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Zakharov, V. A. (author), Bozkurt, A.M. (author), Akhmerov, A.R. (author), Oriekhov, D. (author)We develop a theory of magnetic breakdown (MB) near high-order saddle points in the dispersions of two-dimensional materials, where two or more semiclassical cyclotron orbits approach each other. MB occurs due to quantum tunneling between several trajectories, which leads to nontrivial scattering amplitudes and phases. We show that for any...journal article 2024
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Luna, Juan Daniel Torres (author), Rangaswamy Kuppuswamy, S.K. (author), Akhmerov, A.R. (author)Braiding of Majorana states demonstrates their non-Abelian exchange statistics. One implementation of braiding requires control of the pairwise couplings between all Majorana states in a trijunction device. To have adiabaticity, a trijunction device requires the desired pair coupling to be sufficiently large and the undesired couplings to...journal article 2024
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Spring, H. (author), Könye, Viktor (author), Gerritsma, F.A. (author), Fulga, Ion Cosma (author), Akhmerov, A.R. (author)Disorder can localize the eigenstates of one-dimensional non-Hermitian systems, leading to an Anderson transition with a critical exponent of 1. We show that, due to the lack of energy conservation, the dynamics of individual, real-space wave packets follows a different behavior. Both transitions between localization and unidirectional...journal article 2024
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Araya Day, I.M. (author), Varentcova, A.S. (author), Varjas, D. (author), Akhmerov, A.R. (author)We derive a Z4 topological invariant that extends beyond symmetry eigenvalues and Wilson loops and classifies two-dimensional insulators with a C4T symmetry. To formulate this invariant, we consider an irreducible Brillouin zone and constrain the spectrum of the open Wilson lines that compose its boundary. We fix the gauge ambiguity of the...journal article 2023
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Melo, André (author), Mr Tanev, T. (author), Akhmerov, A.R. (author)Josephson junctions in a two-dimensional electron gas with spin-orbit coupling are a promising candidate to realize topological superconductivity. While it is known that the geometry of the junction strongly influences the size of the topological gap, the question of how to construct optimal geometries remains unexplored. We introduce a...journal article 2023
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Bozkurt, A.M. (author), Brookman, Jasper (author), Fatemi, Valla (author), Akhmerov, A.R. (author)We present a systematic method to design arbitrary energy-phase relations using parallel arms of two series Josephson tunnel junctions each. Our approach employs Fourier engineering in the energy-phase relation of each arm and the position of the arms in real space. We demonstrate our method by engineering the energy-phase relation of a near...journal article 2023
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Vilkelis, K. (author), Wang, L. (author), Akhmerov, A.R. (author)Recent measurements of the out-of-plane magnetoresistance of delafossites (PdCoO<sub>2</sub> and PtCoO<sub>2</sub>) observed oscillations closely resembling the Aharonov-Bohm effect. Here, we show that the magnetoresistance oscillations are explained by the Bloch-like oscillations of the out-of-plane electron trajectories. We develop a...journal article 2023
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De Almeida Nascimento e Melo, A.A. (author), Fatemi, Valla (author), Akhmerov, A.R. (author)The multi-terminal Josephson effect allows DC supercurrent to flow at finite commensurate voltages. Existing proposals to realize this effect rely on nonlocal Andreev processes in superconductor-normal-superconductor junctions. However, this approach requires precise control over microscopic states and is obscured by dissipative current. We...journal article 2022
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Oriekhov, D. O. (author), Osterholt, T. T. (author), Vakhtel, T. (author), Akhmerov, A.R. (author), Beenakker, C. W.J. (author)We consider the propagation of electrons in a lattice with an anisotropic dispersion in the x-y plane (lattice constant a), such that it supports open orbits along the x axis in an out-of-plane magnetic field B. We show that a point source excites a "breathing mode,"a state that periodically spreads out and refocuses after having propagated...journal article 2022
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Araya Day, I.M. (author), Akhmerov, A.R. (author), Varjas, Dániel (author)We show that topological defects in quadrupole insulators do not host quantized fractional charges, contrary to what their Wannier representation indicates. In particular, we test the charge quantization hypothesis based on the Wannier representation of a disclination and a parametric defect. Since disclinations necessarily strain the lattice...journal article 2022
