Quasi-two-dimensional superconductors with tunable spin-orbit coupling are very interesting systems with properties that are also potentially useful for applications. In this manuscript we demonstrate that these systems exhibit undamped collective spin oscillations that can be excited by the application of a supercurrent. We propose to use these collective excitations to realize persistent spin oscillators operating in the frequency range of 10 GHz - 1 THz.
The fractional Aharonov-Bohm oscillation (FABO) of narrow quantum rings with two electrons has been studied and has been explained in an analytical way, the evolution of the period and amplitudes against the magnetic field can be exactly described. Furthermore, the dipole transition of the ground state was found to have essentially two frequencies, their difference appears as an oscillation matching the oscillation of the persistent current exactly. A number of equalities relating the observables and dynamical parameters have been found.
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.
The interaction-induced orbital magnetic response of a nanoscale system, modeled by the persistent current in a ring geometry, is evaluated for a system which is a superconductor in the bulk. The interplay of the renormalized Coulomb and Fröhlich interactions is crucial. The diamagnetic response of the large superconductor may become paramagnetic when the finite-size-determined Thouless energy is larger than or on the order of the Debye energy.
In this work, we investigate the spectra in an Aharonov-Bohm quantum-ring interferometer forming a Josephson junction between two topological superconductors (TSC) nanowires. The TSCs host Majorana bound states at their edges, and both the magnetic flux and the superconducting phase difference between the TSCs are used as control parameters. We use a tight-binding approach to model the quantum ring coupled to both TSCs, described by the Kitaev effective Hamiltonian. We solve the problem by means of exact numerical diagonalization of the Bogoliubov-de Gennes (BdG) Hamiltonian and obtain the spe…
The persistent current $I$ in integrable models of multichannel rings with both short- and long-ranged interactions is investigated. $I$ is found to oscillate in sign and increase in magnitude with increasing interaction strength due to interaction-induced correlations in the currents contributed by different channels. For sufficiently strong interactions, the contributions of all channels are found to add constructively, leading to a giant enhancement of $I$. Numerical results confirm that this parity-locking effect is robust with respect to subband mixing due to disorder.
The effect of the surface curvature on the magnetic moment and persistent currents in two-dimensional (2D) quantum rings and dots is investigated. It is shown that the surface curvature decreases the spacing between neighboring maxima of de Haas -- van Alphen (dHvA) type oscillations of the magnetic moment of a ring and decreases the amplitude and period of Aharonov -- Bohm (AB) type oscillations. In the case of a quantum dot, the surface curvature reduces the level degeneracy at zero magnetic fields. This leads to a suppression of the magnetic moment at low magnetic fields. The relation betwe…
We introduce a calorimetric approach to probe persistent currents in normal metal rings. The heat capacity of a large ensemble of silver rings is measured by nanocalorimetry under a varying magnetic field at different temperatures (60 mK, 100 mK and 150 mK). Periodic oscillations versus magnetic field are detected in the phase signal of the temperature oscillations, though not in the amplitude (both of them directly linked to the heat capacity). The period of these oscillations ($Φ_0/2$, with $Φ_0 = h/e$ the magnetic flux quantum) and their evolution with temperature are in agreement with theo…
The qubit Rabi oscillations are known to be non-decaying (though with a fluctuating phase) if the qubit is continuously monitored in the weak-coupling regime. In this paper we propose an experiment to demonstrate these persistent Rabi oscillations via low-frequency noise correlation. The idea is to measure a qubit by two detectors, biased stroboscopically at the Rabi frequency. The low-frequency noise depends on the relative phase between the two combs of biasing pulses, with a strong increase of telegraph noise in both detectors for the in-phase or anti-phase combs. This happens because of se…
Giant oscillations of the density of electronic states and the differential conductance of a superconductor-ferromagnet-superconductor structure are predicted for the case when the exchange energy, $I_0$, due to the interaction between the electron spin and the spontaneous moment of the ferromagnet is smaller than the superconductor energy gap, $Δ$. The effect is due to the extremely large degeneration of the energy level $ε= I_0$ when the superconductor phase difference $ϕ$ is close to odd multiple of $π$ ($ε$ is the electron energy measured from the Fermi-energy). This quantum interference e…
We investigate persistent currents in metallic rings interrupted by a Coulomb blockaded topological superconducting segment. We show that the presence of Majorana bound states in the superconductor is reflected in the emergence of an h/e harmonics in the persistent current, whose sign is determined by the fermion parity of the superconductor. The Majorana bound states further render the current finite at zero flux, nevertheless the resulting peculiar symmetry of the persistent current is compatible with a free energy that is even in time-reversal symmetry breaking fields. These unique features…
We analyse the periodicity of persistent currents in quantum spin Hall loops, partly covered with an $s$-wave superconductor, in the presence of a flux tube. Much like in normal (non-helical) metals, the periodicity of the single-particle spectrum goes from $Φ_0 = h/e$ to $Φ_0/2$ as the length of the superconductor is increased past the coherence length of the superconductor. We further analyze the periodicity of the persistent current, which is a many-body effect. Interestingly, time reversal symmetry and parity conservation can significantly change the period. We find a $2Φ_0$-periodic persi…
