1
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Midlik Š, Gablech I, Goleňa M, Brodský J, Schmoranzer D. Parylene-bonded micro-fluidic channels for cryogenic experiments at superfluid He-4 temperatures. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2024; 95:033901. [PMID: 38426903 DOI: 10.1063/5.0162532] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 02/06/2024] [Indexed: 03/02/2024]
Abstract
We present the manufacturing process of a (24.5 × 100) μm2-sized on-chip flow channel intended for flow experiments with normal and superfluid phases of 4He and showcase such a proof-of-concept experiment. This work proves the suitability of chip-to-chip bonding using a thin layer of Parylene-C for cryogenic temperatures as a simpler alternative to other techniques, such as anodic bonding. A monocrystalline silicon chip embeds the etched meander-shaped micro-fluidic channel and a deposited platinum heater and is bonded to a Pyrex glass top. We test the leak tightness of the proposed bonding method for superfluid 4He, reaching temperatures of ≈1.6 K and evaluate its possible effects on flow experiments. We demonstrate that powering an on-chip platinum heater affects the superfluid flow rate by local overheating of a section of the micro-fluidic channel.
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Affiliation(s)
- Š Midlik
- Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
| | - I Gablech
- Department of Microelectronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic
| | - M Goleňa
- Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
| | - J Brodský
- Department of Microelectronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic
| | - D Schmoranzer
- Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
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2
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Nguyen MD, Simon J, Scott JW, Zimmerman AM, Tsai YCC, Halperin WP. Orbital-flop transition of superfluid 3He in anisotropic silica aerogel. Nat Commun 2024; 15:201. [PMID: 38172106 PMCID: PMC10764773 DOI: 10.1038/s41467-023-44557-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Accepted: 12/12/2023] [Indexed: 01/05/2024] Open
Abstract
Superfluid 3He is a paradigm for odd-parity Cooper pairing, ranging from neutron stars to uranium-based superconducting compounds. Recently it has been shown that 3He, imbibed in anisotropic silica aerogel with either positive or negative strain, preferentially selects either the chiral A-phase or the time-reversal-symmetric B-phase. This control over basic order parameter symmetry provides a useful model for understanding imperfect unconventional superconductors. For both phases, the orbital quantization axis is fixed by the direction of strain. Unexpectedly, at a specific temperature Tx, the orbital axis flops by 90∘, but in reverse order for A and B-phases. Aided by diffusion limited cluster aggregation simulations of anisotropic aerogel and small angle X-ray measurements, we are able to classify these aerogels as either "planar" and "nematic" concluding that the orbital-flop is caused by competition between short and long range structures in these aerogels.
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Affiliation(s)
- M D Nguyen
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208, USA.
| | - Joshua Simon
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208, USA
| | - J W Scott
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208, USA
| | - A M Zimmerman
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208, USA
| | - Y C Cincia Tsai
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208, USA
| | - W P Halperin
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208, USA.
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3
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Autti S, Haley RP, Jennings A, Pickett GR, Poole M, Schanen R, Soldatov AA, Tsepelin V, Vonka J, Zavjalov VV, Zmeev DE. Transport of bound quasiparticle states in a two-dimensional boundary superfluid. Nat Commun 2023; 14:6819. [PMID: 37919295 PMCID: PMC10622538 DOI: 10.1038/s41467-023-42520-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 10/13/2023] [Indexed: 11/04/2023] Open
Abstract
The B phase of superfluid 3He can be cooled into the pure superfluid regime, where the thermal quasiparticle density is negligible. The bulk superfluid is surrounded by a quantum well at the boundaries of the container, confining a sea of quasiparticles with energies below that of those in the bulk. We can create a non-equilibrium distribution of these states within the quantum well and observe the dynamics of their motion indirectly. Here we show that the induced quasiparticle currents flow diffusively in the two-dimensional system. Combining this with a direct measurement of energy conservation, we conclude that the bulk superfluid 3He is effectively surrounded by an independent two-dimensional superfluid, which is isolated from the bulk superfluid but which readily interacts with mechanical probes. Our work shows that this two-dimensional quantum condensate and the dynamics of the surface bound states are experimentally accessible, opening the possibility of engineering two-dimensional quantum condensates of arbitrary topology.
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Affiliation(s)
- Samuli Autti
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK.
| | - Richard P Haley
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - Asher Jennings
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
- RIKEN Center for Quantum Computing, RIKEN, Wako, 351-0198, Japan
| | - George R Pickett
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - Malcolm Poole
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - Roch Schanen
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - Arkady A Soldatov
- P.L. Kapitza Institute for Physical Problems of RAS, 119334, Moscow, Russia
| | - Viktor Tsepelin
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - Jakub Vonka
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
- Paul Scherrer Institute, Forschungsstrasse 111, 5232, Villigen PSI, Switzerland
| | | | - Dmitry E Zmeev
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
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4
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Baten RN, Tian Y, Smith EN, Mueller EJ, Parpia JM. Observation of suppressed viscosity in the normal state of 3He due to superfluid fluctuations. Nat Commun 2023; 14:5834. [PMID: 37730714 PMCID: PMC10511454 DOI: 10.1038/s41467-023-41422-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 08/31/2023] [Indexed: 09/22/2023] Open
Abstract
Evidence of fluctuations in transport have long been predicted in 3He. They are expected to contribute only within 100μK of Tc and play a vital role in the theoretical modeling of ordering; they encode details about the Fermi liquid parameters, pairing symmetry, and scattering phase shifts. It is expected that they will be of crucial importance for transport probes of the topologically nontrivial features of superfluid 3He under strong confinement. Here we characterize the temperature and pressure dependence of the fluctuation signature, by monitoring the quality factor of a quartz tuning fork oscillator. We have observed a fluctuation-driven reduction in the viscosity of bulk 3He, finding data collapse consistent with the predicted theoretical behavior.
