Topological superconductors, characterized by spin-triplet Cooper pairing, are important for exploring unconventional pairing mechanisms and protected quantum states. Yet experimentally established odd-parity, spin-triplet superconductors remain scarce. Here we demonstrate that the heavy-fermion compound YbRh2Si2 hosts distinct magnetic-field-tuned superconducting states, both Pauli limited and beyond this limit, revealed by high-resolution measurements of the complex electrical impedance. We also find that superconductivity is abruptly suppressed at the critical field associated with the primary antiferromagnetic transition of this compound. The onset of electro-nuclear spin density wave order enhances the superconductivity. We propose that this behaviour can be explained by the formation of a pair density wave that boosts a selected spin-triplet superconducting order parameter. Together, our findings indicate odd-parity superconductivity in YbRh2Si2 and point to one of the superconducting states being the topological helical phase.

Topological superconductors are essential elements of the periodic table of topological quantum matter. However, the relevant odd-parity spin-triplet superconductors are rare. We report high-resolution measurements of the complex electrical impedance of YbRh$_2$Si$_2$ down to 0.4 mK, that reveal the presence of several superconducting states, suppressed differently by magnetic field, both Pauli-limited and beyond the Pauli limit. Superconductivity is abruptly switched off at the critical field of the primary antiferromagnetic order. The onset of electro-nuclear spin density wave order enhances the superconductivity, which we account for by the simultaneous formation of a spin-triplet pair density wave. Together these observations provide compelling evidence for odd-parity superconductivity, and its underpinning by antiferromagnetism, and allow us to identify the topological helical state.

Anisotropic pair breaking close to surfaces favors the chiral A phase of the superfluid ^{3}He over the time-reversal invariant B phase. Confining the superfluid ^{3}He into a cavity of height D of the order of the Cooper pair size characterized by the coherence length ξ_{0}-ranging between 16 nm (34 bar) and 77 nm (0 bar)-extends the surface effects over the whole sample volume, thus allowing stabilization of the A phase at pressures P and temperatures T where otherwise the B phase would be stable. In this Letter, the surfaces of such a confined sample are covered with a superfluid ^{4}He film to create specular quasiparticle scattering boundary conditions, preventing the suppression of the superfluid order parameter. We show that the chiral A phase is the stable superfluid phase under strong confinement over the full P-T phase diagram down to a quasi-two-dimensional limit D/ξ_{0}=1, where D=80  nm. The planar phase, which is degenerate with the chiral A phase in the weak-coupling limit, is not observed. The gap inferred from measurements over the wide pressure range from 0.2 to 21.0 bar leads to an empirical ansatz for temperature-dependent strong-coupling effects. We discuss how these results pave the way for the realization of the fully gapped two-dimensional p_{x}+ip_{y} superfluid under more extreme confinement.

We have designed and constructed a magnet surrounding a cylindrical volume of superfluid helium-3 to isolate a region of metastable, supercooled A phase, entirely surrounded by bulk A phase - isolating the ‘bubble’ from rough surfaces that can trigger the transition to the stable B phase. We outline the design of the experimental cell and magnet and show that the performance of the magnet is consistent with simulations, including the capability to produce the high field gradient required for generating a bubble. Future plans include the investigation of possible intrinsic mechanisms underpinning the A-B transition, with potential implications for early-universe cosmological phase transitions.

We report the determination of the magnetic phase diagram of the heavy fermion metal YbRh2Si2 in magnetic fields up to 70 mT applied perpendicular to the crystallographic c-axis. By a combination of heat capacity, magneto-caloric, and magneto-resistance measurements we map two antiferromagnetic phases: the electronic AFM1 below 70 mK and electro-nuclear AFM2 below 1.5 mK. The measurements extend into the microkelvin regime to explore the quantum phase transitions in this system. We demonstrate how the hyperfine interaction significantly modifies the phase diagram and the putative field-tuned quantum critical point. The determination of the rich magnetic properties of YbRh2Si2 is essential to understanding the interplay of the two magnetic orders and superconductivity in this compound.

