several explanations and find that the ZBAs are consistent with a reduced local density of states (LDOS) in the disordered metal. We suggest that this is a result of Coulomb interactions in a granular metal with moderate intergrain coupling. Magnetoconductance of atomic scale junctions also differs significantly from that of less geo…
We calculate the Andreev conductance of a superconducting ring interrupted by a flux-biased Josephson junction, searching for electrical signatures of circulating edge states. Two-dimensional pair potentials of spin-singlet d-wave and spin-triplet p-wave symmetry support, respectively, (chiral) Dirac modes and (chiral or helical) Majorana modes. These produce h/e-periodic magnetoconductance oscillations of amplitude \simeq (e^{2}/h)N^{-1/2}, measured via an N-mode point contact at the inner or outer perimeter of the grounded ring. For Dirac modes the oscillations in the two contacts are indepe…
The effect of a magnetic field on the equilibrium spectral and transport properties of a single-molecule junction is studied using the numerical renormalization group method. The molecule is described by the Anderson-Holstein model in which a single vibrational mode is coupled to the electron density. The effect of an applied magnetic field on the conductance in the Kondo regime is qualitatively different in the weak and strong electron-phonon coupling regimes. In the former case, the Kondo resonance is split and the conductance is strongly suppressed by a magnetic field $g mu_B B \gtrsim k_BT…
Snake states and Aharonov-Bohm interferences are examples of magnetoconductance oscillations that can be observed in a graphene p-n junction. Even though they have already been reported in suspended and encapsulated devices including different geometries, a direct comparison remains challenging as they were observed in separate measurements. Due to the similar experimental signatures of these effects a consistent assignment is difficult, leaving us with an incomplete picture. Here we present measurements on p-n junctions in encapsulated graphene revealing several sets of magnetoconductance osc…
Transport measurement of electron optics in monolayer graphene p-n junction devices has been traditionally studied with negative refraction and chiral transmission experiments in Hallbar magnetic focusing set-ups. We show direct signatures of Klein (monolayer) and anti-Klein (bilayer) tunneling with a circular 'edgeless' Corbino geometry made out of gated graphene p-n junctions. Noticeable in particular is the appearance of angular sweet spots (Brewster angles) in the magnetoconductance data of bilayer graphene, which minimizes head-on transmission, contrary to conventional Fresnel optics or m…
Magnetotransport through cylindrical topological insulator (TI) nanowires is governed by the interplay between quantum confinement and geometric (Aharonov-Bohm and Berry) phases. Here, we argue that the much broader class of TI nanowires with varying radius -- for which a homogeneous coaxial magnetic field induces a varying Aharonov-Bohm flux that gives rise to a non-trivial mass-like potential along the wire -- is accessible by studying its simplest member, a TI nanocone. Such nanocones allow to observe intriguing mesoscopic transport phenomena: While the conductance in a perpendicular magnet…
We theoretically investigate the role of spin fluctuations in charge transport through a magnetic junction. Motivated by recent experiments that measure a nonlinear dependence of the current on electrical bias, we develop a systematic understanding of the interplay of charge and spin dynamics in nanoscale magnetic junctions. Our model captures two distinct features arising from these fluctuations: magnon-assisted transport and the effect of spin-transfer torque on the magnetoconductance. The latter stems from magnetic misalignment in the junction induced by spin-current fluctuations. As the te…
We study the magnetotransport properties of patterned 3D topological insulator nanostructures with several leads, such as kinks or Y-junctions, near the Dirac point with analytical as well as numerical techniques. The interplay of the nanostructure geometry, the external magnetic field and the spin-momentum locking of the topological surface states lead to a richer magnetoconductance phenomenology as compared to straight nanowires. Similar to straight wires, a quantized conductance with perfect transmission across the nanostructure can be realized across a kink when the input and output channe…
Topological surface states of three-dimensional topological insulator nanoribbons and their distinct magnetoconductance properties are promising for topoelectronic applications and topological quantum computation. A crucial building block for nanoribbon-based circuits are three-terminal junctions. While the transport of topological surface states on a planar boundary is not directly affected by an in-plane magnetic field, the orbital effect cannot be neglected when the surface states are confined to the boundary of a nanoribbon geometry. Here, we report on the magnetotransport properties of su…
Application of Bardeen's tunneling theory to magnetic tunnel junctions having a general degree of atomic disorder reveals the close relationship between magneto-conduction and voltage-driven pseudo-torque, as well as the thickness dependence of tunnel-polarization factors. Among the results: 1) The torque generally varies as sin theta at constant applied voltage. 2) Whenever polarization factors are well defined, the voltage-driven torque on each moment is uniquely proportional to the polarization factor of the other magnet. 3) At finite applied voltage, this relation predicts significant volt…