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Affiliation(s)
- Rakin N Baten
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA
| | - Yefan Tian
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA
| | - Eric N Smith
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA
| | - Erich J Mueller
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA
| | - Jeevak M Parpia
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA.
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5
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Wu H, Sauls JA. Weyl Fermions and broken symmetry phases of laterally confined 3He films. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:495402. [PMID: 37625425 DOI: 10.1088/1361-648x/acf42b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2023] [Accepted: 08/25/2023] [Indexed: 08/27/2023]
Abstract
Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D)3He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum,Lz=(N/2)ℏ, forN/2Cooper pairs. The power law suppression of the angular momentum,Lz(T)≃(N/2)ℏ[1-23(πT/Δ)2]for0⩽T≪Tc, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid3He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry atDc2∼16ξ0. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement lengthD→Dc2. The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral 'polar phase' atDc1∼9ξ0, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.
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Affiliation(s)
- Hao Wu
- Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, United States of America
| | - J A Sauls
- Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, United States of America
- Hearne Institute of Theoretical Physics, Louisiana State University, Baton Rouge, LA 70803, United States of America
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6
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Kamppinen T, Rysti J, Volard MM, Volovik GE, Eltsov VB. Topological nodal line in superfluid 3He and the Anderson theorem. Nat Commun 2023; 14:4276. [PMID: 37460543 DOI: 10.1038/s41467-023-39977-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Accepted: 07/06/2023] [Indexed: 07/20/2023] Open
Abstract
Superconductivity and superfluidity with anisotropic pairing-such as d-wave in cuprates and p-wave in superfluid 3He-are strongly suppressed by impurities. Meanwhile, for applications, the robustness of Cooper pairs to disorder is highly desired. Recently, it has been suggested that unconventional systems become robust if the impurity scattering mixes quasiparticle states only within individual subsystems obeying the Anderson theorem that protects conventional superconductivity. Here, we experimentally verify this conjecture by measuring the temperature dependence of the energy gap in the polar phase of superfluid 3He. We show that oriented columnar non-magnetic defects do not essentially modify the energy spectrum, which has a Dirac nodal line. Although the scattering is strong, it preserves the momentum along the length of the columns and forms robust subsystems according to the conjecture. This finding may stimulate future experiments on the protection of topological superconductivity against disorder and on the nature of topological fermionic flat bands.
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Affiliation(s)
- T Kamppinen
- Department of Applied Physics, Aalto University, POB 15100, FI-00076, AALTO, Finland
| | - J Rysti
- Department of Applied Physics, Aalto University, POB 15100, FI-00076, AALTO, Finland
| | - M-M Volard
- Department of Applied Physics, Aalto University, POB 15100, FI-00076, AALTO, Finland
| | - G E Volovik
- Department of Applied Physics, Aalto University, POB 15100, FI-00076, AALTO, Finland
- Landau Institute for Theoretical Physics, 142432, Chernogolovka, Russia
| | - V B Eltsov
- Department of Applied Physics, Aalto University, POB 15100, FI-00076, AALTO, Finland.
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7
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Mäkinen JT, Zhang K, Eltsov VB. Vortex-bound solitons in topological superfluid 3He. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:214001. [PMID: 36881912 DOI: 10.1088/1361-648x/acc227] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Accepted: 03/07/2023] [Indexed: 06/18/2023]
Abstract
The different superfluid phases of3He are described byp-wave order parameters that include anisotropy axes both in the orbital and spin spaces. The anisotropy axes characterize the broken symmetries in these macroscopically coherent quantum many-body systems. The systems' free energy has several degenerate minima for certain orientations of the anisotropy axes. As a result, spatial variation of the order parameter between two such regions, settled in different energy minima, forms a topological soliton. Such solitons can terminate in the bulk liquid, where the termination line forms a vortex with trapped circulation of mass and spin superfluid currents. Here we discuss possible soliton-vortex structures based on the symmetry and topology arguments and focus on the three structures observed in experiments: solitons bounded by spin-mass vortices in the B phase, solitons bounded by half-quantum vortices (HQVs) in the polar and polar-distorted A phases, and the composite defect formed by a half-quantum vortex, soliton and the Kibble-Lazarides-Shafi wall in the polar-distorted B phase. The observations are based on nuclear magnetic resonance (NMR) techniques and are of three types: first, solitons can form a potential well for trapped spin waves, observed as an extra peak in the NMR spectrum at shifted frequency; second, they can increase the relaxation rate of the NMR spin precession; lastly, the soliton can present the boundary conditions for the anisotropy axes in bulk, modifying the bulk NMR signal. Owing to solitons' prominent NMR signatures and the ability to manipulate their structure with external magnetic field, solitons have become an important tool for probing and controlling the structure and dynamics of superfluid3He, in particular HQVs with core-bound Majorana modes.
