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A system with charge conservation and lattice translation symmetry has a well-defined fillingν, which is a real number representing the average charge per unit cell. We show that ifνis fractional (i.e., not an integer), this imposes very strong constraints on the low-energy theory of the system and give a framework to understand such constraints in great generality, vastly generalizing the Luttinger and Lieb-Schultz-Mattis theorems. The most powerful constraint comes about ifνis continuously tunable (i.e., the system is charge compressible), in which case, we show that the low-energy theory must have a very large emergent symmetry group—larger than any compact Lie group. An example is the Fermi surface of a Fermi liquid, where the charge at every point on the Fermi surface is conserved. We expect that in many, if not all, cases, even exotic non-Fermi liquids will have the same emergent symmetry group as a Fermi liquid, even though they could have very different dynamics. We call a system with this property an ersatz Fermi liquid. We show that ersatz Fermi liquids share a number of properties in common with Fermi liquids, including Luttinger’s theorem (which is thus extended to a large class of non-Fermi liquids) and periodic “quantum oscillations” in the response to an applied magnetic field. We also establish versions of Luttinger’s theorem for the composite Fermi liquid in quantum Hall systems and for spinon Fermi surfaces in Mott insulators. Our work makes a connection between filling constraints and the theory of symmetry-protected topological phases, in particular through the concept of “’t Hooft anomalies.”

We demonstrate a remarkable property of metallic Fermi liquids: the transverse conductivity assumes a universal value in the quasi-static (ω → 0) limit for wavevectors q in the regime \\({l}_{\\text{mfp}}^{-1}\\ll q\\ll {p}_{\\text{F}}\\), where l mfp is the mean free path and p F is the Fermi momentum. This value is \\(({e}^{2}/h){\\mathcal{R}}_{\\text{FS}}/q\\) in two dimensions (2D), where \\({\\mathcal{R}}_{\\text{FS}}\\) measures the local radius of curvature of the Fermi surface (FS) in momentum space. Even more surprisingly, we find that U(1) spin liquids with a spinon FS have the same universal transverse conductivity. This means such spin liquids behave effectively as metals in this regime, even though they appear insulating in standard transport experiments. Moreover, we show that transverse current fluctuations result in a universal low-frequency magnetic noise that can be directly probed by a spin qubit, such as a nitrogen-vacancy (NV) center in diamond, placed at a distance z above of the 2D metal or spin liquid. Specifically the magnetic noise is given by \\(C\\omega {\\mathcal{P}}_{\\text{FS}}/z\\), where \\({\\mathcal{P}}_{\\text{FS}}\\) is the perimeter of the FS in momentum space and C is a combination of fundamental constants of nature. Therefore these observables are controlled purely by the geometry of the FS and are independent of kinematic details of the quasi-particles, such as their effective mass and interactions. This behavior can be used as a new technique to measure the size of the FS of metals and as a smoking gun probe to pinpoint the presence of the elusive spinon FS in two-dimensional systems. We estimate that this universal regime is within reach of current NV center spectroscopic techniques for several spinon FS candidate materials.

The recently discovered three-dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit interaction or the crystal lattice, driving the system through a topological quantum phase transition. By directly measuring the topological quantum numbers and invariants, we report the observation of a phase transition in a tunable spin-orbit system, BiTl(S₁— δ Se δ )₂, in which the topological state formation is visualized. In the topological state, vortex-like polarization states are observed to exhibit three-dimensional vectorial textures, which collectively feature a chirality transition as the spin momentum—locked electrons on the surface go through the zero carrier density point. Such phase transition and texture inversion can be the physical basis for observing fractional charge (±e/2) and other fractional topological phenomena.

The magnetoresistance (MR) of a material is typically insensitive to reversing the applied field direction and varies quadratically with magnetic field in the low-field limit. Quantum effects, unusual topological band structures, and inhomogeneities that lead to wandering current paths can induce a cross-over from quadratic to linear MR with increasing magnetic field. Here we explore a series of metallic charge- and spin-density-wave systems that exhibit extremely large positive linear MR. By contrast to other linear MR mechanisms, this effect remains robust down to miniscule magnetic fields of tens of Oersted at low temperature. We frame an explanation of this phenomenon in a semiclassical narrative for a broad category of materials with partially gapped Fermi surfaces due to density waves.

Three-dimensional topological semi-metals carry quasiparticle states that mimic massless relativistic Dirac fermions, elusive particles that have never been observed in nature. As they appear in the solid body, they are not bound to the usual symmetries of space-time and thus new types of fermionic excitations that explicitly violate Lorentz-invariance have been proposed, the so-called type-II Dirac fermions. We investigate the electronic spectrum of the transition-metal dichalcogenide PtSe2 by means of quantum oscillation measurements in fields up to 65 T. The observed Fermi surfaces agree well with the expectations from band structure calculations, that recently predicted a type-II Dirac node to occur in this material. A hole- and an electron-like Fermi surface dominate the semi-metal at the Fermi level. The quasiparticle mass is significantly enhanced over the bare band mass value, likely by phonon renormalization. Our work is consistent with the existence of type-II Dirac nodes in PtSe2, yet the Dirac node is too far below the Fermi level to support free Dirac-fermion excitations.

Charge density wave (CDW) is an important concept in condensed matter physics, germane to a number of physical phenomena. But the origin of CDW is still under debate, partly because the origin and properties of CDW are highly material-dependent. The concept of a CDW has been applied to many materials without a clear definition of the fundamental nature of CDW. As a result, misconceptions about CDW can be seen in the literature. In this review, we will try to describe and explain the possible existing misconceptions associated with the origin of CDWs.