We study the magneto-transport properties on the disordered surface of a topological insulator attached with a ferromagnet/ferromagnet junction. Since, in the surface Dirac Hamiltonian, out-of-plane magnetization induces a mass gap, while in-plane magnetization has a role of the effective vector potential, the mechanism of magneto-transport is different between these two cases. The former is similar to the conventional one in ferromagnetic metals, while the latter is due to the shift of Fermi circles in momentum space. Our numerical calculations show that the magnetoconductance in in-plane con…
We theoretically study the stability of more than one Majorana Fermion appearing in a $p$-wave superconductor/dirty normal metal/$p$-wave superconductor junction in two-dimension by using chiral symmetry of Hamiltonian. At the phase difference across the junction $φ$ being $π$, we will show that all of the Majorana bound states in the normal metal belong to the same chirality. Due to this pure chiral feature, the Majorana bound states retain their high degree of degeneracy at the zero energy even in the presence of random potential. As a consequence, the resonant transmission of a Cooper pair …
We investigate 1D quantum systems that support Majorana bound states at interfaces between topologically distinct regions. In particular, we show that there exists a duality between particle-hole and spin degrees of freedom in certain spin-orbit-coupled 1D platforms such as topological insulator edges. This duality results in a spin analogue of previously explored `fractional Josephson effects'---that is, the spin current flowing across a magnetic junction exhibits 4π-periodicity in the relative magnetic field angle across the junction. Furthermore, the interplay between the particle-hole and …
We study the Josephson effect in small one-dimensional (1D) Josephson junction arrays. For weak Josephson tunneling, topologically different regions in the charge-stability diagram generate distinct current-phase relationships (I$Φ$). We present results for a three-junction system in the vicinity of charge degeneracy lines and triple points. We explain the generalization to larger arrays, show that discontinuities of the I$Φ$ at phase $π$ persist and that, at maximum degeneracy, the problem can be mapped to a tight-binding model providing analytical results for arbitrary system size.
We propose a new qubit consisting of a superconducting ring with two ordinary zero junctions and one ferromagnetic pi junction. In the system, two degenerate stable states appear in the phase space without an external magnetic field because of a competition between the zero and pi states. Quantum tunneling between the two degenerate states leads to a formation of bonding and antibonding states (coherent states) which are used as a bit. For manipulating the states of the qubit, only small external magnetic field around zero is required. This feature leads to a large-scale integration and a cons…
We consider the conductivity quantization in two-dimensional arrays of mesoscopic Josephson junctions, and examine the associated degeneracy in various regimes of the system. The filling factor of the system may be controlled by the gate voltage as well as the magnetic field, and its appropriate values for quantization is obtained by employing the Jain hierarchy scheme both in the charge description and in the vortex description. The duality between the two descriptions then suggests the possibility that the system undergoes a change in degeneracy while the quantized conductivity remains fixed…
We investigate experimentally the supercurrent in a clean carbon nanotube quantum dot, close to orbital degeneracy, connected to superconducting leads in a regime of strong competition between local electronic correlations and superconducting proximity effect. For an odd occupancy of the dot and intermediate coupling to the reservoir, the Kondo effect can develop in the normal state and screen the local magnetic moment of the dot. This leads to singlet-doublet transitions that strongly affect the Josephson effect in a single-level quantum dot: the sign of the supercurrent changes from positive…
We study a Josephson junction in a Kitaev chain with particle-hole symmetric nearest neighbor interactions. When the phase difference across the junction is $π$, we show analytically that the full spectrum is fourfold degenerate up to corrections that vanish exponentially in the system size. The Majorana bound states at the ends of the chain are known to survive interactions. Our result proves that the same is true for the zero-energy quasiparticle localized at the junction. We further study finite size corrections numerically, and show how repulsive interactions lead to stronger end-to-end co…
We study a Josephson junction made with a spin-textured bridge, when both Rashba and Zeeman interactions combine to generate a magneto-electric coupling between the superconducting current and the in-plane magnetic texture in the normal region. In particular, we unambiguously obtain the so-called anomalous current-phase relation $j=j_{c}\sinφ+j_{a}\cosφ$ in a two-dimensional ballistic Josephson junction close to the critical temperature of the heterostructure, when an anomalous current $j_{a}\neq0$ subsists even at zero phase-difference between the superconductors, and is responsible for the c…