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Affiliation(s)
- J T Mäkinen
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
| | - K Zhang
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
- Department of Physics and Helsinki Institute of Physics, University of Helsinki, PO Box 64, FI-00014 Helsinki, Finland
- Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom
| | - V B Eltsov
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
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8
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Supercooling of the A phase of 3He. Nat Commun 2023; 14:148. [PMID: 36627275 PMCID: PMC9832038 DOI: 10.1038/s41467-022-35532-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Accepted: 12/07/2022] [Indexed: 01/11/2023] Open
Abstract
Because of the extreme purity, lack of disorder, and complex order parameter, the first-order superfluid 3He A-B transition is the leading model system for first order transitions in the early universe. Here we report on the path dependence of the supercooling of the A phase over a wide range of pressures below 29.3 bar at nearly zero magnetic field. The A phase can be cooled significantly below the thermodynamic A-B transition temperature. While the extent of supercooling is highly reproducible, it depends strongly upon the cooling trajectory: The metastability of the A phase is enhanced by transiting through regions where the A phase is more stable. We provide evidence that some of the additional supercooling is due to the elimination of B phase nucleation precursors formed upon passage through the superfluid transition. A greater understanding of the physics is essential before 3He can be exploited to model transitions in the early universe.
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9
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Abstract
A time crystal is a macroscopic quantum system in periodic motion in its ground state. In our experiments, two coupled time crystals consisting of spin-wave quasiparticles (magnons) form a macroscopic two-level system. The two levels evolve in time as determined intrinsically by a nonlinear feedback, allowing us to construct spontaneous two-level dynamics. In the course of a level crossing, magnons move from the ground level to the excited level driven by the Landau-Zener effect, combined with Rabi population oscillations. We demonstrate that magnon time crystals allow access to every aspect and detail of quantum-coherent interactions in a single run of the experiment. Our work opens an outlook for the detection of surface-bound Majorana fermions in the underlying superfluid system, and invites technological exploitation of coherent magnon phenomena – potentially even at room temperature. Recent work has reported a realization of a time crystal in the form of the Bose-Einstein condensate of magnons in superfluid 3He. Here, the authors study the dynamics of a pair of such quantum time crystals and show that it closely resembles the evolution of a two-level system, modified by nonlinear feedback.
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10
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Yapa PS, Boyack R, Maciejko J. Triangular Pair Density Wave in Confined Superfluid ^{3}He. PHYSICAL REVIEW LETTERS 2022; 128:015301. [PMID: 35061481 DOI: 10.1103/physrevlett.128.015301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Revised: 10/21/2021] [Accepted: 12/15/2021] [Indexed: 06/14/2023]
Abstract
Recent advances in experiment and theory suggest that superfluid ^{3}He under planar confinement may form a pair density wave (PDW) whereby superfluid and crystalline orders coexist. While a natural candidate for this phase is a unidirectional stripe phase predicted by Vorontsov and Sauls in 2007, recent nuclear magnetic resonance measurements of the superfluid order parameter rather suggest a two-dimensional PDW with noncollinear wave vectors, of possibly square or hexagonal symmetry. In this Letter, we present a general mechanism by which a PDW with the symmetry of a triangular lattice can be stabilized, based on a superfluid generalization of Landau's theory of the liquid-solid transition. A soft-mode instability at a finite wave vector within the translationally invariant planar-distorted B phase triggers a transition from uniform superfluid to PDW that is first order due to a cubic term generally present in the PDW free-energy functional. This cubic term also lifts the degeneracy of possible PDW states in favor of those for which wave vectors add to zero in triangles, which in two dimensions uniquely selects the triangular lattice.
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Affiliation(s)
| | - Rufus Boyack
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
- Theoretical Physics Institute, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - Joseph Maciejko
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
- Theoretical Physics Institute, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
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11
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Rysti J, Mäkinen JT, Autti S, Kamppinen T, Volovik GE, Eltsov VB. Suppressing the Kibble-Zurek Mechanism by a Symmetry-Violating Bias. PHYSICAL REVIEW LETTERS 2021; 127:115702. [PMID: 34558928 DOI: 10.1103/physrevlett.127.115702] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Accepted: 07/16/2021] [Indexed: 06/13/2023]
Abstract
The formation of topological defects in continuous phase transitions is driven by the Kibble-Zurek mechanism. Here we study the formation of single- and half-quantum vortices during transition to the polar phase of ^{3}He in the presence of a symmetry-breaking bias provided by the applied magnetic field. We find that vortex formation is suppressed exponentially when the length scale associated with the bias field becomes smaller than the Kibble-Zurek length. We thus demonstrate an experimentally feasible shortcut to adiabaticity-an important aspect for further understanding of phase transitions as well as for engineering applications such as quantum computers or simulators.
