Oscillations of conductance observed in strong magnetic fields are a striking manifestation of the quantum dynamics of charge carriers in solids. The large charge carrier density in typical metals sets the scale of oscillations in both electrical and thermal conductivity, which characterize the Fermi surface. In semimetals, thermal transport at low-charge carrier density is expected to be phonon dominated, yet several experiments observe giant quantum oscillations in thermal transport. This raises the question of whether there is an overarching mechanism leading to sizable oscillations that survives in phonon-dominated semimetals. In this work, we show that such a mechanism exists. It relies on the peculiar phase-space allowed for phonon scattering by electrons when only a few Landau levels are filled. Our measurements on the Dirac semimetal ZrTe5 support this counter-intuitive mechanism through observation of pronounced thermal quantum oscillations, since they occur in similar magnitude and phase in directions parallel and transverse to the magnetic field. Our phase-space argument applies to all low-density semimetals, topological or not, including graphene and bismuth. Our work illustrates that phonon absorption can be leveraged to reveal degrees of freedom through their imprint on longitudinal thermal transport.

Topological states of matter exhibit unique protection against scattering by disorder. Different topological classes exhibit distinct forms and degrees of protection. Here, we investigate the response of the ferromagnetic nodal line semimetal Fe$_3$GeTe$_2$ to disorder and electronic interactions. By combining global magneto-transport with atomic-scale scanning tunneling spectroscopy we find a simultaneous onset of diverse phenomena below a common temperature scale of about 15 K: A crossover from metallic to insulating temperature dependence of the longitudinal resistivity, saturation of the anomalous Hall conductivity to its maximal value, formation of a sharp zero-bias dip in the tunneling density of state, and emergence of multi-fractal structure of the electronic wavefunction peaking at the Fermi energy. These concurrent observations reflect the emergence of a novel energy scale possibly related to the opening of a gap in the nodal line band of Fe$_3$GeTe$_2$. Our study provides overarching insight into the role of disorder, electronic interactions and Berry curvature in setting the micro- and macro-scale responses of topological semimetals.

We analyze the transport properties of curved, three-dimensional graphite samples in strong magnetic fields. Focusing on a millimeter-scale graphite cylinder as a prototypical curved object, we perform longitudinal and Hall voltage measurements while applying quantizing magnetic fields. These measurements are investigated as a function of field strength and angles. Most importantly, we find that angle-dependent Shubnikov-de Hass oscillations are superimposed with angle-independent features. Reproducing the experimental observations, we introduce a network model that accounts for the cylindrical geometry effect by conceptualizing the cylinder as composed of strips of planar graphite in an effectively inhomogeneous magnetic field. Our work highlights how the interplay between geometric curvature and quantizing magnetic fields can be leveraged to engineer tunable spatial current densities within solid-state systems, and paves the way for understanding transport properties of curved and bent three-dimensional samples more generally.

The electron-phonon interaction is in many ways a solid state equivalent of quantum electrodynamics. Being always present, the e-p coupling is responsible for the intrinsic resistance of metals at finite temperatures, making it one of the most fundamental interactions present in solids. In typical metals, different regimes of e-p scattering are separated by a characteristic phonon energy scale-the Debye temperature. However, in metals harboring very small Fermi surfaces a new scale emerges-the Bloch-Gr & uuml;neisen temperature. This is a temperature at which the average phonon momentum becomes comparable to the Fermi momentum of the electrons. Here we report sub-Kelvin transport and sound propagation experiments on the Dirac semimetal ZrTe5. The combination of the simple band structure with only a single small Fermi surface sheet allowed us to directly observe the Bloch-Gr & uuml;neisen temperature and its consequences on electronic transport of a 3D metal in the limit where the small size of the Fermi surface leads to effective restoration of translational invariance of free space. Our results indicate that on entering this hydrodynamic transport regime, the viscosity of the Dirac electronic liquid undergoes an anomalous increase beyond the theoretically predicted T 5 temperature dependence. Extension of our measurements to strong magnetic fields reveal that, despite the dimensional reduction of the electronic band structure, the electronic liquid retains characteristics of the zero-field hydrodynamic regime up to the quantum limit. This is vividly reflected by an anomalous suppression of the amplitude of quantum oscillations seen in the Shubnikov-de Haas effect.

