Abstract The miniaturisation of electronic building blocks is of uttermost importance. Efficient nanoscopic inductors and capacitors could pave the way to better energy economics and therewith more powerful processors. Topological materials which exhibit emergent electromagnetism are promising candidates for such future technologies. Due to its helical crystal structure and strong spin-orbit interaction, tellurium exhibits an experimentally verified internal inductance. By formulating the constitutive equations which describe electromagnetism in tellurium, we show how capacitive and inductive properties naturally emerge in the material. We demonstrate on the basis of AC-impedance measurements that elemental tellurium exhibits an unusually high virtual capacitance and inductance, far exceeding previously studied materials. The highest capacitance we detect in our samples is 130 mF and in one of our samples we measure an extremely impressive virtual inductance of 1.5 H. For low current densities a single piece of tellurium mimics the reactance of an RLC-circuit.

Single crystals of the d-electron antiferromagnetic metal V5S8 can be prepared by chemical vapour transport with gaseous iodine as a transport agent. We present the outcomes of an endeavour to synthesise high-purity single crystals of V5S8 with reduced crystalline disorder, important to the formation of novel quantum orders. We report results on the residual resistivity ratio of the single crystals as growth parameters are varied including growth temperature, temperature gradient and pre-growth processing of the initial apparatus and reagents. We demonstrate that single crystals of at least a few mm in size can be successfully grown at relatively low temperatures in the range 550–600 °C. The optimisation of this method may imply a better crystallographic organisation, reducing sulphur vacancies and increasing vanadium positional order. The resulting longer electron mean free paths may enhance the probability of finding exotic quantum states of matter at low temperatures. The results presented here may also be of relevance to the development of vanadium sulphide-based energy storage and spintronic devices.

We report the observation of an unexpected quadratic temperature dependence of the heat capacity in the vanadium sulphide metal V5S8 at low temperatures which is independent of applied magnetic field. We find that the behaviour of the heat capacity is consistent with an unconventional phonon spectrum which is linear in wavevector in the c direction but quadratic in the a-b plane, indicating a form of geometrical elastic criticality. In the case of V5S8 we also observe an unusual intermediate transition at high magnetic fields between the expected spin-flop and spin-flip transitions. We demonstrate that the intermediate field-induced transition is in agreement with a model of two sublattices with frustrated inter- and intra-sublattice spin couplings.

Elemental tellurium is a small band-gap semiconductor, which is always p-doped due to the natural occurrence of vacancies. Its chiral non-centrosymmetric structure, characterized by helical chains arranged in a triangular lattice, and the presence of a spin-polarized Fermi surface, render tellurium a promising candidate for future applications. Here, we use a theoretical framework, appropriate for describing the corrections to conductivity from quantum interference effects, to show that a high-quality tellurium single crystal undergoes a quantum phase transition at low temperatures from an Anderson insulator to a correlated disordered metal at around 17 kbar. Such insulator-to-metal transition manifests itself in all measured physical quantities and their critical exponents are consistent with a scenario in which a pressure-induced Lifshitz transition shifts the Fermi level below the mobility edge, paving the way for a genuine Anderson-Mott transition. We conclude that previously puzzling quantum oscillation and transport measurements might be explained by a possible Anderson-Mott ground state and the observed phase transition.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

The dielectric and magnetic polarizations of quantum paraelectrics and paramagnetic materials have in many cases been found to initially increase with increasing thermal disorder and hence, exhibit peaks as a function of temperature. A quantitative description of these examples of "order-by-disorder" phenomena has remained elusive in nearly ferromagnetic metals and in dielectrics on the border of displacive ferroelectric transitions. Here, we present an experimental study of the evolution of the dielectric susceptibility peak as a function of pressure in the nearly ferroelectric material, strontium titanate, which reveals that the peak position collapses toward absolute zero as the ferroelectric quantum critical point is approached. We show that this behavior can be described in detail without the use of adjustable parameters in terms of the Larkin-Khmelnitskii-Shneerson-Rechester (LKSR) theory, first introduced nearly 50 y ago, of the hybridization of polar and acoustic modes in quantum paraelectrics, in contrast to alternative models that have been proposed. Our study allows us to construct a detailed temperature-pressure phase diagram of a material on the border of a ferroelectric quantum critical point comprising ferroelectric, quantum critical paraelectric, and hybridized polar-acoustic regimes. Furthermore, at the lowest temperatures, below the susceptibility maximum, we observe a regime characterized by a linear temperature dependence of the inverse susceptibility that differs sharply from the quartic temperature dependence predicted by the LKSR theory. We find that this non-LKSR low-temperature regime cannot be accounted for in terms of any detailed model reported in the literature, and its interpretation poses an empirical and conceptual challenge.