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Affiliation(s)
- J Rysti
- Department of Applied Physics, Aalto University, POB 15100, FI-00076 AALTO, Espoo, Finland
| | - J T Mäkinen
- Department of Applied Physics, Aalto University, POB 15100, FI-00076 AALTO, Espoo, Finland
| | - S Autti
- Department of Applied Physics, Aalto University, POB 15100, FI-00076 AALTO, Espoo, Finland
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - T Kamppinen
- Department of Applied Physics, Aalto University, POB 15100, FI-00076 AALTO, Espoo, Finland
| | - G E Volovik
- Department of Applied Physics, Aalto University, POB 15100, FI-00076 AALTO, Espoo, Finland
- L.D. Landau Institute for Theoretical Physics, Moscow, 142432, Russia
| | - V B Eltsov
- Department of Applied Physics, Aalto University, POB 15100, FI-00076 AALTO, Espoo, Finland
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12
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Lotnyk D, Eyal A, Zhelev N, Sebastian A, Tian Y, Chavez A, Smith E, Saunders J, Mueller E, Parpia J. Path-Dependent Supercooling of the ^{3}He Superfluid A-B Transition. PHYSICAL REVIEW LETTERS 2021; 126:215301. [PMID: 34114839 DOI: 10.1103/physrevlett.126.215301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Revised: 03/22/2021] [Accepted: 04/27/2021] [Indexed: 06/12/2023]
Abstract
We examine the discontinuous first-order superfluid ^{3}He A to B transition in the vicinity of the polycritical point (2.232 mK and 21.22 bar). We find path-dependent transitions: cooling at fixed pressure yields a well-defined transition line in the temperature-pressure plane, but this line can be reliably crossed by depressurizing at nearly constant temperature after transiting T_{c} at a higher pressure. This path dependence is not consistent with any of the standard B-phase nucleation mechanisms in the literature. This symmetry breaking transition is a potential simulator for first order transitions in the early Universe.
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Affiliation(s)
- Dmytro Lotnyk
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Anna Eyal
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
- Physics Department, Technion, Haifa 3200003, Israel
| | - Nikolay Zhelev
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Abhilash Sebastian
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
- VTT Technical Research Centre of Finland Ltd, Espoo 02150, Finland
| | - Yefan Tian
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Aldo Chavez
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Eric Smith
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - John Saunders
- Department of Physics, Royal Holloway University of London, Egham TW20 0EX, Surrey, United Kingdom
| | - Erich Mueller
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Jeevak Parpia
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
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13
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Fragility of surface states in topological superfluid 3He. Nat Commun 2021; 12:1574. [PMID: 33692358 PMCID: PMC7946958 DOI: 10.1038/s41467-021-21831-y] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Accepted: 01/28/2021] [Indexed: 11/23/2022] Open
Abstract
Superfluid 3He, with unconventional spin-triplet p-wave pairing, provides a model system for topological superconductors, which have attracted significant interest through potential applications in topologically protected quantum computing. In topological insulators and quantum Hall systems, the surface/edge states, arising from bulk-surface correspondence and the momentum space topology of the band structure, are robust. Here we demonstrate that in topological superfluids and superconductors the surface Andreev bound states, which depend on the momentum space topology of the emergent order parameter, are fragile with respect to the details of surface scattering. We confine superfluid 3He within a cavity of height D comparable to the Cooper pair diameter ξ0. We precisely determine the superfluid transition temperature Tc and the suppression of the superfluid energy gap, for different scattering conditions tuned in situ, and compare to the predictions of quasiclassical theory. We discover that surface magnetic scattering leads to unexpectedly large suppression of Tc, corresponding to an increased density of low energy bound states. Surface states in topological quantum matter are protected by their band structure. Here, on confined superfluid 3He as a model for topological superconductors, the authors report experimental evidence on the fragility of surface Andreev bound states with respect to the details of surface scattering.
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14
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Yan J, Yao J, Shvarts V, Du RR, Lin X. Cryogen-free one hundred microkelvin refrigerator. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2021; 92:025120. [PMID: 33648063 DOI: 10.1063/5.0036497] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Accepted: 02/04/2021] [Indexed: 06/12/2023]
Abstract
A temperature below 100 µK is achieved in a customized cryogen-free dilution refrigerator with a copper-nuclear demagnetization stage. The lowest temperature of conduction electrons of the demagnetization stage is below 100 µK as measured by using a pulsed platinum nuclear magnetic resonance thermometer, and the temperature can remain below 100 µK for over 10 h. A demagnetization magnetic field of up to 9 T and a research magnetic field of up to 12 T can be controlled independently, provided by a coaxial room-temperature-bore cryogen-free magnet.
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Affiliation(s)
- Jiaojie Yan
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Jianing Yao
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Vladimir Shvarts
- Janis Research Company LLC, Wilmington, Massachusetts 01887, USA
| | - Rui-Rui Du
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Xi Lin
- International Center for Quantum Materials, Peking University, Beijing 100871, China
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15
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Lotnyk D, Eyal A, Zhelev N, Abhilash TS, Smith EN, Terilli M, Wilson J, Mueller E, Einzel D, Saunders J, Parpia JM. Thermal transport of helium-3 in a strongly confining channel. Nat Commun 2020; 11:4843. [PMID: 32973182 PMCID: PMC7515880 DOI: 10.1038/s41467-020-18662-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2019] [Accepted: 09/02/2020] [Indexed: 11/09/2022] Open
Abstract
The investigation of transport properties in normal liquid helium-3 and its topological superfluid phases provides insights into related phenomena in electron fluids, topological materials, and putative topological superconductors. It relies on the measurement of mass, heat, and spin currents, due to system neutrality. Of particular interest is transport in strongly confining channels of height approaching the superfluid coherence length, to enhance the relative contribution of surface excitations, and suppress hydrodynamic counterflow. Here we report on the thermal conduction of helium-3 in a 1.1 μm high channel. In the normal state we observe a diffusive thermal conductivity that is approximately temperature independent, consistent with interference of bulk and boundary scattering. In the superfluid, the thermal conductivity is only weakly temperature dependent, requiring detailed theoretical analysis. An anomalous thermal response is detected in the superfluid which we propose arises from the emission of a flux of surface excitations from the channel.
