arXiv subjects

A. J. Schofield

Publications and source records attributed to A. J. Schofield.

At least 19 recordsLinked to original sources

arXiv2022

Observing separate spin and charge Fermi seas in a strongly correlated one-dimensional conductor

An electron is usually considered to have only one form of kinetic energy, but could it have more, for its spin and charge, by exciting other electrons? In one dimension (1D), the physics of interacting electrons is captured well at low energies by the Tomonaga-Luttinger model, yet little has been observed experimentally beyond this linear regime. Here, we report on measurements of many-body modes in 1D gated-wires using tunnelling spectroscopy. We observe two parabolic dispersions, indicative of separate Fermi seas at high energies, associated with spin and charge excitations, together with the emergence of two additional 1D 'replica' modes that strengthen with decreasing wire length. The effective interaction strength is varied by changing the amount of 1D inter-subband screening by over 45%. Our findings demonstrate the existence of spin-charge separation in the whole energy band outside the low-energy limit of validity of the Tomonaga-Luttinger model, and also set a constraint on the validity of the newer nonlinear Tomonaga-Luttinger theory.

cond-mat.mes-hall↗

arXiv2019

Quenched nematic criticality separating two superconducting domes in an iron-based superconductor under pressure

The nematic electronic state and its associated nematic critical fluctuations have emerged as potential candidates for superconducting pairing in various unconventional superconductors. However, in most materials their coexistence with other magnetically-ordered phases poses significant challenges in establishing their importance. Here, by combining chemical and hydrostatic physical pressure in FeSe$_{0.89}$S$_{0.11}$, we provide a unique access to a clean nematic quantum phase transition in the absence of a long-range magnetic order. We find that in the proximity of the nematic phase transition, there is an unusual non-Fermi liquid behavior in resistivity at high temperatures that evolves into a Fermi liquid behaviour at the lowest temperatures. From quantum oscillations in high magnetic fields, we trace the evolution of the Fermi surface and electronic correlations as a function of applied pressure. We detect experimentally a Lifshitz transition that separates two distinct superconducting regions: one emerging from the nematic electronic phase with a small Fermi surface and strong electronic correlations and the other one with a large Fermi surface and weak correlations that promotes nesting and stabilization of a magnetically-ordered phase at high pressures. The lack of mass divergence suggests that the nematic critical fluctuations are quenched by the strong coupling to the lattice. This establishes that superconductivity is not enhanced at the nematic quantum phase transition in the absence of magnetic order.

cond-mat.supr-con↗

arXiv2018

Momentum-dependent power law measured in an interacting quantum wire beyond the Luttinger limit

Power laws in physics have until now always been associated with a scale invariance originating from the absence of a length scale. Recently, an emergent invariance even in the presence of a length scale has been predicted by the newly-developed nonlinear-Luttinger-liquid theory for a one-dimensional (1D) quantum fluid at finite energy and momentum, at which the particle's wavelength provides the length scale. We present the first experimental example of this new type of power law in the spectral function of interacting electrons in a quantum wire using a transport-spectroscopy technique. The observed momentum dependence of the power law in the high-energy region matches the theoretical predictions, supporting not only the 1D theory of interacting particles beyond the linear regime but also the existence of a new type of universality that emerges at finite energy and momentum.

cond-mat.mes-hall↗

arXiv2016

Evolution of the Fermi surface of the nematic superconductors FeSe1-xSx

We investigate the evolution of the Fermi surfaces and electronic interactions across the nematic phase transition in single crystals of FeSe1-xSx using Shubnikov-de Haas oscillations in high magnetic fields up to 45 tesla in the low temperature regime. The unusually small and strongly elongated Fermi surface of FeSe increases monotonically with chemical pressure, x, due to the suppression of the in-plane anisotropy except for the smallest orbit which suffers a Lifshitz-like transition once nematicity disappears. Even outside the nematic phase the Fermi surface continues to increase, in stark contrast to the reconstructed Fermi surface detected in FeSe under applied external pressure. We detect signatures of orbital-dependent quasiparticle mass renomalization suppressed for those orbits with dominant dxz=yz character, but unusually enhanced for those orbits with dominant dxy character. The lack of enhanced superconductivity outside the nematic phase in FeSe1-xSx suggest that nematicity may not play the essential role in enhancing Tc in these systems.

