Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session M19: Majorana Zero Modes in Topological Superconductors |
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Sponsoring Units: DCMP Chair: Valerio Peri, Caltech Room: Room 211 |
Wednesday, March 8, 2023 8:00AM - 8:12AM |
M19.00001: Fate of Majorana zero modes in a one-dimensional superconductor with fixed charge Ivar Martin, Kartiek Agarwal, Rohith Sajith While the properties of Majorana zero modes are well understood within BCS mean-field theory, it remains an ongoing challenge to demonstrate these excitations in a real condensed-matter setting. Since such systems have a fixed number of particles, it is a closely-related theoretical question whether the exponential localization and non-Abelian statistics of Majorana particles survive in a manifestly particle number conserving regime. Utilizing combinatorial arguments, we analytically study an interacting, number-conserving model on a single wire that shows signatures of topological edge excitations in edge-to-bulk correlation functions and its entanglement spectrum. With exact diagonalization and DMRG, we numerically explore an exchange and braiding protocol to verify whether the number-conserving quasiparticles show non-trivial statistics. |
Wednesday, March 8, 2023 8:12AM - 8:24AM |
M19.00002: Possibility of topological superconductivity in one-dimensional systems Oladunjoye A Awoga In this work we study the stability of topological one-dimensional superconductor in the presence of disorder and how to control the hybridization of the Majorana bound states at the ends of the topological superconductors. We find a regime where the topological phase is robust against disorder as well as control knobs for the control of Majorana hybrodization. |
Wednesday, March 8, 2023 8:24AM - 8:36AM |
M19.00003: Proximity-induced zero-energy states indistinguishable from topological edge states Igor J Califrer, Poliana H Penteado, J. Carlos Egues, Wei Chen When normal metals (NMs) are attached to topological insulators or topological superconductors, the quantum states in these finite adjacent materials can intermix and affect the topological zero-energy edge state. To address this issue, we consider three prototype lattice models, namely a Su-Schrieffer-Heeger/NM, a Kitaev/NM, and a Chern insulator/NM. For all these junctions, we find that there exist trivial zero-energy states caused by fine-tuning the chemical potential in the NM that can percolate into the topological region, thus mimicking a topological state. Interestingly, these fine-tuned states cannot cross the true Majorana end modes of the Kitaev/NM model as protected by the particle-hole symmetry, but the crossing is allowed in the Su-Schrieffer-Heeger/NM due to breaking of the chiral symmetry. In addition, even in Chern insulators where the topological edge state self-generates a symmetry eigenvalue, such a fine-tuned zero-energy state can still occur. Our results indicate that when a topological material is attached to a metallic layer, one has to be cautious as to identify true topological edge states merely from their energy spectra and wave function profiles near the interface, since it may be obscured by these fine-tuned zero energy states. |
Wednesday, March 8, 2023 8:36AM - 8:48AM |
M19.00004: Critical current as a signature of bulk topological phase transition in a quasi-1D Rashba nanowire Tatiana de Picoli Ferreira, Jukka Vayrynen, Ian Wojtowicz In a normal phase of a Rashba spin-orbit coupled semiconductor nanowire, the measurement of conductance can probe the bulk helical gap opened by a Zeeman field along the wire. However, for a nanowire with proximity-induced superconductivity, we cannot rely on the measurement of two-terminal conductance to probe a bulk topological phase transition. Here, we consider a Rashba spin-orbit coupled superconductor in a Zeeman field in different confinement potentials that allow the system to have single or multiple channels. To study the helical topological gap in this superconducting system, we propose to use another physical observable, the critical current. We consider the limit where the critical current is determined by depairing conditions (closing of quasiparticle excitation gap). We use a low-energy model to calculate the critical current analytically and a tight-binding approximation to verify and go beyond the analytical calculation. Our results quantify how the topological gap can be estimated from the critical current as a function of chemical potential and magnetic field. |
Wednesday, March 8, 2023 8:48AM - 9:00AM |