We describe a compact calorimeter that opens ultra-low-temperature heat capacity studies of small metal crystals in moderate magnetic fields. The performance is demonstrated on the canonical heavy fermion metal YbRh _2 Si _2 . Thermometry is provided by a fast current sensing noise thermometer. This single thermometer enables us to cover a wide temperature range of interest from 175 µK to 90 mK with temperature-independent relative precision. Temperatures are tied to the international temperature scale with a single-point calibration. A superconducting solenoid surrounding the cell provides the sample field for tuning its properties and operates a superconducting heat switch. Both adiabatic and relaxation calorimetry techniques, as well as magnetic field sweeps, are employed. The design of the calorimeter results in an addendum heat capacity which is negligible for the study reported. The keys to sample and thermometer thermalisation are the lack of dissipation in the temperature measurement and the steps taken to reduce the parasitic heat leak into the cell to the tens of fW level.

The symmetry-breaking first-order phase transition between superfluid phases $^3$He-A and $^3$He-B can be triggered extrinsically by ionising radiation or heterogeneous nucleation arising from the details of the sample cell construction. However, the role of potential homogeneous intrinsic nucleation mechanisms remains elusive. Discovering and resolving the intrinsic processes may have cosmological consequences, since an analogous first-order phase transition, and the production of gravitational waves, has been predicted for the very early stages of the expanding Universe in many extensions of the Standard Model of particle physics. Here we introduce a new approach for probing the phase transition in superfluid $^3$He. The setup consists of a novel stepped-height nanofluidic sample container with close to atomically smooth walls. The $^3$He is confined in five tiny nanofabricated volumes and assayed non-invasively by NMR. Tuning of the state of $^3$He by confinement is used to isolate each of these five volumes so that the phase transitions in them can occur independently and free from any obvious sources of heterogeneous nucleation. The small volumes also ensure that the transitions triggered by ionising radiation are strongly suppressed. Here we present the preliminary measurements using this setup, showing both strong supercooling of $^3$He-A and superheating of $^3$He-B, with stochastic processes dominating the phase transitions between the two. The objective is to study the nucleation as a function of temperature and pressure over the full phase diagram, to both better test the proposed extrinsic mechanisms and seek potential parallel intrinsic mechanisms.

Abstract The focus of dark matter searches to date has been on Weakly Interacting Massive Particles (WIMPs) in the GeV/ $$c^2$$ c 2 -TeV/ $$c^2$$ c 2 mass range. The direct, indirect and collider searches in this mass range have been extensive but ultimately unsuccessful, providing a strong motivation for widening the search outside this range. Here we describe a new concept for a dark matter experiment, employing superfluid $$^3$$ 3 He as a detector for dark matter that is close to the mass of the proton, of order 1 GeV/ $$c^2$$ c 2 . The QUEST-DMC detector concept is based on quasiparticle detection in a bolometer cell by a nanomechanical resonator. In this paper we develop the energy measurement methodology and detector response model, simulate candidate dark matter signals and expected background interactions, and calculate the sensitivity of such a detector. We project that such a detector can reach sub-eV nuclear recoil energy threshold, opening up new windows on the parameter space of both spin-dependent and spin-independent interactions of light dark matter candidates.

We report the results of radioactivity assays and heat leak calculations for a range of common cryogenic materials, considered for use in the QUEST-DMC superfluid 3He dark matter detector. The bolometer, instrumented with nanomechanical resonators, will be sensitive to energy deposits from dark matter interactions. Events from radioactive decays and cosmic rays constitute a significant background and must be precisely modelled, using a combination of material screening and Monte Carlo simulations. However, the results presented here are of wider interest for experiments and quantum devices sensitive to minute heat leaks and spurious events, thus we present heat leak per unit mass or surface area for every material studied. This can inform material choices for other experiments, especially if underground operation is considered where the radiogenic backgrounds will dominate even at shallow depths.

First order phase transitions in the very early universe are a prediction of many extensions of the Standard Model of particle physics and could provide the departure from equilibrium needed for a dynamical explanation of the baryon asymmetry of the Universe. They could also produce gravitational waves of a frequency observable by future space-based detectors such as the Laser Interferometer Space Antenna (LISA). All calculations of the gravitational wave power spectrum rely on a relativistic version of the classical nucleation theory of Cahn-Hilliard and Langer, due to Coleman and Linde. The high purity and precise control of pressure and temperature achievable in the laboratory made the first-order A to B transition of superfluid $^3$He an ideal for test of classical nucleation theory. As Leggett and others have noted the theory fails dramatically. The lifetime of the metastable A phase is measurable, typically of order minutes to hours, far faster than classical nucleation theory predicts. If the nucleation of B phase from the supercooled A phase is due to a new, rapid intrinsic mechanism that would have implications for first-order cosmological phase transitions as well as predictions for gravitational wave (GW) production in the early universe. Here we discuss studies of the AB phase transition dynamics in $^3$He, both experimental and theoretical, and show how the computational technology for cosmological phase transition can be used to simulate the dynamics of the A-B transition, support the experimental investigations of the A-B transition in the QUEST-DMC collaboration with the goal of identifying and quantifying the mechanism(s) responsible for nucleation of stable phases in ultra-pure metastable quantum phases.