We present results for a Au-Ge alloy that is useful as a resistance-based thermometer from room temperature down to at least 0.2 K. Over a wide range, the electrical resistivity of the alloy shows a logarithmic temperature dependence, which simultaneously retains the sensitivity required for practical thermometry while also maintaining a relatively modest and easily measurable value of resistivity. We characterize the sensitivity of the alloy as a possible thermometer and show that it compares favorably with commercially available temperature sensors. We experimentally identify that the characteristic logarithmic temperature dependence of the alloy stems from Kondo-like behavior induced by the specific heat treatment it undergoes.

We have synthesized ceramic specimens of the tetragonal tungsten bronze K3Li2Ta5O15 (KLT) and characterized its phase transition via x-ray diffraction, dielectric permittivity, resonant ultrasonic spectroscopy, and heat capacity measurements. The space group of KLT is reported as both P4/mbm and Cmmm with the orthorhombic distortion occurring when there are higher partial pressures of volatileKand Li used inside the closed crucibles for the solid state synthesis. The data show strong relaxor behavior, with the temperature at which the two dielectric relative permittivity peaks decreasing, with 104 >= T-m1 >= 69K and 69 > T-m2 >= 46 K as probe frequency f is reduced from 1 MHz to 316 Hz. F tests show that the data satisfies a Vogel-Fulcher model better than Arrhenius with an extrapolated freezing temperature for epsilon' and e '' of T-f1 = + 15.8 and -11.8 K and T-f2 = -5.0 and -15.0 K for f -> 0 (tending to dc). This difference between T-f from real and imaginary values, albeit counterintuitive, is mandatory, according to the theory of Tagantsev. Therefore, by tuning frequency, the transition could be shifted to absolute zero, suggesting KLT has a relaxor-type quantum critical point. In addition, we have reanalyzed the conflicting literature for Pb2Nb2O7 pyrochlore which suggests that this also has a relaxor-type quantum critical point since the freezing temperature from the Vogel-Fulcher fitting is below absolute zero. Since the transition temperature evidenced in the dielectric data at approximately 100 kHz shifts below 0 K for very low frequencies, this transition would not be seen with heat capacity data collected in the zero-frequency (dc) limit. Both of these materials showpromise for possible newrelaxor-type quantum critical pointswith nonperovskite based structures.

Quantum melting of magnetism or ferroelectricity can lead to novel forms of order characterized by exotic excitations and unconventional superconductivity. Here we show by means of high precision measurements of the temperature and pressure dependence of the dielectric susceptibility that quantum melting of a displacive ferroelectric leads to an unconventional quantum paraelectric state exhibiting the phenomenon of u0027order by disorderu0027, namely a fluctuation induced enhancement of electric polarization extending up to a characteristic coherence temperature T*. T* vanishes at the ferroelectric quantum critical point and the square of T* increases with a characteristic linear dependence on the applied pressure. We show that in the vicinity of T* this thermal activation phenomenon can be understood quantitatively, without the use of adjustable parameters, in terms of the hybridization of the critical electric polarization field and the volume strain field of the lattice. At still lower temperatures, well below T*, we observe a breakdown of this unconventional form of quantum paraelectricity and the emergence of a still more exotic state characterized by slowly fluctuating micro-domains of the lattice structure. We suggest that this low temperature state may be viewed as a type of instanton liquid arising from anisotropic strain induced long-range correlations of the electric polarization field.