We investigate the Little-Parks oscillations caused by a persistent current loop set on the top edge of a mesoscopic superconducting thin-walled cylinder with a finite height. For a short cylinder the Little-Parks oscillations are approximately the same ones as the standard effect, as there is only one magnetic flux piercing the cylinder. For a tall cylinder the inhomogeneity of the magnetic field makes different magnetic fluxes pierce the cylinder at distinct heights and we show here that this produces two distinct Little-Parks oscillatory regimes according to the persistent current loop. We …
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 find the current voltage characteristics of a 2DEG-S interface in magnetic field taking into account the surface roughness. Typically in experiments $L/2R_c\gtrsim 3$, where $L$ is the surface length and $R_c$ is the cyclotron radius. The conductance behaves in experiments usually as $G=g_0+g_1\cos(2πν+δ_1)$; higher harmonics, $g_2\cos(4πν+δ_2),...$, are hardly seen. Theories based on the assumption of the interface perfectness can hardly describe qualitatively the visibility of the condctance oscillations and the amplitudes of the harmonics: they predict $g_1\sim g_2\sim g_3,...$. Our appr…
We demonstrate theoretically the noise-stimulated enhancement of quantum coherence in a superconducting flux qubit. First, an external classical noise can increase the off-diagonal components of the qubit density matrix. Second, in the presence of noise, the Rabi oscillations survive for times significantly longer than the Rabi decay time in a noiseless system. These Rabi oscillations appear as a modulation of the forced response of the qubit to the ac driving field. These effects can be considered as a manifestation of quantum stochastic resonance and are relevant to experimental techniques, …
We investigate theoretically electron spin states in one dimensional (1D) and two dimensional (2D) hard-wall mesoscopic rings in the presence of both the Rashba spin-orbit interaction (RSOI) and the Dresselhaus spin-orbit interaction (DSOI) in a perpendicular magnetic field. The Hamiltonian of the RSOI alone is mathematically equivalent to that of the DSOI alone using an SU(2) spin rotation transformation. Our theoretical results show that the interplay between the RSOI and DSOI results in an effective periodic potential, which consequently leads to gaps in the energy spectrum. This periodic p…
We present transport measurements in superconductor-nanowire devices with a gated constriction forming a quantum point contact. Zero-bias features in tunneling spectroscopy appear at finite magnetic fields, and oscillate in amplitude and split away from zero bias as a function of magnetic field and gate voltage. A crossover in magnetoconductance is observed: Magnetic fields above ~ 0.5 T enhance conductance in the low-conductance (tunneling) regime but suppress conductance in the high-conductance (multichannel) regime. We consider these results in the context of Majorana zero modes as well as …
At the interface of an s-wave superconductor and a three-dimensional topological insulator, Ma- jorana zero modes and Majorana helical states have been proposed to exist respectively around magnetic vortices and geometrical edges. Here we first show that a single magnetic impurity at such an interface splits each resonance state of a given spin channel outside the superconducting gap, and also induces two new symmetric impurity states inside the gap. Next we find that an increase in the superconducting gap suppresses both the oscillation magnitude and period of the RKKY inter- action between t…
We investigate the effect of a non-Markovian, structured reservoir on an open Heisenberg spin chain. We establish a coherent self-feedback mechanism as the reservoir couples frequency-dependent to the spin chain. Thus, loss and driving take place due to the interaction of the spin chain with its own past. This new paradigm of non-Markovian imposed boundary-driving allows to discuss a new kind of non-equilibrium steady-state. We show that for certain parameters even in the long-time limit persistent oscillations occur within the chain. Moreover, we demonstrate that the conditions for these osci…
We experimentally investigate electron transport through the interface between a superconductor and the edge of a two-dimensional electron system with band inversion. The interface is realized as a tunnel NbN side contact to a narrow 8~nm HgTe quantum well. It demonstrates a typical Andreev behavior with finite conductance within the superconducting gap. Surprisingly, the conductance is modulated by a number of equally-spaced oscillations. The oscillations are present only within the superconducting gap and at lowest, below 1~K, temperatures. The oscillations disappear completely in magnetic f…
Two opposite chiralities of Dirac electrons in a 2D graphene sheet modify the Friedel oscillations strongly: electrostatic potential around an impurity in graphene decays much faster than in 2D electron gas. At distances $r$ much larger than the de Broglie wavelength, it decays as $1/r^3$. Here we show that a weak uniform magnetic field affects the Friedel oscillations in an anomalous way. It creates a field-dependent contribution which is {\em dominant} in a parametrically large spatial interval $p_0^{-1}\lesssim r\lesssim k_Fl^2$, where $l$ is the magnetic length, $k_F$ is Fermi momentum and…
We have measured the evolution of the tunneling density of states (DOS) in superconductor/ferromagnet (S/F) bilayers with increasing F-layer thickness, where F in our experiment is the strong ferromagnet Ni. As a function of increasing Ni thickness, we detect multiple oscillations in the DOS at the Fermi energy from differential conductance measurements. The features in the DOS associated with the proximity effect change from normal to inverted twice as the Ni thickness increases from 1 to 5 nm.