cond-mat.supr-con↗

arXiv2016

Nonlinear spectra of spinons and holons in short GaAs quantum wires

One-dimensional electronic fluids are peculiar conducting systems, where the fundamental role of interactions leads to exotic, emergent phenomena, such as spin-charge (spinon-holon) separation. The distinct low-energy properties of these 1D metals are successfully described within the theory of linear Luttinger liquids, but the challenging task of describing their high-energy nonlinear properties has long remained elusive. Recently, novel theoretical approaches accounting for nonlinearity have been developed, yet the rich phenomenology that they predict remains barely explored experimentally. Here, we probe the nonlinear spectral characteristics of short GaAs quantum wires by tunnelling spectroscopy, using an advanced device consisting of 6000 wires. We find evidence for the existence of an inverted (spinon) shadow band in the main region of the particle sector, one of the central predictions of the new nonlinear theories. A (holon) band with reduced effective mass is clearly visible in the particle sector at high energies.

cond-mat.mes-hall↗

arXiv2015

Nature of the many-body excitations in a quantum wire: theory and experiment

The natural excitations of an interacting one-dimensional system at low energy are hydrodynamic modes of Luttinger liquid, protected by the Lorentz invariance of the linear dispersion. We show that beyond low energies, where quadratic dispersion reduces the symmetry to Galilean, the main character of the many-body excitations changes into a hierarchy: calculations of dynamic correlation functions for fermions (without spin) show that the spectral weights of the excitations are proportional to powers of $\mathcal{R}^{2}/L^{2}$, where $\mathcal{R}$ is a length-scale related to interactions and $L$ is the system length. Thus only small numbers of excitations carry the principal spectral power in representative regions on the energy-momentum planes. We have analysed the spectral function in detail and have shown that the first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalised single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power-laws at the spectral edge. We have illustrated crossover to Luttinger liquid at low energy by calculating the local density of state through all energy scales: from linear to non-linear, and to above the chemical potential energies. In order to test this model, we have carried out experiments to measure momentum-resolved tunnelling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure. We observe well-resolved spin-charge separation at low energy with appreciable interaction strength and only a parabolic dispersion of the first-level mode at higher energies. We find structure resembling the second-level excitations, which dies away rapidly at high momentum in line with the theoretical predictions here.

cond-mat.str-el↗

arXiv2015

Quantum Multicriticality

Several quantum critical compounds have been argued to have multiple instabilities towards orders with distinct dynamical exponents. We present an analysis of a quantum multicritical point in an itinerant magnet with competition between ferro- and antiferromagnetic order, modelled using Hertz-Millis theory. We perform a one-loop renormalization group treatment of this action in the presence of two dynamical exponents. In two and in three dimensions, when both incipient orders are quantum critical, we find that the specific heat, thermal expansion and Grüneisen parameter obey the same power laws as those expected for a single ferromagnetic quantum critical point. The antiferromagnetic correlation length and boundary of the antiferromagnetic ordered phase are suppressed by the dangerously irrelevant interactions with quantum critical ferromagnetic fluctuations. We find no difference between a quantum bicritical point and a quantum tetracritical point. Our results are compared with experiments on NbFe$_2$.

cond-mat.str-el↗

arXiv2015

Emergence of the nematic electronic state in FeSe

We present a comprehensive study of the evolution of the nematic electronic structure of FeSe using high resolution angle-resolved photoemission spectroscopy (ARPES), quantum oscillations in the normal state and elastoresistance measurements. Our high resolution ARPES allows us to track the Fermi surface deformation from four-fold to two-fold symmetry across the structural transition at ~87 K which is stabilized as a result of the dramatic splitting of bands associated with dxz and dyz character. The low temperature Fermi surface is that a compensated metal consisting of one hole and two electron bands and is fully determined by combining the knowledge from ARPES and quantum oscillations. A manifestation of the nematic state is the significant increase in the nematic susceptibility as approaching the structural transition that we detect from our elastoresistance measurements on FeSe. The dramatic changes in electronic structure cannot be explained by the small lattice effects and, in the absence of magnetic fluctuations above the structural transition, points clearly towards an electronically driven transition in FeSe stabilized by orbital-charge ordering.

cond-mat.supr-con↗

arXiv2015

Dichotomy between the hole and electrons behavior in the multiband FeSe probed by ultra high magnetic fields