The conformal anomaly indicates the breaking of conformal symmetry (angle-preserving transformations) in the quantum theory by quantum fluctuations and is a close cousin of the gravitational anomaly. We show, for the first time, that the conformal anomaly controls the variance of the local magnetization M loc at finite temperatures in spin chains and spin ladders. This effect is perceived at constant and variable temperature across the sample. The change of M loc induced by the conformal anomaly is of the order of 3-5% of the maximal spin at one Kelvin for DIMPY or CuPzN and increases linearly with temperature. Further, for a temperature gradient of 10% across the sample, the time-relaxation of the non-equilibrium M loc is of the order of nanoseconds. Thus, we believe that experimental techniques such as neutron scattering, nuclear magnetic resonance (NMR), spin noise and ultrafast laser pumping should pinpoint the presence of the conformal anomaly. There-fore, we pave the road to detect the conformal anomaly in spin observables of strongly interacting low-dimensional magnets.

2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the existence of 1D spin-momentum locked metallic edge states-both helical and chiral-surrounding an electrically insulating bulk. Forty years since the first discoveries of topological phases in condensed matter, the abstract concept of band topology has sprung into realization with several materials now available in which sizable bulk energy gaps-up to a few hundred meV-promise to enable topology for applications even at room-temperature. Further, the possibility of combining 2D TIs in heterostructures with functional materials such as multiferroics, ferromagnets, and superconductors, vastly extends the range of applicability beyond their intrinsic properties. While 2D TIs remain a unique testbed for questions of fundamental condensed matter physics, proposals seek to control the topologically protected bulk or boundary states electrically, or even induce topological phase transitions to engender switching functionality. Induction of superconducting pairing in 2D TIs strives to realize non-Abelian quasiparticles, promising avenues towards fault-tolerant topological quantum computing. This roadmap aims to present a status update of the field, reviewing recent advances and remaining challenges in theoretical understanding, materials synthesis, physical characterization and, ultimately, device perspectives.

We introduce a new stress dilatometer with exactly the same size and mass as the world's smallest miniature capacitance dilatometer (height × width × depth = 15 × 14 × 15 mm3, mass: 12 g). To develop this new device, only a single part of the most recently developed mini-dilatometer, the so-called "body," needs to be replaced. Therefore, the new mini-dilatometer with an interchangeable body can be used for high-resolution measurements of thermal expansion and magnetostriction with and without large stress. We also report two novel applications of both mini-dilatometer cell types. Our new setup was installed for the first time in a cryogen-free system (PPMS DynaCool). The first new setup allows the rotation of both dilatometers in situ at any angle between -90° ≥ μ ≥ +90° in the temperature range from 320 to 1.8 K. We also installed our mini-cells in a dilution refrigerator insert of a PPMS DynaCool, in which dilatometric measurements are now possible in the temperature range from 4 to 0.06 K. Because of the limited sample space, such measurements could not be performed so far. For both new applications, we can resolve the impressive length changes to 0.01 Å.

Real-world topological semimetals typically exhibit Dirac and Weyl nodes that coexist with trivial Fermi pockets. This tends to mask the physics of the relativistic quasiparti-cles. Using the example of ZrTe5, we show that strain provides a powerful tool for in-situ tuning of the band structure such that all trivial pockets are pushed far away from the Fermi energy, but only for a certain range of Van der Waals gaps. Our results naturally reconcile contradicting reports on the presence or absence of additional pockets in ZrTe5, and provide a clear map of where to find a pure three-dimensional Dirac semimetallic phase in the structural parameter space of the material.