M19.00005: Optimizing Transport of Majorana Zero Modes in One-Dimensional Topological Superconductors Bill P Truong, Tami Pereg-Barnea, Kartiek Agarwal Topological quantum computing is based on the notion of braiding non-Abelian anyons, such as Majorana zero modes (MZMs), to perform gate operations. Braiding protocols involving MZMs are often envisioned on networks of topological superconducting wires with a key ingredient being the way by which MZMs are shuttled. We consider the “piano key” approach [1], where MZMs are transported by using local electric gates to tune sections (“keys”) of a wire between trivial and topological phases. We numerically simulate this transport on a single wire and calculate the diabatic error, defined to be the probability of transitions between the ground state manifold and excited states. We determine that the diabatic error typically improves when transport is facilitated by using multiple keys, however this advantage is lost when an abundance of keys is used. We demonstrate that there exists an optimal number of keys and establish its dependence on parameters. Furthermore, we show that the behaviour of the diabatic error can be adequately described by usual Landau-Zener physics with corrections originating from the specific model used to tune each key. |
Wednesday, March 8, 2023 9:00AM - 9:12AM |
M19.00006: Electron teleportation in a $p$-wave superconducting Kitaev wire with Coulomb interaction. Mehdi Zarea, James A Sauls, Ivar Martin We study the problem of electron teleportation in a $p$-wave superconducting wire [1] as a function of the Coulomb interaction strength. We calculate the change in the probability $delta ho$ of finding an electron at one edge of the wire when another electron is injected at the other edge site. In the absence of Coulomb interaction there is no change in this probability. Including the global charging energy for the wire [2] makes $delta ho$ finite but length-dependent, tending to zero with increasing wire length. We also investigate a modified model in which the Coulomb charging energy is included only between the two edge sites. For this model the change in the probability becomes length-independent. However unlike the canonical spin-teleportation i) this effect is transient (time-dependent) ii) it relies on existence of instantaneous Coulomb correlation between edge sites iii) the value of $delta ho$ is lower than the corresponding normal metal wire. These limitations argue for impossibility of teleportation via Majorana fermions even in the presence of Coulomb interactions. |
Wednesday, March 8, 2023 9:12AM - 9:24AM |
M19.00007: Hunting for the topological Kondo effect: tensor network simulations of transport phenomena in Coulomb-blockaded topological superconductors. Matteo M Wauters, Michele Burrello, Chia-Min Chung Majorana zero-energy modes lie at the center of the efforts for creating topologically protected qubits but, so far, they eluded a clear experimental detection due to the difficulty of distinguishing them from Andreev bound states. An unambiguous signature of their presence is the appearance of the topological Kondo effect (TKE) in a Coulomb-blockaded device connected with more than two metallic leads each coupled with an individual Majorana mode. The TKE emerges as an effective low-energy description of such devices via a renormalization group approach but a quantitative microscopic characterization of the energy scales at which it appears is still missing. In our work, we propose an analysis of transport phenomena in Coulomb-blockaded topological superconductors based on tensor network simulations of their real-time dynamics after a quantum quench. We combine a Wilson chain construction for the leads and a mean-field BCS description for the superconducting scatterers, alongside a bosonic auxiliary degree of freedom to keep track of the charge of the device. This approach allows for the exploration of the strong coupling regime and nonperturbative transport effects linked to the presence of Majorana modes such as the quantization of the conductance in a two-terminal device. When more than two leads are present, each coupled with a single Majorana mode, we observe an anomalous current that suggests the emergence of a topological Kondo phase. |
Wednesday, March 8, 2023 9:24AM - 9:36AM |