We propose two new approaches for regulating spin polarization and spin inversion in a conducting junction within a tight-binding framework based on wave-guide theory. The system comprises a magnetic quantum ring with finite modulation in site potential is coupled to two non-magnetic electrodes. Due to close proximity an additional tunneling is established between the electrodes which regulates electronic transmission significantly. At the same time the phase associated with site potential, which can be tuned externally yields controlled transmission probabilities. Our results are valid for a …
We study spin and valley transports in junctions composed of silicene and topological crystalline insulators. We consider normal/magnetic/normal Dirac metal junctions where a gate electrode is attached to the magnetic region. In normal/antiferromagnetic/normal silicene junction, we show that the current through this junction is valley and spin polarized due to the coupling between valley and spin degrees of freedom, and the valley and spin polarizations can be tuned by local application of a gate voltage. In particular, we find a fully valley and spin polarized current by applying the electric…
We investigate interference of Majorana fermions (MFs) in NS junctions. A general formula of charge conductance G for NS junctions with two MFs is derived based on the low energy effective model. It is found that G for two MFs takes various values 0 \leq G \leq 4e^2/h owing to interference of the MFs, while G is quantized as G = 2e^2/h for a single MF. The value of G is determined by symmetry of the system. As an example, we investigate the complete destructive interference of two degenerate MFs reported by Ii et al. [A. Ii, A. Yamakage, K. Yada, M. Sato, and Y. Tanaka, Phys. Rev. B 86, 174512…
We study coherent quantum phase-slips which lift the ground state degeneracy in a Josephson junction ring, pierced by a magnetic flux of the magnitude equal to half of a flux quantum. The quantum phase-slip amplitude is sensitive to the normal mode structure of superconducting phase oscillations in the ring (Mooij-Schön modes). These, in turn, are affected by spatial inhomogeneities in the ring. We analyze the case of weak periodic modulations of the system parameters and calculate the corresponding modification of the quantum phase-slip amplitude.
When two superconductors are connected across a ferromagnet, the spin configuration of the transferred Cooper pairs can be modulated due to magnetic exchange interaction. The resulting supercurrent can reverse its sign across the Josephson junction (JJ) [1-4]. Here we demonstrate Josephson phase modulation in van der Waals heterostructures when Cooper pairs from superconducting NbSe$_2$ tunnel through atomically thin magnetic insulator (MI) Cr$_2$Ge$_2$Te$_6$. Employing a superconducting quantum interference device based on MI JJs, we probe a doubly degenerate non-trivial JJ phase ($ϕ$) origin…
We study magnetoconductance of the small bandgap carbon nanotube quantum dots in the presence of spin-orbit coupling in the strong correlations regime. The finite-U mean field slave boson approach is used to study many-body effects. Different degeneracies are restored in magnetic field and Kondo effects of different symmetries arise including SU(3) effects of different types. Full spin-orbital degeneracy might be recovered for zero field and correspondingly SU(4) Kondo effect sets in. We point out on the possibility of the occurrence of electron-hole Kondo effects in slanting magnetic fields, …
We show how the superconducting phase difference in a Josephson junction may be used to split the Kramers degeneracy of its energy levels and to remove all the properties associated with time reversal symmetry. The superconducting phase difference is known to be ineffective in two-terminal short Josephson junctions, where irrespective of the junction structure the induced Kramers degeneracy splitting is suppressed and the ground state fermion parity must stay even, so that a protected zero-energy Andreev level crossing may never appear. Our main result is that these limitations can be complete…
Nanoscale magnetic junction provides a useful approach to act as the building block for magnetoresistive random access memories (MRAM), where one of the key issues is to control the magnetic domain configuration. Here, we study the domain structure and the magnetic switching in the Permalloy (Fe20Ni80) nanoscale magnetic junctions with different thicknesses by using micromagnetic simulations. It is found that both the 90-degree and 45-degree domain walls can be formed between the junctions and the wire arms depending on the thickness of the device. The magnetic switching fields show distinct t…
In a quantum dot hybrid superconducting junction, the behavior of the supercurrent is dominated by Coulomb blockade physics, which determines the magnetic state of the dot. In particular, in a single level quantum dot singly occupied, the sign of the supercurrent can be reversed, giving rise to a pi-junction. This 0-pi transition, corresponding to a singlet-doublet transition, is then driven by the gate voltage or by the superconducting phase in the case of strong competition between the superconducting proximity effect and Kondo correlations. In a two-level quantum dot, such as a clean carbon…