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Affiliation(s)
- D Lotnyk
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA
| | - A Eyal
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA
- Physics Department, Technion, Haifa, Israel
| | - N Zhelev
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA
| | - T S Abhilash
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA
- VTT Technical Research Centre of Finland Ltd, Espoo, Finland
| | - E N Smith
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA
| | - M Terilli
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA
| | - J Wilson
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA
- SUNY Geneseo, Geneseo, NY, 14454, USA
| | - E Mueller
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA
| | - D Einzel
- Walther Meissner Institut, Garching, Germany
| | - J Saunders
- Department of Physics, Royal Holloway University of London, Egham, TW20 0EX, Surrey, UK
| | - J M Parpia
- Department of Physics, Cornell University, Ithaca, NY, 14853, USA.
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16
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Autti S, Ahlstrom SL, Haley RP, Jennings A, Pickett GR, Poole M, Schanen R, Soldatov AA, Tsepelin V, Vonka J, Wilcox T, Woods AJ, Zmeev DE. Fundamental dissipation due to bound fermions in the zero-temperature limit. Nat Commun 2020; 11:4742. [PMID: 32958764 PMCID: PMC7506006 DOI: 10.1038/s41467-020-18499-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2020] [Accepted: 08/26/2020] [Indexed: 11/12/2022] Open
Abstract
The ground state of a fermionic condensate is well protected against perturbations in the presence of an isotropic gap. Regions of gap suppression, surfaces and vortex cores which host Andreev-bound states, seemingly lift that strict protection. Here we show that in superfluid 3He the role of bound states is more subtle: when a macroscopic object moves in the superfluid at velocities exceeding the Landau critical velocity, little to no bulk pair breaking takes place, while the damping observed originates from the bound states covering the moving object. We identify two separate timescales that govern the bound state dynamics, one of them much longer than theoretically anticipated, and show that the bound states do not interact with bulk excitations.
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Affiliation(s)
- S Autti
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK.
| | - S L Ahlstrom
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - R P Haley
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - A Jennings
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - G R Pickett
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - M Poole
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - R Schanen
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - A A Soldatov
- P.L. Kapitza Institute for Physical Problems of RAS, Moscow, 119334, Russia
| | - V Tsepelin
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - J Vonka
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
- Paul Scherrer Institute, Forschungsstrasse 111, 5232, Villigen PSI, Switzerland
| | - T Wilcox
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - A J Woods
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
- Department of Physics and NHMFL High B/T Facility, University of Florida, Gainesville, FL, 32611, USA
| | - D E Zmeev
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
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17
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Xin T, Li Y, Fan YA, Zhu X, Zhang Y, Nie X, Li J, Liu Q, Lu D. Quantum Phases of Three-Dimensional Chiral Topological Insulators on a Spin Quantum Simulator. PHYSICAL REVIEW LETTERS 2020; 125:090502. [PMID: 32915602 DOI: 10.1103/physrevlett.125.090502] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2020] [Revised: 07/07/2020] [Accepted: 08/04/2020] [Indexed: 05/22/2023]
Abstract
The detection of topological phases of matter has become a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or quantum transport signature of a real material, which may be imperfect or even absent. On the other hand, quantum simulation offers an alternative approach to directly measure the topological invariant on a universal quantum computer. However, experimentally demonstrating high-dimensional topological phases remains a challenge due to the technical limitations of current experimental platforms. Here, we investigate the three-dimensional topological insulators in the AIII (chiral unitary) symmetry class, which yet lack experimental realization. Using the nuclear magnetic resonance system, we experimentally demonstrate their topological properties, where a dynamical quenching approach is adopted and the dynamical bulk-boundary correspondence in the momentum space is observed. As a result, the topological invariants are measured with high precision on the band-inversion surface, exhibiting robustness to the decoherence effect. Our Letter paves the way toward the quantum simulation of topological phases of matter in higher dimensions and more complex systems through controllable quantum phases transitions.
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Affiliation(s)
- Tao Xin
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yishan Li
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yu-Ang Fan
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xuanran Zhu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yingjie Zhang
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xinfang Nie
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jun Li
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Qihang Liu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Dawei Lu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
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18
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Shook AJ, Vadakkumbatt V, Senarath Yapa P, Doolin C, Boyack R, Kim PH, Popowich GG, Souris F, Christani H, Maciejko J, Davis JP. Shook et al. Reply. PHYSICAL REVIEW LETTERS 2020; 125:059602. [PMID: 32794878 DOI: 10.1103/physrevlett.125.059602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2020] [Accepted: 07/10/2020] [Indexed: 06/11/2023]
Affiliation(s)
- A J Shook
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - V Vadakkumbatt
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - P Senarath Yapa
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - C Doolin
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - R Boyack
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
- Theoretical Physics Institute, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - P H Kim
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - G G Popowich
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - F Souris
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - H Christani
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - J Maciejko
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
- Theoretical Physics Institute, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - J P Davis
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
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19
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Shook AJ, Vadakkumbatt V, Senarath Yapa P, Doolin C, Boyack R, Kim PH, Popowich GG, Souris F, Christani H, Maciejko J, Davis JP. Stabilized Pair Density Wave via Nanoscale Confinement of Superfluid ^{3}He. PHYSICAL REVIEW LETTERS 2020; 124:015301. [PMID: 31976679 DOI: 10.1103/physrevlett.124.015301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2019] [Indexed: 06/10/2023]
Abstract
Superfluid ^{3}He under nanoscale confinement has generated significant interest due to the rich spectrum of phases with complex order parameters that may be stabilized. Experiments have uncovered a variety of interesting phenomena, but a complete picture of superfluid ^{3}He under confinement has remained elusive. Here, we present phase diagrams of superfluid ^{3}He under varying degrees of uniaxial confinement, over a wide range of pressures, which elucidate the progressive stability of both the A phase, as well as a growing region of stable pair density wave state.