M19.00008: Nonlocality of local Andreev reflection as a signature of topological superconductivity Rodrigo A Dourado, Poliana H Penteado, J. Carlos Egues We propose a method of distinguishing trivial and topological phases in Majorana wires by exploiting a peculiar nonlocality of the Majorana-mediated local Andreev reflection (LAR). To this end, we calculate the conductance and the local density of states (LDOS) in a three-terminal device. By combining the scattering matrix formalism and the Green's function approach, we show that in the trivial phase the local conductances are not affected by the decrease in the coupling to the normal lead at the opposite end of the wire. In the topological phase, however, LAR is suppressed by this lead-asymmetry. We explain this by showing that a zero-energy dip in the LDOS develops as the asymmetry in the couplings to the left and right normal leads increases. In addition, the local conductances show the exact same dependence on the lead-asymmetry in the presence of Majorana zero modes (MZMs), in stark contrast to trivial subgap states arising from inhomogeneities in the wire. Furthermore, by exploiting the control over the LDOS afforded by the lead-asymmetry, we propose a Majorana-based transistor in a Majorana wire-quantum dot setup [1]. Our work shows a distinctive signature of the Majorana nonlocality in terms of nonlocal effects on LAR, thus providing an additional diagnostic tool for a conclusive observation of MZMs. |
Wednesday, March 8, 2023 9:36AM - 9:48AM |
M19.00009: Dislocation and Vortex Majorana Modes in Higher-Order Topological Superconductors Aidan Burleson, Lun-Hui Hu, Ruixing Zhang In this work, we show that an inversion-symmetric higher-order topological superconductor (HOTSC) features a new non-Abelian Majorana response to the insertion of either a lattice dislocation or a superconducting vortex. As a proof of concept, we consider a minimal lattice model of a doped topological insulator with an odd-parity pairing symmetry. A plethora of topological superconducting phases is found by tuning the chemical potential, including those with 1st-order, 2nd-order, and weak topologies. In particular, the 2nd-order topological phase features 0D Majorana zero modes at the ends of a dislocation/vortex line, while 1D helical Majorana modes will show up in the same defect of the 1st-order phase. Candidate materials and experimental consequences for the defect Majorana physics are also discussed. |
Wednesday, March 8, 2023 9:48AM - 10:00AM |
M19.00010: Topological Superconducting Vortex From Trivial Electronic Bands Lun-Hui Hu, Rui-Xing Zhang Superconducting vortices are promising traps to confine non-Abelian Majorana quasi-particles. It has been widely believed that bulk-state topology, of either normal-state or Cooper-paired electron wavefunctions, is crucial for enabling Majorana zero modes. This common belief has shaped two major search directions for Majorana modes, in either intrinsic topological superconductors or trivial superconductors with topological electronic band structures. Here we show that the Majorana-carrying vortex is not a privilege of bulk-state topology, but can arise from superconducting trivial bands as well. Notably, even for superconductors with topological band structures, the existence of ubiquitous low-energy trivial bands can significantly change the conclusion of vortex Majorana physics that is based on simplified topological-band-only models. We predict that the trivial bands in superconducting HgTe-class materials are responsible for inducing anomalous vortex topology that goes beyond any existing theoretical paradigms. A feasible scheme of strain-controlled Majorana engineering and a new experimental "smoking gun" are also discussed. Our work provides new guidelines for Majorana search in general superconductors. |
Wednesday, March 8, 2023 10:00AM - 10:12AM |
M19.00011: Theory of the Little-Parks effect in spin-triplet superconductors Chengyun Hua, Eugene F Dumitrescu, Gábor Halász The celebrated Little-Parks effect in thin mesoscopic superconducting rings has recently gained great attention due to its potential to probe half-quantum vortices in spin-triplet superconductors. However, there remain puzzles like how to stabilize these half-quantum vortices and what time scale of intrinsic resistive fluctuations between stable states is observable in a spin-triplet superconducting ring. Here, we theoretically investigate the magnetoresistance of mesoscopic spin-triplet superconducting rings resulting from thermal vortex tunneling below the critical temperature based on the Ginzburg- Landau theory. Assuming a spin triplet superconductor with predominantly (↑↑) and (↓↓) Cooper pairs, we show that a coupling term that imposes a penalty to the charge supercurrents is necessary to stabilize the half quantum vortex fluxoid states. We solve the differential Ginzburg-Landau equations of such a spin-triplet superconducting ring to obtain the saddle point configuration of the order parameters, from which we calculate the decay rate for persistent current in a ring due to thermal vortex tunneling. We identify a characteristic two peak Little parks oscillation in resistance. We analyze the differentiablity criterion for the two peak structure which is maximized for large inter-spin coupling, applied magnetic field, and a very large thin-wall superconducting ring close to the critical temperature. |