The focus of dark matter searches to date has been on Weakly Interacting Massive Particles (WIMPs) in the GeV/$c^2$-TeV/$c^2$ mass range. The direct, indirect and collider searches in this mass range have been extensive but ultimately unsuccessful, providing a strong motivation for widening the search outside this range. Here we describe a new concept for a dark matter experiment, employing superfluid $^3$He as a detector for dark matter that is close to the mass of the proton, of order 1 GeV/$c^2$. The QUEST-DMC detector concept is based on quasiparticle detection in a bolometer cell by a nanomechanical resonator. In this paper we develop the energy measurement methodology and detector response model, simulate candidate dark matter signals and expected background interactions, and calculate the sensitivity of such a detector. We project that such a detector can reach sub-eV nuclear recoil energy threshold, opening up new windows on the parameter space of both spin-dependent and spin-independent interactions of light dark matter candidates.

The motivation to develop materials for quantum technologies has put exploration of novel quantum states of matter at the focus of several research fields, with particular efforts towards understanding and controlling the behaviour of quantum entangled and other strongly interacting electronic states. Experimental investigation is of primary importance, but requires measurements at ultra-low temperatures where the quantum states of interest have long lifetimes. Under these conditions, low energy interactions, such as hyperfine or nuclear exchange interactions, become relevant, and can modify electronic ground states and their associated excitations in multiple ways that are not well understood or characterised. In this work, we use a recently developed magnetic susceptibility technique, compatible with ultra-low temperatures and high magnetic fields, to probe the influence of nuclear interactions on superconducting and multipole ordered ground states in the strongly correlated electron system PrOs4Sb12. We find that the multipole order develops a novel, entangled nuclear-electronic character at the lowest temperatures, which significantly modifies the phase boundary and leads to a nuclear quantum critical point. In the superconducting phase, we find that hyperfine interactions suppress superconductivity in a manner that provides evidence for superconducting pairing mediated by crystal field excitations. Our results on PrOs4Sb12 experimentally establish a new type of non-magnetic, nuclear quantum critical point, and give revealing insight into a highly unusual superconducting state. They also demonstrate more generally the feasibility of exploiting hyperfine interactions as a tuning parameter for experimental creation and investigation of a variety of quantum states and phenomena in correlated electron materials.

The nature of the antiferromagnetic order in the heavy fermion metal YbRh_{2}Si_{2}, its quantum criticality, and superconductivity, which appears at low mK temperatures, remain open questions. We report measurements of the heat capacity over the wide temperature range 180  μK-80  mK, using current sensing noise thermometry. In zero magnetic field we observe a remarkably sharp heat capacity anomaly at 1.5 mK, which we identify as an electronuclear transition into a state with spatially modulated electronic magnetic order of maximum amplitude 0.1  μ_{B}. We also report results of measurements in magnetic fields in the range 0 to 70 mT, applied perpendicular to the c axis, which show eventual suppression of this order. These results demonstrate a coexistence of a large moment antiferromagnet with putative superconductivity.

Electrical and thermal transport were studied in a vacuum-annealed polycrystalline silver wire with residual resistivity ratio 200 – 400, in the temperature range 0.1 - 1.2 K and in magnetic fields up to 5 T. Both at zero field and at 5 T the wire exhibits the Wiedemann–Franz law with the fundamental Lorenz number, contrary to an earlier report (Gloos et al., in Cryogenics 30:14–18, 1990). Our result demonstrates that silver is an excellent material for thermal links in ultra-low-temperature experiments operating at high magnetic fields.