Magnetoresistivity \r{ho}xx and Hall resistivity \r{ho}xy in ultra high magnetic fields up to 88T are measured down to 0.15K to clarify the multiband electronic structure in high-quality single crystals of superconducting FeSe. At low temperatures and high fields we observe quantum oscillations in both resistivity and Hall effect, confirming the multiband Fermi surface with small volumes. We propose a novel and independent approach to identify the sign of corresponding cyclotron orbit in a compensated metal from magnetotransport measurements. The observed significant differences in the relative amplitudes of the quantum oscillations between the \r{ho}xx and \r{ho}xy components, together with the positive sign of the high-field \r{ho}xy , reveal that the largest pocket should correspond to the hole band. The low-field magnetotransport data in the normal state suggest that, in addition to one hole and one almost compensated electron bands, the orthorhombic phase of FeSe exhibits an additional tiny electron pocket with a high mobility.

cond-mat.supr-con↗

arXiv2014

Hierarchy of modes in an interacting system

Studying interacting fermions in 1D at high energy, we find a hierarchy in the spectral weights of the excitations theoretically and we observe evidence for second-level excitations experimentally. Diagonalising a model of fermions (without spin), we show that levels of the hierarchy are separated by powers of $\mathcal{R}^{2}/L^{2}$, where $\mathcal{R}$ is a length-scale related to interactions and $L$ is the system length. The first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalised single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power-laws at the spectral edge. We measure momentum-resolved tunnelling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure, which shows parabolic dispersion of the first-level mode and well-resolved spin-charge separation at low energy with appreciable interaction strength. We find structure resembling the second-level excitations, which dies away quite rapidly at high momentum.

cond-mat.str-el↗

arXiv2014

Spectral edge mode in interacting one-dimensional systems

A continuum of excitations in interacting one-dimensional systems is bounded from below by a spectral edge that marks the lowest possible excitation energy for a given momentum. We analyse short-range interactions between Fermi particles and between Bose particles (with and without spin) using Bethe-Ansatz techniques and find that the dispersions of the corresponding spectral edge modes are close to a parabola in all cases. Based on this emergent phenomenon we propose an empirical model of a free, non-relativistic particle with an effective mass identified at low energies as the bare electron mass renormalised by the dimensionless Luttinger parameter $K$ (or $K_σ$ for particles with spin). The relevance of the Luttinger parameters beyond the low energy limit provides a more robust method for extracting them experimentally using a much wide range of data from the bottom of the one-dimensional band to the Fermi energy. The empirical model of the spectral edge mode complements the mobile impurity model to give a description of the excitations in proximity of the edge at arbitrary momenta in terms of only the low energy parameters and the bare electron mass. Within such a framework, for example, exponents of the spectral function are expressed explicitly in terms of only a few Luttinger parameters.

cond-mat.str-el↗

arXiv2013

Luttinger parameters of interacting fermions in 1D at high energies

Interactions between electrons in one-dimension are fully described at low energies by only a few parameters of the Tomonaga-Luttinger model which is based on linearisation of the spectrum. We consider a model of spinless fermions with a short range interaction via the Bethe-Ansatz technique and show that a Luttinger parameter emerges in an observable beyond the low energy limit. A distinct feature of the spectral function, the edge that marks the lowest possible excitation energy for a given momentum, is parabolic for arbitrary momenta and the prefactor is a function of the Luttinger parameter, K.

cond-mat.str-el↗

arXiv2012

Hall effect in heavy-fermion metals

The heavy fermion systems present a unique platform in which strong electronic correlations give rise to a host of novel, and often competing, electronic and magnetic ground states. Amongst a number of potential experimental tools at our disposal, measurements of the Hall effect have emerged as a particularly important one in discerning the nature and evolution of the Fermi surfaces of these enigmatic metals. In this article, we present a comprehensive review of Hall effect measurements in the heavy-fermion materials, and examine the success it has had in contributing to our current understanding of strongly correlated matter. Particular emphasis is placed on its utility in the investigation of quantum critical phenomena which are thought to drive many of the exotic electronic ground states in these systems. This is achieved by the description of measurements of the Hall effect across the putative zero-temperature instability in the archetypal heavy-fermion metal YbRh$_2$Si$_2$. Using the Ce$M$In$_5$ (with $M =$ Co, Ir) family of systems as a paradigm, the influence of (antiferro-)magnetic fluctuations on the Hall effect is also illustrated. This is compared to prior Hall effect measurements in the cuprates and other strongly correlated systems to emphasize on the generality of the unusual magnetotransport in materials with non-Fermi liquid behavior.