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Affiliation(s)
- A J Shook
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - V Vadakkumbatt
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - P Senarath Yapa
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - C Doolin
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - R Boyack
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
- Theoretical Physics Institute, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - P H Kim
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - G G Popowich
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - F Souris
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - H Christani
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - J Maciejko
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
- Theoretical Physics Institute, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - J P Davis
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
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20
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Perron JK, Kimball MO, Gasparini FM. A review of giant correlation-length effects via proximity and weak-links coupling in a critical system: 4He near the superfluid transition. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:114501. [PMID: 31437826 DOI: 10.1088/1361-6633/ab3df5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We review measurements of 4He near the superfluid transition in arrangements whereby an array of weak links couple relatively larger, more bulk-like 4He regions. In contrast to experiments which focus on the dependence of the superflow on the chemical potential difference across the links, these studies focus on the specific heat of both the weak links and that of the larger coupled regions, as well as the behavior of the superfluid fraction within the weak links. The data show unexpected results which reflect a very long range coupling as well as modification of the weak link itself due to the proximity to bulk-like helium. One finds that while the three-dimensional correlation length [Formula: see text], where [Formula: see text], is involved in these long-range effects, the distance over which these can be seen is of the order of 100 to 1000 times [Formula: see text]. These results call into question our understanding of the meaning of the correlation length at a critical point as the 'range' over which information can propagate. These studies are the first to measure the thermodynamic properties of weak links for a critical system where fluctuations are important. They differ in essential ways with expectations from mean-field considerations. We compare results with other 4He measurements, with superconductors and the theoretical calculations of the Ising model.
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Affiliation(s)
- J K Perron
- Department of Physics, California State University San Marcos, San Marcos, CA 92069, United States of America
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21
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Levitin LV, Yager B, Sumner L, Cowan B, Casey AJ, Saunders J, Zhelev N, Bennett RG, Parpia JM. Evidence for a Spatially Modulated Superfluid Phase of ^{3}He under Confinement. PHYSICAL REVIEW LETTERS 2019; 122:085301. [PMID: 30932601 DOI: 10.1103/physrevlett.122.085301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Revised: 12/12/2018] [Indexed: 06/09/2023]
Abstract
In superfluid ^{3}He-B confined in a slab geometry, domain walls between regions of different order parameter orientation are predicted to be energetically stable. Formation of the spatially modulated superfluid stripe phase has been proposed. We confined ^{3}He in a 1.1 μm high microfluidic cavity and cooled it into the B phase at low pressure, where the stripe phase is predicted. We measured the surface-induced order parameter distortion with NMR, sensitive to the formation of domains. The results rule out the stripe phase, but are consistent with 2D modulated superfluid order.
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Affiliation(s)
- Lev V Levitin
- Department of Physics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom
| | - Ben Yager
- Department of Physics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom
| | - Laura Sumner
- Department of Physics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom
| | - Brian Cowan
- Department of Physics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom
| | - Andrew J Casey
- Department of Physics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom
| | - John Saunders
- Department of Physics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom
| | - Nikolay Zhelev
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Robert G Bennett
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Jeevak M Parpia
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
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22
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Mäkinen JT, Dmitriev VV, Nissinen J, Rysti J, Volovik GE, Yudin AN, Zhang K, Eltsov VB. Half-quantum vortices and walls bounded by strings in the polar-distorted phases of topological superfluid 3He. Nat Commun 2019; 10:237. [PMID: 30651558 PMCID: PMC6335426 DOI: 10.1038/s41467-018-08204-8] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2018] [Accepted: 12/21/2018] [Indexed: 11/13/2022] Open
Abstract
Symmetries of the physical world have guided formulation of fundamental laws, including relativistic quantum field theory and understanding of possible states of matter. Topological defects (TDs) often control the universal behavior of macroscopic quantum systems, while topology and broken symmetries determine allowed TDs. Taking advantage of the symmetry-breaking patterns in the phase diagram of nanoconfined superfluid 3He, we show that half-quantum vortices (HQVs)-linear topological defects carrying half quantum of circulation-survive transitions from the polar phase to other superfluid phases with polar distortion. In the polar-distorted A phase, HQV cores in 2D systems should harbor non-Abelian Majorana modes. In the polar-distorted B phase, HQVs form composite defects-walls bounded by strings hypothesized decades ago in cosmology. Our experiments establish the superfluid phases of 3He in nanostructured confinement as a promising topological media for further investigations ranging from topological quantum computing to cosmology and grand unification scenarios.