Abstract Quantum circuits interact with the environment via several temperature-dependent degrees of freedom. Multiple experiments to-date have shown that most properties of superconducting devices appear to plateau out at T ≈ 50 mK – far above the refrigerator base temperature. This is for example reflected in the thermal state population of qubits, in excess numbers of quasiparticles, and polarisation of surface spins – factors contributing to reduced coherence. We demonstrate how to remove this thermal constraint by operating a circuit immersed in liquid 3He. This allows to efficiently cool the decohering environment of a superconducting resonator, and we see a continuous change in measured physical quantities down to previously unexplored sub-mK temperatures. The 3He acts as a heat sink which increases the energy relaxation rate of the quantum bath coupled to the circuit a thousand times, yet the suppressed bath does not introduce additional circuit losses or noise. Such quantum bath suppression can reduce decoherence in quantum circuits and opens a route for both thermal and coherence management in quantum processors.

Improved accessibility to the microkelvin temperature regime is important for future research in quantum materials; for quantum information science; and for applications of quantum sensors. Here we report the design and performance of a microkelvin platform based on a nuclear demagnetization stage, engineered and well optimized for operation on a standard cryogen-free dilution refrigerator. PrNi5 is used as the dominant refrigerant. The platform provides a large area for mounting experiments in an ultralow temperature, low electromagnetic noise environment. The performance is characterized using current sensing noise thermometry. Temperatures as low as 395 $\mu$K have been reached, and a protocol has been established in which it is possible to operate experiments below 1 mK for 95% of the time, providing an efficient cryogen-free microkelvin environment for a wide range of science applications

The discovery of superconductivity in the quantum critical Kondo-lattice system YbRh2Si2 at an extremely low temperature of 2 mK has inspired efforts to perform high-resolution electrical resistivity measurements down to this temperature range in highly conductive materials. Here we show that control over the sample geometry by microstructuring using focused-ion-beam techniques allows to reach ultra-low temperatures and increase signal-to-noise ratios (SNRs) tenfold, without adverse effects to sample quality. In five experiments we show four-terminal sensing resistance and magnetoresistance measurements which exhibit sharp phase transitions at the Neel temperature, and Shubnikov-de-Haas (SdH) oscillations between 13 T and 18 T where we identified a new SdH frequency of 0.39 kT. The increased SNR allowed resistance fluctuation (noise) spectroscopy that would not be possible for bulk crystals, and confirmed intrinsic 1/f-type fluctuations. Under controlled strain, two thin microstructured samples exhibited a large increase of T-N from 67 mK up to 188 mK while still showing clear signatures of the phase transition and SdH oscillations. Superconducting quantum interference device-based thermal noise spectroscopy measurements in a nuclear demagnetization refrigerator down to 0.95 mK, show a sharp superconducting transition at T-c = 1.2 mK. These experiments demonstrate microstructuring as a powerful tool to investigate the resistance and the noise spectrum of highly conductive correlated metals over wide temperature ranges.

Two-dimensional electron gases (2DEGs) with high mobility, engineered in semiconductor heterostructures host a variety of ordered phases arising from strong correlations, which emerge at sufficiently low temperatures. The 2DEG can be further controlled by surface gates to create quasi-one dimensional systems, with potential spintronic applications. Here we address the long-standing challenge of cooling such electrons to below 1 mK, potentially important for identification of topological phases and spin correlated states. The 2DEG device was immersed in liquid 3 He, cooled by the nuclear adiabatic demagnetization of copper. The temperature of the 2D electrons was inferred from the electronic noise in a gold wire, connected to the 2DEG by a metallic ohmic contact. With effective screening and filtering, we demonstrate a temperature of 0.9 ± 0.1 mK, with scope for significant further improvement. This platform is a key technological step, paving the way to observing new quantum phenomena, and developing new generations of nanoelectronic devices exploiting correlated electron states.

The nature of the antiferromagnetic order in the heavy fermion metal YbRh$_2$Si$_2$, its quantum criticality, and superconductivity, which appears at low mK temperatures, remain open questions. We report measurements of the heat capacity over the wide temperature range 180 $μ$K - 80 mK, using current sensing noise thermometry. In zero magnetic field we observe a remarkably sharp heat capacity anomaly at 1.5 mK, which we identify as an electro-nuclear transition into a state with spatially modulated electronic magnetic order of maximum amplitude 0.1$μ_B$. We also report results of measurements in magnetic fields in the range 0 to 70 mT, applied perpendicular to the c-axis, which show eventual suppression of this order. These results demonstrate a coexistence of a large moment antiferromagnet with putative superconductivity.