Quantum melting of magnetism or ferroelectricity can lead to novel forms of order characterized by exotic excitations and unconventional superconductivity. Here we show by means of high precision measurements of the temperature and pressure dependence of the dielectric susceptibility that quantum melting of a displacive ferroelectric leads to an unconventional quantum paraelectric state exhibiting the phenomenon of 'order by disorder', namely a fluctuation induced enhancement of electric polarization extending up to a characteristic coherence temperature T*. T* vanishes at the ferroelectric quantum critical point and the square of T* increases with a characteristic linear dependence on the applied pressure. We show that in the vicinity of T* this thermal activation phenomenon can be understood quantitatively, without the use of adjustable parameters, in terms of the hybridization of the critical electric polarization field and the volume strain field of the lattice. At still lower temperatures, well below T*, we observe a breakdown of this unconventional form of quantum paraelectricity and the emergence of a still more exotic state characterized by slowly fluctuating micro-domains of the lattice structure. We suggest that this low temperature state may be viewed as a type of instanton liquid arising from anisotropic strain induced long-range correlations of the electric polarization field.

Superconductivity has been observed in doped SrTiO$_3$ at charge-carrier densities below 10$^{18}$ cm$^{-3}$, where the density of states at the Fermi level of the itinerant electrons is several orders of magnitude lower than that of conventional metals. In terms of the Bardeen-Cooper-Schrieffer description, this implies the existence of an extraordinarily strong interaction driving the formation of Cooper pairs, potentially comparable in order of magnitude to that in some high Tc superconductors. Under suitable conditions the interaction might remain effective at densities approaching metallic densities, leading to the possibility of pair formation at elevated temperatures. Here we investigate the pressure dependence of the resistivity and superconducting transition temperature, Tc, of SrTiO$_3$ at a carrier density near to optimal doping. Our experiments show that Tc collapses rapidly with pressure and hence with increasing frequency of the soft transverse-optical phonon mode connected to the ferroelectric quantum critical point. We show that the superconductivity phase diagram can be understood in terms of the coupling of electrons via two hybrid longitudinal polar modes, based on a model of dipolar fluctuations of the charge carrier-ion system. In particular, we predict that for carrier densities above the order of 10$^{18}$ cm$^{-3}$, Tc can be strongly enhanced on approaching the ferroelectric quantum critical point, as seen in our measurements of SrTiO$_3$ and as found in many electrically conducting magnetic analogues. However below this density we predict the reverse behaviour, namely that Tc is suppressed on approaching the ferroelectric quantum critical point. Our model is also relevant to superconductivity found in gated ferroelectric quantum critical systems such as KTaO$_3$ and can guide searches for new superconductors in a diversity of materials.

In this paper we describe physical properties arising in the vicinity of two coupled quantum phase transitions. We consider a phenomenological model based on two scalar order parameter fields locally coupled biquadratically and having a common quantum critical point as a function of a quantum tuning parameter such as pressure or magnetic field. A self-consistent treatment suggests that the uniform static susceptibilities of the two order parameter fields may have the same qualitative form at low temperature even where the forms differ sharply in the absence of the biquadratic coupling. The possible limitations of the self-consistent analysis leading to this prediction are considered.

SER and EBS acknowledge support from a CONFAP Newton grant. T.V. acknowledges support from the NSF under Grant No. DMR-1506152.

The emergence of complex and fascinating states of quantum matter in the neighborhood of zero temperature phase transitions suggests that such quantum phenomena should be studied in a variety of settings. Advanced technologies of the future may be fabricated from materials where the cooperative behavior of charge, spin and current can be manipulated at cryogenic temperatures. The progagating lattice dynamics of displacive ferroelectrics make them appealing for the study of quantum critical phenomena that is characterized by both space- and time-dependent quantities. In this key issues article we aim to provide a self-contained overview of ferroelectrics near quantum phase transitions. Unlike most magnetic cases, the ferroelectric quantum critical point can be tuned experimentally to reside at, above or below its upper critical dimension; this feature allows for detailed interplay between experiment and theory using both scaling and self-consistent field models. Empirically the sensitivity of the ferroelectric T c's to external and to chemical pressure gives practical access to a broad range of temperature behavior over several hundreds of Kelvin. Additional degrees of freedom like charge and spin can be added and characterized systematically. Satellite memories, electrocaloric cooling and low-loss phased-array radar are among possible applications of low-temperature ferroelectrics. We end with open questions for future research that include textured polarization states and unusual forms of superconductivity that remain to be understood theoretically.