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Affiliation(s)
- J T Mäkinen
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, FI-00076, Aalto, Finland.
| | - V V Dmitriev
- P. L. Kapitza Institute for Physical Problems of RAS, Moscow, Russian Federation, 119334
| | - J Nissinen
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, FI-00076, Aalto, Finland
| | - J Rysti
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, FI-00076, Aalto, Finland
| | - G E Volovik
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, FI-00076, Aalto, Finland
- Landau Institute for Theoretical Physics, Chernogolovka, Russian Federation, 142432
| | - A N Yudin
- P. L. Kapitza Institute for Physical Problems of RAS, Moscow, Russian Federation, 119334
| | - K Zhang
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, FI-00076, Aalto, Finland
- Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014, Helsinki, Finland
| | - V B Eltsov
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, FI-00076, Aalto, Finland
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23
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Vorontsov AB. Andreev bound states in superconducting films and confined superfluid 3He. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 376:rsta.2015.0144. [PMID: 29941623 PMCID: PMC6030148 DOI: 10.1098/rsta.2015.0144] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/27/2018] [Indexed: 06/08/2023]
Abstract
This paper reviews confinement-driven phase transitions in superconductors and Bardeen-Cooper-Schrieffer superfluids, and the appearance in thin films of new phases that break the time-reversal or translational symmetry. The origins of the new phases are closely tied to the Andreev scattering processes involving particle-hole conversions that create surface quasiparticle states with energies inside the superconducting gap. Restructuring of the low-energy spectrum in the surface region of several coherence lengths ξ0 results in large spatial variations of the superconducting order parameter. In confined geometry, such as slabs, films, pores or nano-dots, with one or more physical dimensions D∼10ξ0, the Andreev bound states can dominate properties of a superconductor, leading to modified experimental signatures. They can significantly change the energy landscape, and drive transitions into new superconducting phases. The new phases are expected in a variety of materials, from singlet d-wave superconductors to multi-component triplet superfluid 3He, but properties of the new phases will depend on the symmetry of the parent state. I will highlight the connection between the Andreev surface states and confinement-stabilized phases with additional broken symmetries, describe recent progress and open questions in the theoretical and experimental investigation of superfluids in confined geometry.This article is part of the theme issue 'Andreev bound states'.
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Affiliation(s)
- Anton B Vorontsov
- Department of Physics, Montana State University, Bozeman, MT 59717, USA
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24
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Zhelev N, Abhilash TS, Bennett RG, Smith EN, Ilic B, Parpia JM, Levitin LV, Rojas X, Casey A, Saunders J. Fabrication of microfluidic cavities using Si-to-glass anodic bonding. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2018; 89:073902. [PMID: 30068088 DOI: 10.1063/1.5031837] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We demonstrate the fabrication of ∼1.08 μm deep microfluidic cavities with characteristic size as large as 7 mm × 11 mm or 11 mm diameter, using a silicon-glass anodic bonding technique that does not require posts to act as separators to define cavity height. Since the phase diagram of 3He is significantly altered under confinement, posts might act as pinning centers for phase boundaries. The previous generation of cavities relied on full wafer-bonding which is more prone to failure and requires dicing post-bonding, whereas these cavities are made by bonding a pre-cut piece of Hoya SD-2 glass to a patterned piece of silicon in which the cavity is defined by etching. Anodic bonding was carried out at 425 °C with 200 V, and we observe that pressurizing the cavity to failure (>30 bars pressure) results in glass breaking, rather than the glass-silicon bond separation. In this article, we discuss the detailed fabrication of the cavity, its edges, and details of the junction between the coin silver fill line and the silicon base of the cavity that enables a low internal-friction joint. This feature is important for mass coupling torsional oscillator experimental assays of the superfluid inertial contribution where a high quality factor (Q) improves frequency resolution. The surface preparation that yields well-characterized smooth surfaces to eliminate pinning sites, the use of transparent glass as a cover permitting optical access, low temperature capability, and attachment of pressure-capable ports for fluid access may be features that are important in other applications.
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Affiliation(s)
- N Zhelev
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - T S Abhilash
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - R G Bennett
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - E N Smith
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - B Ilic
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - J M Parpia
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - L V Levitin
- Department of Physics, Royal Holloway University of London, Egham TW20 0EX, Surrey, United Kingdom
| | - X Rojas
- Department of Physics, Royal Holloway University of London, Egham TW20 0EX, Surrey, United Kingdom
| | - A Casey
- Department of Physics, Royal Holloway University of London, Egham TW20 0EX, Surrey, United Kingdom
| | - J Saunders
- Department of Physics, Royal Holloway University of London, Egham TW20 0EX, Surrey, United Kingdom
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25
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The A-B transition in superfluid helium-3 under confinement in a thin slab geometry. Nat Commun 2017; 8:15963. [PMID: 28671184 PMCID: PMC5500879 DOI: 10.1038/ncomms15963] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2016] [Accepted: 05/16/2017] [Indexed: 11/09/2022] Open
Abstract
The influence of confinement on the phases of superfluid helium-3 is studied using the torsional pendulum method. We focus on the transition between the A and B phases, where the A phase is stabilized by confinement and a spatially modulated stripe phase is predicted at the A–B phase boundary. Here we discuss results from superfluid helium-3 contained in a single 1.08-μm-thick nanofluidic cavity incorporated into a high-precision torsion pendulum, and map the phase diagram between 0.1 and 5.6 bar. We observe only small supercooling of the A phase, in comparison to bulk or when confined in aerogel, with evidence for a non-monotonic pressure dependence. This suggests that an intrinsic B-phase nucleation mechanism operates under confinement. Both the phase diagram and the relative superfluid fraction of the A and B phases, show that strong coupling is present at all pressures, with implications for the stability of the stripe phase. Superfluid helium-3 provides a clean testing ground for the understanding of quantum phases and their transitions. Here the authors show that when helium is confined in a nanofluidic cavity supercooling across the first-order A–B transition is suppressed, indicating an intrinsic nucleation mechanism.
