arXiv subjects

Roman M. Lutchyn

Publications and source records attributed to Roman M. Lutchyn.

At least 37 records · Page 2Linked to original sources

arXiv2017

Odd-frequency superconductivity in a nanowire coupled to Majorana zero modes

Odd-frequency superconductivity, originally proposed by Berezinskii in 1974, is an exotic phase of matter in which Cooper pairing between electrons is entirely dynamical in nature. The pair potential is an odd function of frequency, leading to a vanishing static superconducting order parameter and exotic types of pairing seemingly inconsistent with Fermi statistics. Motivated by recent experimental progress in the realization of Majorana zero modes in semiconducting nanowires, we show that odd-frequency superconductivity generically appears in a spin-polarized nanowire coupled to Majorana zero modes. We explicitly calculate the superfluid response and show that it is characterized by a paramagnetic Meissner effect.

cond-mat.supr-con↗

arXiv2017

Coulomb Blockade in Fractional Topological Superconductors

We study charge transport through a floating mesoscopic superconductor coupled to counterpropagating fractional quantum Hall edges at filling fraction $ν=2/3$. We consider a superconducting island with finite charging energy and investigate its effect on transport through the device. We calculate conductance through such a system as a function of temperature and gate voltage applied to the superconducting island. We show that transport is strongly affected by the presence of parafermionic zero modes, leading at zero temperature to a zero-bias conductance quantized in units of $νe^2/h$ independent of the applied gate voltage.

cond-mat.str-el↗

arXiv2017

Transport through a Majorana island: strong tunneling regime

In the presence of Rashba spin-orbit coupling, magnetic field can drive a proximitized nanowire into a topological superconducting phase. We study transport properties of such nanowires in the Coulomb blockade regime. The associated with the topological superconductivity Majorana modes significantly modify transport and lead to single-electron coherent transmission through the nanowire - a non-local signature of topological superconductivity. In this work, we focus on the case of strong hybridization of the Majorana modes with the normal leads. The induced by hybridization broadening of the Majorana zero-energy states competes with the charging energy, leading to a considerable modification of the Coulomb blockade in a nanowire contacted by two normal leads. We evaluate the two-terminal conductance as a function of the gate voltage, junctions transmission coefficients, the geometric capacitance of and the induced superconducting gap in the nanowire.

cond-mat.supr-con↗

arXiv2016

Keldysh approach to periodically driven systems with a fermionic bath: non-equilibrium steady state, proximity effect and dissipation

We study properties of a periodically driven system coupled to a thermal bath. As a nontrivial example, we consider periodically driven metallic system coupled to a superconducting bath. The effect of the superconductor on the driven system is two-fold: it (a) modifies density of states in the metal via the proximity effect and (b) acts as a thermal bath for light-excited quasi-particles. Using Keldysh formalism, we calculate, nonpertubatively in the system-bath coupling, the steady-state properties of the system and obtain non-equilibrium distribution function. The latter allows one to calculate observable quantities which can be spectroscopically measured in tunneling experiments.

cond-mat.supr-con↗

arXiv2016

Signatures of Majorana Kramers pairs in superconductor-Luttinger liquid and superconductor-quantum dot-normal lead junctions

Time-reversal invariant topological superconductors are characterized by the presence of Majorana Kramers pairs localized at defects. One of the transport signatures of Majorana Kramers pairs is the quantized differential conductance of $4e^2/h$ when such a one-dimensional superconductor is coupled to a normal-metal lead. The resonant Andreev reflection, responsible for this phenomenon, can be understood as the boundary condition change for lead electrons at low energies. In this paper, we study the stability of the Andreev reflection fixed point with respect to electron-electron interactions in the Luttinger liquid. We first calculate the phase diagram for the Luttinger liquid-Majorana Kramers pair junction and show that its low-energy properties are determined by Andreev reflection scattering processes in the spin-triplet channel, i.e. the corresponding Andreev boundary conditions are similar to that in a spin-triplet superconductor - normal lead junction. We also study here a quantum dot coupled to a normal lead and a Majorana Kramers pair and investigate the effect of local repulsive interactions leading to an interplay between Kondo and Majorana correlations. Using a combination of renormalization group analysis and slave-boson mean-field theory, we show that the system flows to a new fixed point which is controlled by the Majorana interaction rather than the Kondo coupling. This Majorana fixed point is characterized by correlations between the localized spin and the fermion parity of each spin sector of the topological superconductor. We investigate the stability of the Majorana phase with respect to Gaussian fluctuations.