We observed quantum oscillations in thermoelectric and magnetic torque signals in non-centrosymmetric superconductor PbTaSe$_2$. One oscillatory frequency stems from the orbits formed by magnetic breakdown, while others are from two-dimensional-like Fermi surfaces near the topological nodal rings. Our comprehensive understanding of the Fermi surface topology of PbTaSe$_2$, including nailing down the Fermi level and detecting the Berry phases near the nodal rings, is crucial for searching plausible topological superconductivity in its bulk and surface states.
We study a chain of magnetic impurities on a conventional superconductor with spin-orbit coupling, treating the superconducting order fully self-consistently. We find and quantify strong hybridization between the topological edge Majorana bound states (MBSs) and in-gap Yu-Shiba-Rusinov (YSR) states, which causes increasing energy oscillations as a function of magnetic impurity strength, even when the direct MBS overlap is negligible. By treating the MBS as a topological boundary state, dependent only on the effective mass gap, we arrive at a fully parameter-free functional form of the its loca…
We present a theoretical study of an escape rate for switching from the superconducting state to a resistive one in series arrays of strongly interacting Josephson junctions. At low temperatures such a switching is determined by macroscopic quantum tunneling (MQT) of a spatially extended Josephson phase. An increase of the crossover temperature from the thermal to quantum regimes, and a giant enhancement of MQT escape rate is obtained. Such an effect is explained by excitation of collective charge oscillations forming a {\it charge instanton}. Using a model of screened Coulomb interaction we f…
We study the quantum Andreev oscillation induced by interference of the edge chiral Majorana fermions in junctions made of quantum anomalous Hall (QAH) insulators and superconductors (SCs). We show two chiral Majorana fermions on a QAH edge with SC proximity generically have a momentum difference $Δk$, which depends on the chemical potentials of both the QAH insulator and the SC. Due to the spatial interference induced by $Δk$, the longitudinal conductance of QAH-SC junctions oscillates with respect to the edge lengths and the chemical potentials, which can be probed via charge transport. Furt…
The obtained periodic magnetic-field dependencies of the critical current, measured in opposite directions on asymmetric superconducting aluminum rings, allow to explain observed earlier quantum oscillations of a dc voltage as a result of alternating current rectification. It is found, that the high efficiency of the rectification of both individual rings and ring systems is connected to a hysteresis of the current-voltage characteristics. The asymmetry of the current-voltage characteristics providing the rectification effect is due to the relative shifts of the magnetic dependencies of the cr…
I consider the quantum interference of electrons moving along knotted trajectories under external magnetic field. The induced persistent current is formulated in terms of characteristic parameters that classify the torus knot geometry. The current is found to show a periodic oscillation whose period depends strongly both on the knot's class and the field direction. The shift in the oscillation period caused by geometric distortion is also discussed.