BaFe12O19 is a popular M-type hexaferrite with a Néel temperature of 720 K and is of enormous commercial value ($3 billion/year). It is an incipient ferroelectric with an expected ferroelectric phase transition extrapolated to lie at 6 K but suppressed due to quantum fluctuations. The theory of quantum criticality for such uniaxial ferroelectrics predicts that the temperature dependence of the electric susceptibility χ diverges as 1/T3, in contrast to the 1/T2 dependence found in pseudo-cubic materials such as SrTiO3 or KTaO3. In this paper we present evidence of the susceptibility varying as 1/T3, i.e. with a critical exponent γ = 3. In general γ = (d + z – 2)/z, where the dynamical exponent for a ferroelectric z = 1 and the dimension is increased by 1 from deff = 3 + z to deff = 4 + z due to the effect of long-range dipole interactions in uniaxial as opposed to multiaxial ferroelectrics. The electric susceptibility of the incipient ferroelectric SrFe12O19, which is slightly further from the quantum phase transition is also found to vary as 1/T3.

In this paper we analyze the effects of electron band hybridization in a superconducting material studying the effects on the binding energy of the Cooper pairs and on their size. We adopt a multi-band model that provides the intra-band pairing correlation functions. The hybridization can be tuned by an externally applied pressure or doping, and couple both bands acting to suppress the superconducting gap amplitude. Our analysis extends for all ranges of interactions coming from the usual BCS limit (weak coupling) going to the BEC limit of Cooper pairs (strong coupling) where these pairs become an effective bosonic particle. Our results show the dependence of the Cooper-pair binding energy and size as a function of the hybridization for T=0. We propose a theoretical description for the intra-band binding-energy of the effective bosons in the BEC limit as a function of the hybridization. We also propose a description for the dependence of doping parameter as a function of the hybridization for the La2−xSrxCuO4 compound.

Tris-sarcosine calcium chloride (TSCC) is a highly uniaxial ferroelectric with a Curie temperature of approximately 130 K. By suppressing ferroelectricity with bromine substitution on the chlorine sites, pure single crystals were tuned through a ferroelectric quantum phase transition. The resulting quantum critical regime was investigated in detail and was found to persist up to temperatures of at least 30-40 K. The nature of long-range dipole interactions in uniaxial materials, which lead to non-analytical terms in the free-energy expansion in the polarization, predict a dielectric susceptibility varying as 1/T(3)close to the quantum critical point. Rather than this, we find that the dielectric susceptibility varies as 1/T(2) as expected and observed in better known multi-axial systems. We explain this result by identifying the ultra-weak nature of the dipole moments in the TSCC family of crystals. Interestingly, we observe a shallow minimum in the inverse dielectric function at low temperatures close to the quantum critical point in paraelectric samples that may be attributed to the coupling of quantum polarization and strain fields. Finally, we present results of the heat capacity and electro-caloric effect and explain how the time dependence of the polarization in ferroelectrics and paraelectrics should be considered when making quantitative estimates of temperature changes induced by applied electric fields.

BaFe12O19 is a popular M-type hexaferrite with T(Neel) = 720 K of enormous commercial value (3 billion dollars/year). It exhibits an incipient ferroelectric phase transition (in violation of the Spaldin-Hill rule) extrapolated to lie at 6.0 K Kelvin but suppressed due to quantum fluctuations (as in SrTiO3). The QCP theory of Khmelnitskii for such uniaxial ferroelectrics predicts that the inverse isothermal electric susceptibility varies as T cubed, in contrast to that for pseudo-cubic materials such as SrTiO3 or KTaO3, a hypothesis we verify.

We describe some unsolved problems of current interest; these involve quantum critical points in ferroelectrics and problems which are not amenable to the usual density functional theory, nor to classical Landau free energy approaches (they are kinetically limited), nor even to the Landau-Kittel relationship for domain size (they do not satisfy the assumption of infinite lateral diameter) because they are dominated by finite aperiodic boundary conditions.