cond-mat.mes-hall↗

arXiv2016

Quantum charge fluctuations of a proximitized nanowire

Motivated by recent experiment, we consider charging of a nanowire which is proximitized by a superconductor and connected to a normal-state lead by a single-channel junction. The charge $Q$ of the nanowire is controlled by gate voltage $e{\cal N}_g/C$. A finite conductance of the contact allows for quantum charge fluctuations, making the function $Q(\mathcal{N}_g)$ continuous. It depends on the relation between the superconducting gap $Δ$ and the effective charging energy $E^*_C$. The latter is determined by the junction conductance, in addition to the geometrical capacitance of the proximitized nanowire. We investigate $Q(\mathcal{N}_g)$ at zero magnetic field $B$, and at fields exceeding the critical value $B_c$ corresponding to the topological phase transition. Unlike the case of $Δ= 0$, the function $Q(\mathcal{N}_g)$ is analytic even in the limit of negligible level spacing in the nanowire. At $B=0$ and $Δ>E^*_C$, the maxima of $dQ/d\mathcal{N}_g$ are smeared by $2e$-fluctuations described by a single-channel "charge Kondo" physics, while the $B=0$, $Δ<E^*_C$ case is described by a crossover between the Kondo and mixed-valence regimes of the Anderson impurity model. In the topological phase, $Q(\mathcal{N}_g)$ is analytic function of the gate voltage with $e$-periodic steps. In the weak tunneling limit, $dQ/d\mathcal{N}_g$ has peaks corresponding to Breit-Wigner resonances, whereas in the strong tunneling limit (i.e., small reflection amplitude $r$ ) these resonances are broadened, and $dQ/d\mathcal{N}_g-e \propto r\cos(2π\mathcal{N}_g)$.

cond-mat.mes-hall↗

arXiv2016

Optimizing spin-orbit splittings in InSb Majorana nanowires

Semiconductor-superconductor heterostructures represent a promising platform for the detection of Majorana zero modes and subsequently the processing of quantum information using their exotic non-Abelian statistics. Theoretical modeling of such low-dimensional semiconductors is generally based on phenomenological effective models. However, a more microscopic understanding of their band structure and, especially, of the spin-orbit coupling of electrons in these devices is important for optimizing their parameters for applications in quantum computing. In this paper, we approach this problem by first obtaining a highly accurate effective tight-binding model from ab initio calculations in the bulk. This model is symmetrized and correctly reproduces both the band structure and the wavefunction character. It is then used to determine Dresselhaus and Rashba spin-orbit splittings induced by finite size effects and external electric field in zincblende InSb one- and two-dimensional nanostructures as a function of growth parameters. The method presented here enables reliable simulations of realistic devices, including those used to realize exotic topological states.

cond-mat.mtrl-sci↗

arXiv2015

Topological superconductivity in a multichannel Yu-Shiba-Rusinov chain

Chains of magnetic atoms placed on the surface of an s-wave superconductor with large spin-orbit coupling provide a promising platform for the realization of topological superconducting states characterized by the presence of Majorana zero-energy modes. In this work we study the properties of the one-dimensional chain of Yu-Shiba-Rusinov states induced by magnetic impurities using a realistic model for the magnetic atoms that include the presence of multiple scattering channels. These channels are mixed by the spin-orbit coupling and, via the hybridization of the Yu-Shiba-Rusinov states at different sites of the chain, result in a multi-band structure for the chain. We obtain the topological phase diagram for such band structure. We identify the parameter regimes for which the different bands lead to a topological phase and show that the inclusion of higher bands can greatly enlarge the phase space for the realization of topological states.

cond-mat.supr-con↗

arXiv2015

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. This transport signature is expected to be exhibited in measurements of differential conductance and/or current cross-correlation at low bias.