An ideal layered $\hat{x}$-polarized antiferromagnet (AFM) between two antialigned $\pm \hat{z}$ polarized ferromagnetic (FM) contacts transmits no current due to a $π$ phase difference of the matrix elements coupling the spin degenerate states to the two FM contacts. The ratio of the two matrix elements coupling the two spin degenerate $\hat{x}$ AFM states to a $\hat{z}$ FM contact is determined by the exchange energy and the eigenstate energy. Inserting a normal metal layer or tunnel barrier layer between one FM contact and the AFM alters this phase difference, and, due to the unequal weight…
We study the charge transport and the heat transfer through a nano-junction composed of a small metallic grain weakly coupled to two metallic leads. We focus on the cotunneling regime out-of-equilibrium, where the bias voltage and the temperature gradient between the leads strongly drive electron and phonon degrees of freedom in the grain that in turn have a strong feedback on the transport through the grain. We derive and solve coupled kinetic equations for electron and phonon degrees of freedom in the grain. We obtain the heat fluxes between cotunneling electrons, bosonic electron-hole excit…
The superconducting phase qubit combines Josephson junctions into superconducting loops and defines one of the promising solid state device implementations for quantum computing. While conventional designs are based on magnetically frustrated superconducting loops, here we discuss the advantages offered by $π$-junctions in obtaining naturally degenerate two-level systems. Starting from a basic five-junction loop, we show how to construct degenerate two-level junctions and superconducting phase switches. These elements are then effectively engineered into a superconducting phase qubit which ope…
We calculate the Landau levels of a Kramers-Weyl semimetal thin slab in a perpendicular magnetic field $B$. The coupling of Fermi arcs on opposite surfaces broadens the Landau levels with a band width that oscillates periodically in $1/B$. We interpret the spectrum in terms of a one-dimensional superlattice induced by magnetic breakdown at Weyl points. The band width oscillations may be observed as $1/B$-periodic magnetoconductance oscillations, at weaker fields and higher temperatures than the Shubnikov-de Haas oscillations due to Landau level quantization. No such spectrum appears in a gener…
We introduce a new class of Josephson arrays which have non-trivial topology and exhibit a novel state at low temperatures. This state is characterized by long range order in a two Cooper pair condensate and by a discrete topological order parameter. These arrays have degenerate ground states with this degeneracy 'protected' from the external perturbations (and noise) by the topological order parameter. We show that in ideal conditions the low order effect of the external perturbations on this degeneracy is exactly zero and that deviations from ideality lead to only exponentially small effects…
Low-energy excitations in graphene exhibit relativistic properties due to the linear dispersion relation close to the Dirac points in the first Brillouin zone. Two of the Dirac points located at opposite corners of the first Brillouin zone can be chosen as inequivalent, representing a new valley degree of freedom, in addition to the charge and spin of an electron. Using the valley degree of freedom to encode information has attracted significant interest, both theoretically and experimentally, and gave rise to the field of valleytronics. We study a graphene $p$-$n$ junction in a uniform out-of…
A Josephson qubit is designed via the application of a tensile strain to a topological insulator surface sandwiched between two s-wave superconductors. The strain applied leads to a shift in the Dirac point without changing the pre-existing conducting states, on the surface of a topological insulator. Strain applied can be tuned to form a $π$ junction in such a structure. Combining two such junctions in a ring architecture leads to the ground state of the ring being in doubly degenerate state- the "0" and "1" states of a qubit. A qubit designed this way is quite easily controlled via the tunab…
We study quantum manipulation based on four Majorana bound states in X-junction geometry. The parameter space of this setup is bigger than of the previously studied Y-junction and is described by SO(4) symmetry group. In order for quantum computation to be dephasing free, two Majorana states have to stay degenerate at all times. We find a condition necessary for that and compute the Berry's phase, $2α$, accumulated during the manipulation. We construct simple protocols for the variety of values of $α$, including $π/8$ needed for the purposes of quantum computation. Although the manipulations i…
We present transport measurements of tunnel junctions made between Cu and graphene in a magnetic field. We observe a transition to a Landau level like structure at high fields, as well as a set of sharp features in the tunneling spectra that shift with gate and tunnel probe voltage along the lines of constant charge density. We explain the sharp features with the formation of degeneracy split localized Landau levels, and addition of electrons to those levels one by one. A large capacitive coupling to the tunnel probe also increases the gate voltage spacing between the Landau levels.