We describe a mechanism by which the longitudinal thermal conductivity $κ_{xx}$, measured in an in-plane magnetic field, oscillates as a function of field angle in layered nodal superconductors. These oscillations occur when the spin-orbit splitting at the nodes is larger than the nodal scattering rate, and are complementary to vortex-induced oscillations identified previously. In sufficiently anisotropic materials, the spin-orbit mechanism may be dominant. As a particular application, we focus on the cuprate high-temperature superconductor YBa$_2$Cu$_3$O$_{6+x}$. This material belongs to the …
We consider the superconducting phase in a moving superconductor and show that it depends on the displacement flux. Generalized constitutive relations between the phase of a superconducting interference device (SQUID) and the position of the oscillating loop are then established. In particular, we show that the Josephson current and voltage depend on both the SQUID position and velocity. The two proposed relativistic corrections to the Josephson relations come from the macroscopic displacement of a quantum condensate according to the (non-inertial) Galilean covariance of the Schrödinger equati…
It is shown that in a structure consisting of a superconducting ring-shaped electrode overlapped by a normal metal contact through a thin oxide barrier, measurements of the tunnel current in magnetic field can probe persistent currents in the ring. The effect manifests itself as periodic oscillations of the tunnel current through the junction at a fixed bias voltage as function of perpendicular magnetic field. The magnitude of oscillations depends on bias point. It reaches maximum at energy eV which is close to the superconducting gap and decreases with increase of temperature. The period of o…
The act of measurement bridges the quantum and classical worlds by projecting a superposition of possible states into a single, albeit probabilistic, outcome. The time-scale of this "instantaneous" process can be stretched using weak measurements so that it takes the form of a gradual random walk towards a final state. Remarkably, the interim measurement record is sufficient to continuously track and steer the quantum state using feedback. We monitor the dynamics of a resonantly driven quantum two-level system -- a superconducting quantum bit --using a near-noiseless parametric amplifier. The …
We study the model of a noninteracting spinless electron gas confined to the two-dimensional localized surface of a cone in the presence of external magnetic fields. The localized region is characterized by an annular radial potential. We write the Schrödinger equation and use the thin-layer quantization procedure to calculate the wavefunctions and the energy spectrum. In such a procedure, it arises a geometry induced potential, which depends on both the mean and the Gaussian curvatures. Nevertheless, since we consider a ring with a mesoscopic size, the effects of the Gaussian curvature on the…
The observations of the dc voltage proportional to the persistent current on system of asymmetric superconductor loops at a non-zero resistance raise a question on a nature of this quantum phenomenon and its possibility in semiconductor and normal metal mesoscopic loops.
To understand the role of electron correlation and disorder on persistent currents in isolated 1D rings threaded by magnetic flux $ϕ$, we study the behavior of persistent currents in aperiodic and ordered binary alloy rings. These systems may be regarded as disordered systems with well-defined long-range order so that we do not have to perform any configuration averaging of the physical quantities. We see that in the absence of interaction, disorder suppresses persistent currents by orders of magnitude and also removes its discontinuity as a function of $ϕ$. As we introduce electron correlatio…
We investigate the persistent currents, spin-polarized local density of states, and spectral functions of topological superconductors constructed by placing ferromagnetic impurities on top of an s-wave superconductor with Rashba spin-orbit interaction. We solve self-consistently for the superconducting order parameter and investigate both two-dimensional blocks and one-dimensional wires of ferromagnetic impurities, with the magnetic moments pointing both perpendicular and parallel to the surface. We find that the topologically protected edge states of ferromagnetic blocks give rise to spin-pol…
The magnetoresistance of thin superconducting strips subject to a perpendicular magnetic field B and low temperatures T manifests a sequence of alternating superconductor-insulator transitions (SIT). We study this phenomenon within a quasi one-dimensional (1D) model for the quantum dynamics of vortices in a line-junction between coupled parallel SC wires, at parameters close to their SIT. Mapping the vortex system to 1D Fermions at a chemical potential dictated by B, we find that a quantum phase transition of the Ising type occurs at critical values of the vortex filling, from a SC phase near …
We develop a quasi-classical theory for the superconducting proximity effect in a ballistic ferromagnetic layer in contact with a d-wave superconductor. In agreement with recent experiments we find that the density of states oscillate around the normal state value with varying the thickness of the ferromagnetic layer. We show that the phase, the amplitude, and the period of these oscillations depend on the orientation of the superconductor. This effect reveals spatial oscillations and anisotropy of the induced superconducting correlations in the ferromagnet.
Recently Jang et al. reported the observation of half-height magnetization steps in cantilever magnetometry measurements of mesoscopic annular Sr2RuO4 particles. Such magnetization features were interpreted as the presence of half-quantum vortices. In an attempt to examine our findings, very recently Cai et al. (1202.3146) have performed magnetotransport measurements of micron-size rings fabricated from small Sr2RuO4 crystals. While fabrication of such samples and subsequent verification of our findings is highly desirable, we would like to point out that, at the current state of affairs, the …