cond-mat.mes-hall↗

arXiv2015

Fractional Josephson Effect in Number-Conserving Systems

We study fractional Josephson effect in a particle-number conserving system consisting of a quasi-one-dimensional superconductor coupled to a nanowire or an edge carrying $e/m$ fractional charge excitations with $m$ being an odd integer. We show that, due to the topological ground-state degeneracy in the system, the periodicity of the supercurrent on magnetic flux through the superconducting loop is non-trivial which provides a possibility to detect topological phases of matter by the $dc$ supercurrent measurement. Using a microscopic model for the nanowire and quasi-one-dimensional superconductor, we derived an effective low-energy theory for the system which takes into account effects of quantum phase fluctuations. We discuss the stability of the fractional Josephson effect with respect to the quantum phase slips in a mesoscopic superconducting ring with a finite charging energy.

cond-mat.mes-hall↗

arXiv2015

Probing Majorana Physics in Quantum Dot Shot Noise Experiments

We consider a quantum dot coupled to a topological superconductor and two normal leads and study transport properties of the system. Using Keldysh path-integral approach, we study current fluctuations (shot noise) within the low-energy effective theory. We argue that the combination of the tunneling conductance and the shot noise through a quantum dot allows one to distinguish between the topological (Majorana) and non-topological (e.g., Kondo) origin of the zero-bias conduction peak. Specifically, we show that, while the tunneling conductance might exhibit zero-bias anomaly due to Majorana or Kondo physics, the shot noise is qualitatively different in the presence of Majorana zero modes.

cond-mat.mes-hall↗

arXiv2015

Impurity-induced bound states in superconductors with spin-orbit coupling

We study the effect of strong spin-orbit coupling (SOC) on bound states induced by impurities in superconductors. The presence of spin-orbit coupling breaks the $\mathbb{SU}(2)$-spin symmetry and causes the superconducting order parameter to have generically both singlet (s-wave) and triplet (p-wave) components. We find that in the presence of SOC the spectrum of Yu-Shiba-Rusinov (YSR) states is qualitatively different in s-wave and p-wave superconductor, a fact that can be used to identify the superconducting pairing symmetry of the host system. We also predict that in the presence of SOC the spectrum of the impurity-induced bound states depends on the orientation of the magnetic moment $\bf{S}$ of the impurity and, in particular, that by changing the orientation of $\bf{S}$ the fermion-parity of the lowest energy bound state can be tuned. We then study the case of a dimer of magnetic impurities and show that in this case the YSR spectrum for a p-wave superconductor is qualitatively very different from the one for an s-wave superconductor even in the limit of vanishing SOC. Our predictions can be used to distinguish the symmetry of the order parameter and have implications for the Majorana proposals based on chains of magnetic atoms placed on the surface of superconductors with strong spin-orbit coupling.

cond-mat.supr-con↗

arXiv2015

Majorana zero modes choose Euler numbers - revealed by full counting statistics

We study transport properties of a quantum dot coupled to a Majorana zero mode and two normal leads. We investigate the full counting statistics of charge tunneling events which allows one to extract complete information about current fluctuations. Using a Keldysh path-integral approach, we compute the cumulant generating function. We first consider a noninteracting spinless regime, and find that for the symmetric dot-lead couplings, the zero-frequency cumulants exhibit a universal pattern of Euler numbers, independent of the microscopic parameters. For a spinful case, the Coulomb interaction effects are discussed for both strong interaction (single-electron occupancy regime) and weak interactions (perturbative regime). Compared to the case without Majorana coupling, we show that, while the tunneling conductance might exhibit zero-bias anomaly, the full counting statistics is qualitatively different in the presence of the Majorana coupling.

cond-mat.mes-hall↗

arXiv2014

Interplay between Kondo and Majorana interactions in quantum dots

We study the properties of a quantum dot coupled to a one-dimensional topological superconductor and a normal lead and discuss the interplay between Kondo and Majorana-induced couplings in quantum dot. The latter appears due to the presence of Majorana zero-energy modes localized at the ends of the one-dimensional superconductor. We investigate the phase diagram of the system as a function of Kondo and Majorana interactions using a renormalization-group analysis, a slave-boson mean-field theory and numerical simulations using the density-matrix renormalization group method. We show that, in addition to the well-known Kondo fixed point, the system may flow to a new fixed point controlled by the Majorana-induced coupling which is characterized by non-trivial correlations between a localized spin on the dot and the fermion parity of the topological superconductor and normal lead. We compute several measurable quantities such as differential tunneling conductance and impurity spin susceptibility which highlight some peculiar features characteristic to the Majorana fixed point.