In the present work, we consider a spin 1/2 paramagnetic dimer embedded in a magnetic tunnel junction driven out of equilibrium by means of an applied voltage and an applied temperature gradient, in the presence of an external magnetic bias, which can be turn on/off. Here, we derive the spin excitation spectrum for a two spin 1/2 system analytically and show that an external magnetic field is required to lift the degeneracy in the triplet state, whether both spin units experience the magnetic field in the same direction or in opposite staggered directions. We show that an applied bias voltage …
Superconducting wires without time-reversal and spin-rotation symmetries can be driven into a topological phase that supports Majorana bound states. Direct detection of these zero-energy states is complicated by the proliferation of low-lying excitations in a disordered multi-mode wire. We show that the phase transition itself is signaled by a quantized thermal conductance and electrical shot noise power, irrespective of the degree of disorder. In a ring geometry, the phase transition is signaled by a period doubling of the magnetoconductance oscillations. These signatures directly follow from…
We study the conductance of mesoscopic graphene rings in the presence of a perpendicular magnetic field by means of numerical calculations based on a tight-binding model. First, we consider the magnetoconductance of such rings and observe the Aharonov-Bohm effect. We investigate different regimes of the magnetic flux up to the quantum Hall regime, where the Aharonov-Bohm oscillations are suppressed. Results for both clean (ballistic) and disordered (diffusive) rings are presented. Second, we study rings with smooth mass boundary that are weakly coupled to leads. We show that the valley degener…
We propose a conceptually new way to gather information on the electron bands of buried metal(semiconductor)/insulator interfaces. The bias dependence of low frequency noise in Fe$_{1-x}$V$_{x}$/MgO/Fe (0 $<$ x $<$ 0.25) tunnel junctions show clear anomalies at specific applied voltages, reflecting electron tunneling to the band edges of the magnetic electrodes. The change in magnitude of these noise anomalies with the magnetic state allows evaluating the degree of spin mixing between the spin polarized bands at the ferromagnet/insulator interface. Our results are in qualitative agreement with…
We have calculated the linear magnetoconductance across a vertical parabolic Quantum Dot with a magnetic field in the direction of the current. Gate voltage and magnetic field are tuned at the degeneracy point between the occupancies N=2 and N=3, close to the Singlet-Triplet transition for N=2. We find that the conductance is enhanced prior to the transition by nearby crossings of the levels of the 3 particle dot. Immediately after it is depressed by roughly 1/3, as long as the total spin S of the 3 electron ground state doesn't change from S=1/2 to S=3/2, due to spin selection rule. At low te…
We present measurements of magnetic tunnel junctions made using a self-assembled-monolayer molecular barrier. Ni/octanethiol/Ni samples were fabricated in a nanopore geometry. The devices exhibit significant changes in resistance as the angle between the magnetic moments in the two electrodes is varied, demonstrating that low-energy electrons can traverse the molecular barrier while maintaining spin coherence. An analysis of the voltage and temperature dependence of the data suggests that the spin-coherent transport signals can be degraded by localized states in the molecular barriers.
Magnetic tunnel junctions operating in the superparamagnetic regime are promising devices in the field of probabilistic computing, which is suitable for applications like high-dimensional optimization or sampling problems. Further, random number generation is of interest in the field of cryptography. For such applications, a device's uncorrelated fluctuation time-scale can determine the effective system speed. It has been theoretically proposed that a magnetic tunnel junction designed to have only easy-plane anisotropy provides fluctuation rates determined by its easy-plane anisotropy field, a…
Carbon nanotube Y-junctions are of great interest to the next generation of innovative multi-terminal nanodevices. Topological indices are graph-theoretically based parameters that describe various structural properties of a chemical molecule. The entropy of a graph is a topological descriptor that serves to characterize the complexity of the underlying molecular graph. The concept of entropy is a physical property of a thermodynamic system. Graph entropies are the essential thermophysical quantities defined for various graph invariants and are applied to measure the heterogeneity and relative…
We consider clean cylindrical nanostructures with an applied longitudinal static magnetic field. Without Coulomb interaction, the field induces, for particular values, points of degeneracy where a change of ground state takes place due to Aharonov-Bohm effect. The Coulomb potential introduces interaction between the electronic configurations. As a consequence, when there is degeneracy, the ground state of the system becomes a many body state - unable to be described by a mean-field theory - and a gap is opened. To study this problem, we propose a variational multireference wave function which …
A Josephson bijunction made of three superconductors connected by a quantum dot is considered in the regime where the dot carries a magnetic moment. In the range of parameters where such a dot, if inserted in a two-terminal Josephson junction, creates a $π$-shift of the phase, the bijunction forming a triangular unit is frustrated. This frustration is studied both within a phenomenological and a microscopic model. Frustration stabilizes a phase vortex centered on the dot, with two degenerate states carrying opposite vorticities, independently of the direction of the magnetic moment. Embedding …