Wednesday, March 8, 2023 10:12AM - 10:24AM |
M19.00012: Bulk-Vortex Correspondence of Higher-Order Topological Superconductors Ruixing Zhang Vortices in chiral topological superconductors are known for trapping Majorana zero modes as a signature response to their bulk-state topologies. In this work, we establish a similar bulk-vortex correspondence for two-dimensional Cn-protected class D higher-order topological superconductors, in which a quantum vortex will universally trap a pair of Cn-protected Majorana bound states. This intriguing one-to-one mapping between anomalous vortex modes and higher-order topology can be systematically derived through a model-independent patch construction approach. As proof of concept, we present an exactly solvable model to confirm the proposed vortex Majorana modes. Our theory establishes vortices as an unprecedented experimental measure of higher-order topology in superconductors. |
Wednesday, March 8, 2023 10:24AM - 10:36AM |
M19.00013: Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D Naren Manjunath, Vladimir Calvera, Maissam Barkeshli In (1+1)D topological phases, unpaired Majorana zero modes (MZMs) can arise only if the internal symmetry group Gf of the ground state splits as Gf = Gb × Z2f, where Z2f is generated by fermion parity, (-1)F. In contrast, (2+1)D topological superconductors (TSC) can host unpaired MZMs at defects even when Gf is not of the form Gb × Z2f. In this paper we study how Gf together with the chiral central charge c- strongly constrain the existence of unpaired MZMs and the quantum numbers of symmetry defects. Our results utilize a recent algebraic characterization of (2+1)D invertible fermionic topological states, which provides a non-perturbative approach based on topological quantum field theory, beyond free fermions. We study physically relevant groups such as U(1)f × H,SU(2)f × H, U(2)f × H, generic Abelian groups, as well as more general compact Lie groups, antiunitary symmetries and crystalline symmetries. We present an algebraic formula for the fermionic crystalline equivalence principle, which gives an equivalence between states with crystalline and internal symmetries. In light of our theory, we discuss several previously proposed realizations of unpaired MZMs in TSC materials such as Sr2RuO4, transition metal dichalcogenides and iron superconductors, in which crystalline symmetries are often important; in some cases we present additional predictions for the properties of these models. |
Wednesday, March 8, 2023 10:36AM - 10:48AM |
M19.00014: Creating and detecting poor man's Majorana bound states in interacting quantum dots Athanasios Tsintzis, Ruben Seoane Souto, Martin Leijnse We theoretically study a system of two quantum dots (QDs) coupled via a third – coupler – QD which is additionally proximitized by an s-wave superconductor. For a wide parameter range, the system can be tuned to sweet spots with a doubly-degenerate ground state, as switches between even- and odd-parity ground states are found to be ubiquitous. The necessary ingredients are a) a finite magnetic field to break the spin degeneracy and b) spin-orbit interaction to mix the spin species. The sweet spots harbor poor man’s Majorana bound states (Phys. Rev. B 86, 134528, 2012) whose quality is quantified by calculating the Majorana polarizations of the degenerate ground states (Phys. Rev. B 101, 125431, 2020). The QDs’ electrochemical potentials are the control knobs utilized to reach the sweet spots and local and non-local conductance calculations could provide a useful map for experimentalists navigating the parameter space. The above system can be realized in a semiconductor 2D electron gas or nanowire with gate- or epitaxially-defined QDs coupled to a grounded superconductor. This work provides a path towards near-future demonstration of nonabelian and non-local Majorana properties, with possible (more long-term) applications in topologically protected quantum computing. |
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