cond-mat.mes-hall↗

arXiv2014

Soft superconducting gap in semiconductor-based Majorana nanowires

We develop a theory for the proximity effect in superconductor-semiconductor-normal metal tunneling structures, which have recently been extensively studied experimentally, leading to the observation of transport signatures consistent with the predicted zero-energy Majorana bound states. We show that our model for the semiconductor nanowire having multiple occupied subbands with different transmission probabilities through the barrier reproduces the observed "soft-gap" behavior associated with substantial subgap tunneling conductance. We study the manifestations of the soft gap phenomenon both in the tunneling conductance and in local density of states measurements and discuss the correlations between these two quantities. We emphasize that the proximity effect associated with the hybridization between low-lying states in the multiband semiconductor and the normal metal states in the lead is an intrinsic effect leading to the soft gap problem. In addition to the intrinsic contribution, there may be extrinsic effects, such as, for example, interface disorder, exacerbating the soft gap problem. Our work establishes the generic possibility of an ubiquitous presence of an intrinsic soft gap in the superconductor-semiconductor-normal metal tunneling transport conductance induced by the inverse proximity effect of the normal metal.

cond-mat.supr-con↗

arXiv2014

Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states

We theoretically obtain the phase diagram of localized magnetic impurity spins arranged in a one-dimensional chain on top of a one- or two-dimensional electron gas with Rashba spin-orbit coupling. The interactions between the spins are mediated by the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism through the electron gas. Recent work predicts that such a system may intrinsically support topological superconductivity when a helical spin-density wave is formed in the spins, and superconductivity is induced in the electron gas. We analyze, using both analytical and numerical techniques, the conditions under which such a helical spin state is stable in a realistic situation in the presence of disorder. We show that it becomes unstable towards the formation of (anti) ferromagnetic domains if the disorder in the impurity spin positions $δR$ becomes comparable with the Fermi wave length. We also examine the stability of the helical state against Gaussian potential disorder in the electronic system using a diagrammatic approach. Our results suggest that in order to stabilize the helical spin state, and thus the emergent topological superconductivity, a sufficiently strong Rashba spin-orbit coupling, giving rise to Dzyaloshinskii-Moriya interactions, is required.

cond-mat.mes-hall↗

arXiv2013

Origin and Transport Signatures of Spin-Orbit Interactions in One- and Two-Dimensional SrTiO$_3$-Based Heterostructures

We study origin of Rashba spin-orbit interaction at SrTiO$_3$ surfaces and LaAlO$_3$/SrTiO$_3$ interfaces by considering the interplay between atomic spin-orbit coupling and inversion asymmetry at the surface or interface. We show that, in a simple tight-binding model involving 3d $t_{2g}$ bands of Ti ions, the induced spin-orbit coupling in the $d_{xz}$ and $d_{yz}$ bands is cubic in momentum whereas the spin-orbit interaction in the $d_{xy}$ band has linear momentum dependence. We also find that the spin-orbit interaction in one-dimensional channels at LaAlO$_3$/SrTiO$_3$ interfaces is linear in momentum for all bands. We discuss implications of our results for transport experiments on SrTiO$_3$ surfaces and LaAlO$_3$/SrTiO$_3$ interfaces. In particular, we analyze the effect of a given spin-orbit interaction term on magnetotransport of LaAlO$_3$/SrTiO$_3$ by calculating weak anti-localization corrections to the conductance and to universal conductance fluctuations.

cond-mat.str-el↗

arXiv2013

Transport properties of topological superconductor-Luttinger liquid junctions: a real-time Keldysh approach

Inspired by a recent experimental observation of the zero-bias tunneling conductance in superconductor-semiconductor nanowire devices, we consider here transport properties of the junctions consisting of a nanowire (Luttinger liquid) coupled to a topological superconductor characterized by the presence of Majorana zero-energy end states. The presence of the Majorana modes leads to a quantization of the zero-bias tunneling conductance at zero temperature. In order to understand this phenomenon, we have developed a framework, based on real-time Keldysh technique, which allows one to compute tunneling conductance at finite temperature and voltage in a realistic experimental setup. Our approach allows one to understand this transport phenomenon from a more general perspective by including the effect of interactions in the nanowire, which sometimes results in a drastic departure from the non-interacting predictions. Thus, our results provide a key insight for the tunneling experiments aiming at detecting Majorana particles in one-dimensional nanowire devices.

cond-mat.supr-con↗