Appearance of quantum oscillations (QO) in both thermodynamic and transport properties of metals at low temperatures is the most striking experimental consequence of the existence of a Fermi surface (FS). The frequency of these oscillations and the temperature dependence of their amplitude provides essential information about the FS topology and fermionic quasiparticle properties. Here, we report the observation of an anomalous suppression of the QO amplitude seen in resistivity (Shubnikov de-Haas effect) at sub-kelvin temperatures in ZrTe5 samples with a single small FS sheet comprising less than 5 the magneto-acoustic QO and the recovery of the usual Lifshitz-Kosevich behavior of the Shubnikov de-Haas (SdH) effect in ZrTe_5 samples with a multi-sheet FS, we show that the suppression of the SdH effect originates from a decoupling of the electron liquid from the lattice. On crossing the so-called Bloch-Grüneisen temperature, T_BG, electron-phonon scattering becomes strongly suppressed and in the absence of Umklapp scattering the electronic liquid regains Galilean invariance. In addition, we show, using a combination of zero-field electrical conductivity and ultrasonic-absorption measurements, that entering this regime leads to an abrupt increase of electronic viscosity.

In recent times the chiral semimetal cobalt monosilicide (CoSi) has emerged as a prototypical, nearly ideal topological conductor hosting giant, topologically protected Fermi arcs. Exotic topological quantum properties have already been identified in CoSi bulk single crystals. However, CoSi is also known for being prone to intrinsic disorder and inhomogeneities, which, despite topological protection, risk jeopardizing its topological transport features. Alternatively, topology may be stabilized by disorder, suggesting the tantalizing possibility of an amorphous variant of a topological metal, yet to be discovered. In this respect, understanding how microstructure and stoichiometry affect magnetotransport properties is of pivotal importance, particularly in case of low-dimensional CoSi thin films and devices. Here we comprehensively investigate the magnetotransport and magnetic properties of ≈25 nm Co1–xSix thin films grown on a MgO substrate with controlled film microstructure (amorphous vs textured) and chemical composition (0.40 < x < 0.60). The resistivity of Co1–xSix thin films is nearly insensitive to the film microstructure and displays a progressive evolution from metallic-like (dρxx/dT > 0) to semiconducting-like (dρxx/dT < 0) regimes of conduction upon increasing the silicon content. A variety of anomalies in the magnetotransport properties, comprising for instance signatures consistent with quantum localization and electron–electron interactions, anomalous Hall and Kondo effects, and the occurrence of magnetic exchange interactions, are attributable to the prominent influence of intrinsic structural and chemical disorder. Our systematic survey brings to attention the complexity and the challenges involved in the prospective exploitation of the topological chiral semimetal CoSi in nanoscale thin films and devices.

Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and momentum of the electrons are locked parallel or anti-parallel to each other. Magnetic and non-magnetic Weyl semimetals, for example, exhibit chiral bulk states that have enabled the realization of predictions from high energy and astrophysics involving the chiral quantum number, such as the chiral anomaly, the mixed axial-gravitational anomaly and axions. The potential for connecting chirality as a quantum number to other chiral phenomena across different areas of science, including the asymmetry of matter and antimatter and the homochirality of life, brings topological materials to the fore.

The discovery of the quantum Hall effect (QHE) in 1980 marked a turning point in condensed matter physics: given appropriate experimental conditions, the Hall conductivity σxy of a two-dimensional electron system is exactly quantized. But what happens to the QHE in three dimensions (3D)? Experiments over the past 40 years showed that some of the remarkable physics of the QHE, in particular plateau-like Hall conductivities σxy accompanied by minima in the longitudinal resistivity ρxx , can also be found in 3D materials. However, since typically ρxx remains finite and a quantitative relation between σxy and the conductance quantum e2/h could not be established, the role of quantum Hall physics in 3D remains unsettled. Following a recent series of exciting experiments, the QHE in 3D has now returned to the center stage. Here, we summarize the leap in understanding of 3D matter in magnetic fields emerging from these experiments.