cond-mat.str-el↗

arXiv2010

Probing spin-charge separation in a Tomonaga-Luttinger liquid

In a one-dimensional (1D) system of interacting electrons, excitations of spin and charge travel at different speeds, according to the theory of a Tomonaga-Luttinger Liquid (TLL) at low energies. However, the clear observation of this spin-charge separation is an ongoing challenge experimentally. We have fabricated an electrostatically-gated 1D system in which we observe spin-charge separation and also the predicted power-law suppression of tunnelling into the 1D system. The spin-charge separation persists even beyond the low-energy regime where the TLL approximation should hold. TLL effects should therefore also be important in similar, but shorter, electrostatically gated wires, where interaction effects are being studied extensively worldwide.

cond-mat.str-el↗

arXiv2010

Quantum Criticality and Novel Phases: Summary and Outlook

This conference summary and outlook provides a personal overview of the topics and themes of the August 2009 Dresden meeting on quantum criticality and novel phases. The dichotomy between the local moment and the itinerant views of magnetism is revisited and refreshed in new materials, new probes and new theoretical ideas. New universality and apparent zero temperature phases of matter move us beyond the old ideas of quantum criticality. This is accompanied by alternative pairing interactions and as yet unidentified phases developing in the vicinity of quantum critical points. In discussing novel order, the magnetic analogues of superconductivity are considered as candidate states for the hidden order that sometimes develops in the vicinity of quantum critical points in metallic systems. These analogues can be thought of as "pairing" in the particle-hole channel and are tabulated. This analogy is used to outline a framework to study the relation between ferromagnetic fluctuations and the propensity of a metal to nematic type phases which at weak coupling correspond to Pomeranchuk instabilities. This question can be related to the fundamental relations of Fermi liquid theory.

cond-mat.str-el↗

arXiv2009

Out-of-plane thermopower of strongly correlated layered systems: an application to Bi_2(Sr,La)_2CaCu_2O_{8+δ}

We calculate the out-of-plane thermopower in a quasi-two dimensional system, and argue that this quantity is an effective probe of the asymmetry of the single-particle spectral function. We find that the temperature and doping dependence of the out-of-plane thermopower in Bi_2(Sr,La)_2CaCu_2O_{8+δ} single crystals is broadly consistent with the behavior of the spectral function determined from ARPES and tunneling experiments. We also investigate the relationship between out-of-plane thermopower and entropy in a quasi-two dimensional material. We present experimental evidence that at moderate temperatures, there is a qualitative correspondence between the out-of-plane thermopower in Bi_2(Sr,La)_2CaCu_2O_{8+δ}, and the entropy obtained from specific heat measurements. Finally, we argue that the derivative of the entropy with respect to particle number may be the more appropriate quantity to compare with the thermopower, rather than the entropy per particle.

cond-mat.str-el↗

arXiv2009

Effect of disorder on a Pomeranchuk instability

We study the effect of disorder on the order parameter equation and transition temperature of a Pomeranchuk-type Fermi-surface instability using replica mean field theory. We consider the example of a phase transition to a $d_{x^2 +y^2}$ type Fermi surface distortion, and show that, in the regime where such a transition is second order, the transition temperature is reduced by disorder in essentially the same way as that for a d-wave superconductor. We argue that observing this disorder dependence of metal-to-metal transition might be a useful indicator of a finite angular momentum Fermi surface distortion.

cond-mat.str-el↗

arXiv2008

Thermoelectric Effects in Anisotropic Systems: Measurement and Applications

The Harman method for measuring the thermal conductivity of a sample using the Peltier effect, may also be used to determine the dimensionless figure of merit from just two electrical resistance measurements. We consider a modified version of the Harman method where the current contacts are much smaller than the contact faces of the sample. We calculate the voltage and temperature distributions in a rectangular sample of a material having anisotropy in all of its transport coefficients. The thermoelectric anisotropy has important consequences in the form of thermoelectric eddy currents and the Bridgman effect. We prove that in the limit of a very thin sample of arbitrary shape, there exist van der Pauw formulae relating particular linear combinations of the potential and temperature differences between points on the edges of the sample. We show that the Harman figure of merit can be radically different from the intrinsic figures of merit of the material, and can often be substantially enhanced. By defining an effective figure of merit in terms of the rate of entropy production, we show that the increase in the Harman figure of merit does indicate an improvement in the thermoelectric performance of an anisotropic sample having small current contacts. However, we also prove that in the case of a material with tetragonal symmetry, the effective figure of merit is always bounded from above by the largest intrinsic figure of merit of the material.

cond-mat.mtrl-sci↗