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26
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Saitoh M, Ikegami H, Kono K. Onset of Superfluidity in ^{3}He Films. PHYSICAL REVIEW LETTERS 2016; 117:205302. [PMID: 27886487 DOI: 10.1103/physrevlett.117.205302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2016] [Indexed: 06/06/2023]
Abstract
We elucidate, for the first time, the overall behavior of the onset temperature of superfluidity in ^{3}He films for a wide range of film thicknesses d between 0.06 and 10 μm by taking advantage of the tunability of d implemented using microfabricated devices. We observe a suppression of the onset temperature of superfluidity T_{c}^{f} in a film from the bulk transition temperature as d decreases. In particular, T_{c}^{f} is strongly suppressed when d approaches the coherence length (∼77 nm). The observed T_{c}^{f} as a function of d is similar to that expected from the quasiclassical theory, but it unexpectedly deviates from the theoretical value by several percent when 0.5≲d≲5 μm.
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Affiliation(s)
- Masamichi Saitoh
- The Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
| | - Hiroki Ikegami
- The Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
| | - Kimitoshi Kono
- The Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
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27
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Mizushima T, Tsutsumi Y, Sato M, Machida K. Symmetry protected topological superfluid (3)He-B. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:113203. [PMID: 25730099 DOI: 10.1088/0953-8984/27/11/113203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Owing to the richness of symmetry and well-established knowledge of bulk superfluidity, the superfluid (3)He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of (3)He in a multifaceted manner, including symmetry considerations, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the (3)He-B confined in a slab geometry. The (3)He-B under a magnetic field is separated to two different sub-phases: the symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnetic dipole interaction of the (3)He nucleus. It is also demonstrated that odd-frequency even-parity Cooper pair amplitudes are emergent in low-lying quasiparticles. The key ingredients, symmetry protected Majorana fermions and odd-frequency pairing, bring an important consequence that the coupling of the surface states to an applied field is prohibited by the hidden discrete symmetry, while the topological phase transition with the spontaneous symmetry breaking is accompanied by anomalous enhancement and anisotropic quantum criticality of surface spin susceptibility. We also illustrate common topological features between topological crystalline superconductors and symmetry protected topological superfluids, taking UPt3 and Rashba superconductors as examples.
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28
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Levitin LV, Bennett RG, Surovtsev EV, Parpia JM, Cowan B, Casey AJ, Saunders J. Surface-induced order parameter distortion in superfluid ³He-B measured by nonlinear NMR. PHYSICAL REVIEW LETTERS 2013; 111:235304. [PMID: 24476290 DOI: 10.1103/physrevlett.111.235304] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2013] [Indexed: 06/03/2023]
Abstract
The B phase of superfluid 3He is a three-dimensional time-reversal invariant topological superfluid, predicted to support gapless Majorana surface states. We confine superfluid 3He into a thin nanofluidic slab geometry. In the presence of a weak symmetry-breaking magnetic field, we have observed two possible states of the confined 3He-B phase manifold, through the small tipping angle NMR response. Large tipping angle nonlinear NMR has allowed the identification of the order parameter of these states and enabled a measurement of the surface-induced gap distortion. The results for two different quasiparticle surface scattering boundary conditions are compared with the predictions of weak-coupling quasiclassical theory. We identify a textural domain wall between the two B phase states, the edge of which at the cavity surface is predicted to host gapless states, protected in the magnetic field.
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Affiliation(s)
- Lev V Levitin
- Department of Physics, Royal Holloway University of London, Egham, TW20 0EX Surrey, United Kingdom
| | - Robert G Bennett
- Department of Physics, Royal Holloway University of London, Egham, TW20 0EX Surrey, United Kingdom and Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Evgeny V Surovtsev
- Kapitza Institute for Physical Problems, ul. Kosygina 2, Moscow 119334, Russia
| | - Jeevak M Parpia
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Brian Cowan
- Department of Physics, Royal Holloway University of London, Egham, TW20 0EX Surrey, United Kingdom
| | - Andrew J Casey
- Department of Physics, Royal Holloway University of London, Egham, TW20 0EX Surrey, United Kingdom
| | - John Saunders
- Department of Physics, Royal Holloway University of London, Egham, TW20 0EX Surrey, United Kingdom
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Vadimov V, Silaev M. Predicted nucleation of domain walls in p(x)+ip(y) superconductors by a Z(2) symmetry-breaking transition in external magnetic fields. PHYSICAL REVIEW LETTERS 2013; 111:177001. [PMID: 24206513 DOI: 10.1103/physrevlett.111.177001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2013] [Indexed: 06/02/2023]
Abstract
We show that time reversal symmetry-breaking p(x)+ip(y) wave superconductors undergo several phase transitions subjected to an external magnetic field or supercurrent. In such a system, the discrete Z(2) symmetry can recover before a complete destruction of the order parameter. The domain walls associated with Z(2) symmetry can be created in a controllable way by a magnetic field or current sweep according to the Kibble-Zurek scenario. Such domain wall generation can take place in exotic superconductors like Sr(2)RuO(4), thin films of superfluid (3)He-A, and some heavy fermion compounds.
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Affiliation(s)
- Vasily Vadimov
- Institute for Physics of Microstructures RAS, 603950 Nizhny Novgorod, Russia
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