Double Dirac materials are a topological phase of matter in which a non-symmorphic symmetry enforces greater electronic degeneracy than normally expected – up to eightfold. The cubic palladium bronzes NaPd3O4 and LaPd3S4 are built of Pd3X4 (X = O, S) anionic frameworks that are ionically bonded to A cations (A = Na, La). These materials were recently identified computationally as harboring eightfold fermions. Here we report the preparation of single crystals and electronic properties of LaPd3S4. Measurements down to T = 0.45 K and in magnetic fields up to μ0H = 65 T are consistent with normal Fermi liquid physics of a Dirac metal in the presence of dilute magnetic impurities. This interpretation is further confirmed by analysis of specific heat, magnetization measurements and comparison to density functional theory (DFT) calculations. Through a bonding analysis of the DFT electronic structure of NaPd3O4 and LaPd3S4, we identify the origin of the stability of the anionic Pd3X4 framework at higher electron counts for X = S than X = O, and propose chemical tuning strategies to enable shifting the 8-fold fermion points to the Fermi level.

The kagome metal compounds AV_3Sb_5 (A = K, Rb, and Cs) feature a wealth of phenomena including nontrivial band topology, charge density wave (CDW), and superconductivity. One intriguing property is the time-reversal symmetry breaking in the CDW state without local moments, which leads to anomalous transport responses. Here, we report the investigation of magneto-thermoelectric effects on high-quality CsV_3Sb_5 single crystals. A large anomalous Nernst effect is observed at temperatures below 30 K. Multiple Fermi surfaces with small effective masses are revealed by quantum oscillations in Nernst and Seebeck signals under high magnetic field. Furthermore, we find an unknown frequency, and attribute it to the magnetic breakdown across two smaller Fermi surfaces. A gap around 20 meV can be resolved from the breakdown threshold field, which we propose to be introduced by the CDW. These results shed new light on the CDW-related phenomena, particularly in AV_3Sb_5 compounds.

We describe application of a state-of-the art digital FPGA based Lock-In amplifier to measurements of ultrasound propagation and attenuation at fixed frequency in low temperatures and in high static magnetic fields. Our implementation significantly simplifies electronics required for high resolution measurements, allows to record the full echo train in single measurement and extract changes in both phase and amplitude of an arbitrary number of echa as a function of an external control parameter. The system is simple in operation requiring very little prior knowledge of electrical engineering and can bring the technique to a broad range of solid state physics laboratories. We have tested our setup measuring the magneto-acoustic quantum oscillations in the Weyl semimetal NbP. The results are directly compared with previous results obtained using standard instrumentation.

In insulators, the longitudinal resistivity becomes infinitely large at zero temperature. For classic insulators, the Hall conductivity becomes zero at the same time. However, there are special systems, such as two-dimensional quantum Hall isolators, in which a more complex scenario is observed at high magnetic fields. Here, we report experimental evidence for a quasi-quantized Hall insulator in the quantum limit of the three-dimensional semimetal SrSi2. Our measurements reveal a magnetic field-range, in which the longitudinal resistivity diverges with decreasing temperature, while the Hall conductivity approaches a quasi-quantized value that is given only by the conductance quantum and the Fermi wave vector in the field-direction. The quasi-quantized Hall insulator appears in a magnetic-field induced insulating ground state of three-dimensional materials and is deeply rooted in quantum Hall physics.

Using a combination of neutron scattering, calorimetry, quantum Monte Carlo simulations, and analytic results we uncover confinement effects in depleted, partially magnetized quantum spin ladders. We show that introducing nonmagnetic impurities into magnetized spin ladders leads to the emergence of a new characteristic length L in the otherwise scale-free Tomonaga-Luttinger liquid (serving as the effective low-energy model). This results in universal LT scaling of staggered susceptibilities. Comparison of simulation results with experimental phase diagrams of prototypical spin ladder compounds bis(2,3-dimethylpyridinium)tetrabromocuprate(II) (DIMPY) and bis(piperidinium)tetrabromocuprate(II) (BPCB) yields excellent agreement.