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Rigotti Manesco, A.L. (author), Flór, Ian Matthias (author), Liu, C. (author), Akhmerov, A.R. (author)We simulate a hybrid superconductor-graphene device in the quantum Hall regime to identify the origin of downstream resistance oscillations in a recent experiment [Zhao et al. Nature Physics 16, (2020)]. In addition to the previously studied Mach-Zehnder interference between the valley-polarized edge states, we consider disorder-induced...journal article 2022
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Fatemi, Valla (author), Akhmerov, A.R. (author), Bretheau, Landry (author)We introduce Weyl Josephson circuits: small Josephson junction circuits that simulate Weyl band structures. We first formulate a general approach to design circuits that are analogous to Bloch Hamiltonians of a desired dimensionality and symmetry class. We then construct and analyze a six-junction device that produces a three-dimensional (3D)...journal article 2021
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Pöyhönen, K.K. (author), Varjas, D. (author), Wimmer, M.T. (author), Akhmerov, A.R. (author)Platforms for creating Majorana quasiparticles rely on superconductivity and breaking of time-reversal symmetry. By studying continuous deformations to known trivial states, we find that the relationship between superconducting pairing and time reversal breaking imposes rigorous bounds on the topology of the system. Applying these bounds to s...journal article 2021
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Perez-Piskunow, Pablo M. (author), Bovenzi, Nicandro (author), Akhmerov, A.R. (author), Breitkreiz, Maxim (author)In Weyl semimetals, the application of parallel electric and magnetic fields leads to valley polarization-an occupation disbalance of valleys of opposite chirality-a direct consequence of the chiral anomaly. In this work, we present numerical tools to explore such nonequilibrium effects in spatially confined three-dimensional systems with a...journal article 2021
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Spring, H. (author), Akhmerov, A.R. (author), Varjas, D. (author)Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous topological materials, where the Hamiltonian is invariant on average under reflection over any axis due to...journal article 2021
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Akhmerov, A.R. (author), Bonet-Monroig, Xavier (author), Fatemi, Valla (author), Greplová, E. (author), Van Nieuwenburg, Evert (author), Seradjeh, Babak (author), Varjas, D. (author)With the lockdowns caused by the COVID-19 pandemic, researchers turn to online conferencing. While posing new challenges, this format also brings multiple advantages. We argue that virtual conferences will become part of our regular scientific communication and invite community members to join the movement.journal article 2020
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Laeven, T.M. (author), Nijholt, B. (author), Wimmer, M.T. (author), Akhmerov, A.R. (author)High density superconductor-semiconductor-superconductor junctions have a small induced superconducting gap due to the quasiparticle trajectories with a large momentum parallel to the junction having a very long flight time. Because a large induced gap protects Majorana modes, these long trajectories constrain Majorana devices to a low...journal article 2020
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Computation of topological phase diagram of disordered Pb1-xSnxTe using the kernel polynomial methodVarjas, D. (author), Fruchart, Michel (author), Akhmerov, A.R. (author), Perez Piskunow, P.M. (author)We present an algorithm to determine topological invariants of inhomogeneous systems, such as alloys, disordered crystals, or amorphous systems. Based on the kernel polynomial method, our algorithm allows us to study samples with more than 107 degrees of freedom. Our method enables the study of large complex compounds, where disorder is...journal article 2020
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De Almeida Nascimento e Melo, A.A. (author), Rubbert, S.H.P. (author), Akhmerov, A.R. (author)We propose a new setup for creating Majorana bound states in a two-dimensional electron gas Josephson junction. Our proposal relies exclusively on a supercurrent parallel to the junction as a mechanism of breaking time-reversal symmetry. We show that combined with spin-orbit coupling, supercurrents induce a Zeeman-like spin splitting. Further,...journal article 2019
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Beenakker, C.W.J. (author), Baireuther, P. (author), Herasymenko, Y. (author), Adagideli, I. (author), Wang, L. (author), Akhmerov, A.R. (author)Majorana zero modes in a superconductor are midgap states localized in the core of a vortex or bound to the end of a nanowire. They are anyons with non-Abelian braiding statistics, but when they are immobile one cannot demonstrate this by exchanging them in real space and indirect methods are needed. As a real-space alternative, we propose to...journal article 2019