The quantum limit (QL) of an electron liquid, realised at strong magnetic fields, has long been proposed to host a wealth of strongly correlated states of matter. Electronic states in the QL are, for example, quasi-one dimensional (1D), which implies perfectly nested Fermi surfaces prone to instabilities. Whereas the QL typically requires unreachably strong magnetic fields, the topological semimetal ZrTe$_5$ has been shown to reach the QL at fields of only a few Tesla. Here, we characterize the QL of ZrTe$_5$ at fields up to 64 T by a combination of electrical-transport and ultrasound measurements. We find that the Zeeman effect in ZrTe$_5$ enables an efficient tuning of the 1D Landau band structure with magnetic field. This results in a Lifshitz transition to a 1D Weyl regime in which perfect charge neutrality can be achieved. Since no instability-driven phase transitions destabilise the 1D electron liquid for the investigated field strengths and temperatures, our analysis establishes ZrTe$_5$ as a thoroughly understood platform for potentially inducing more exotic interaction-driven phases at lower temperatures.

Interactions of charge carriers with lattice vibrations, or phonons, play a critical role in unconventional electronic transport of metals and semimetals. Recent observations of phonon-mediated collective electron flow in bulk semimetals, termed electron hydrodynamics, present new opportunities in the search for strong electron-electron interactions in high carrier density materials. Here we present the general transport signatures of such a second-order scattering mechanism, along with analytical limits at the Eliashberg level of theory. We study electronic transport, using $ab$ $initio$ calculations, in finite-size channels of semimetallic ZrSiS and TaAs$_2$ with and without topological band crossings, respectively. The order of magnitude separation between momentum-relaxing and momentum-conserving scattering length-scales across a wide temperature range make both of them promising candidates for further experimental observation of electron hydrodynamics. More generally, our calculations show that the hydrodynamic transport regime can be realized in a much broader class of anisotropic metals and does not, to first order, rely on the topological nature of the bands. Finally, we discuss general design principles guiding future search for hydrodynamic candidates, based on the analytical formulation and our $ab$ $initio$ predictions. We find that systems with strong electron-phonon interactions, reduced electronic phase space, and suppressed phonon-phonon scattering at temperatures of interest are likely to feature hydrodynamic electron transport. We predict that layered and/or anisotropic semimetals composed of half-filled $d$-shells and light group V/VI elements with lower crystal symmetry are ideal candidates to observe hydrodynamic phenomena in future.

Abstract The quasi-quantized Hall effect (QQHE) is the three-dimensional (3D) counterpart of the integer quantum Hall effect (QHE), exhibited only by two-dimensional (2D) electron systems. It has recently been observed in layered materials, consisting of stacks of weakly coupled 2D platelets that are yet characterized by a 3D anisotropic Fermi surface. However, it is predicted that the quasi-quantized 3D version of the 2D QHE should occur in a much broader class of bulk materials, regardless of the underlying crystal structure. Here, we compare the observation of quasi-quantized plateau-like features in the Hall conductivity of the n-type bulk semiconductor InAs with the predictions for the 3D QQHE in presence of parabolic electron bands. InAs takes form of a cubic crystal without any low-dimensional substructure. The onset of the plateau-like feature in the Hall conductivity scales with $$\sqrt{2/3}k_{\text {F}}^{z}/\pi$$ 2 / 3 k F z / π in units of the conductance quantum and is accompanied by a Shubnikov–de Haas minimum in the longitudinal resistivity, consistent wit the results of calculations. This confirms the suggestion that the 3D QQHE may be a generic effect directly observable in materials with small Fermi surfaces, placed in sufficiently strong magnetic fields.