In recent times, Bogoliubov Fermi surfaces (BFSs) in superconductors (SCs) have drawn significant attention due to a substantial population of Bogoliubov quasiparticles (BQPs) together with Cooper pairs (CPs) in them. The BQPs as zero energy excitations give rise to captivating and intricate charge dynamics within the BFSs. In this theoretical study, we propose to reveal the unique signatures of the topologically protected BFSs in bulk d -wave SCs using normal metal/time-reversal symmetry (TRS) broken d -wave SC hybrid setup, in terms of the differential conductance and Fano factor (FF). Orientation of crystal a axis with respect to junction normal, quantified by the parameter α , is crucial for transport properties in these hybrid devices. For α  = 0, an enhancement in zero-bias conductance (ZBC) can be identified as a key signature of BFSs. However, for α ≠ 0 , this feature does not replicate due to the presence of the localized Andreev bound state (ABS) at the interface. The interplay of ABS and BFSs gives rise to an anomalous behavior in ZBC compared to the α  = 0 case. This behavior remains qualitatively similar even at finite temperatures. Finally, we explain this anomalous behavior by analyzing the effective charge of the carriers in terms of the FF. The simplicity of our setup based on d -wave SC makes our proposal persuasive.

Recent experimental [I. Jo et al., Phys. Rev. Lett. 119, 016402 (2017)] and numerical [M. Ippoliti, S. D. Geraedts, R. N. Bhatt, Phys. Rev. B 95, 201104 (2017)] evidence suggests an intriguing universal relationship between the Fermi surface anisotropy of the noninteracting parent 2-dimensional (2D) electron gas and the strongly correlated composite Fermi liquid formed in a strong magnetic field close to half-filling. Inspired by these observations, we explore more generally the question of anisotropy renormalization in interacting 2D Fermi systems. Using a recently developed [H. -K. Tang et al., Science 361, 570 (2018)] nonperturbative and numerically exact projective quantum Monte Carlo simulation as well as other numerical and analytic techniques, only for Dirac fermions with long-range Coulomb interactions do we find a universal square-root decrease of the Fermi-surface anisotropy. For the ν = 1/2 composite Fermi liquid, this result is surprising since a Dirac fermion ground state was only recently proposed as an alternative to the usual Halperin–Lee–Read state. Our proposed universality can be tested in several anisotropic Dirac materials including graphene, topological insulators, organic conductors, and magic-angle twisted bilayer graphene.

Electronic systems with quasi-one-dimensional (Q1D) Fermi surface tend to form either a charge-density-wave (CDW) or a spin-density-wave ground state at low temperatures due to one-dimensional instabilities. Among various CDW states, surface CDWs are different from that within the bulk due to the reduced dimensionality. Here we report the systematic investigation of charge density modulation on the surface of in situ cleaved TaTe4 crystal by means of low temperature scanning tunneling microscopy/spectroscopy, corroborated with density functional theory calculation. Well-defined Q1D modulation (4a, 6c) accompanied with a periodic lattice distortion is clearly observed on the (010) cleaved surface, distinct from that of its bulk CDW (2a × 2a × 3c). Tunneling spectroscopic measurements reveal a partially-opened energy gap about 23 meV around Fermi level. Such gap shows similar spatial variation with the periodicity of surface modulation and diminishes subsequently as temperature rises, which indicates a novel surface-related CDW gap states. The surface modulation vectors fit well with the Fermi surface nesting vectors, derived from the calculated Fermi surfaces. Surprisingly, such surface modulation can be suppressed greatly by applying vertical magnetic field and a critical field about 9.05 T can be estimated from field-dependent data. Our results demonstrate that this unique CDW modulation is strongly related to Fermi surface nesting mediated electron-electron coupling due to the reduced dimensionality of the surface, and can be readily tuned by relatively small magnetic field.

Many-body dipolar effects in Fermi gases are quite subtle as they energetically compete with the large kinetic energy at and below the Fermi surface (FS). Recently it was experimentally observed in a sample of erbium atoms that its FS is deformed from a sphere to an ellipsoid due to the presence of the anisotropic and long-range dipole-dipole interaction Aikawa et al (2014 Science 345 1484). Moreover, it was suggested that, when the dipoles are rotated by means of an external field, the FS follows their rotation, thereby keeping the major axis of the momentum-space ellipsoid parallel to the dipoles. Here we generalise a previous Hartree-Fock mean-field theory to systems confined in an elongated triaxial trap with an arbitrary orientation of the dipoles relative to the trap. With this we study for the first time the effects of the dipoles' arbitrary orientation on the ground-state properties of the system. Furthermore, taking into account the geometry of the system, we show how the ellipsoidal FS deformation can be reconstructed, assuming ballistic expansion, from the experimentally measurable real-space aspect ratio after a free expansion. We compare our theoretical results with new experimental data measured with erbium Fermi gas for various trap parameters and dipole orientations. The observed remarkable agreement demonstrates the ability of our model to capture the full angular dependence of the FS deformation. Moreover, for systems with even higher dipole moment, our theory predicts an additional unexpected effect: the FS does not simply follow rigidly the orientation of the dipoles, but softens showing a change in the aspect ratio depending on the dipoles' orientation relative to the trap geometry, as well as on the trap anisotropy itself. Our theory provides the basis for understanding and interpreting phenomena in which the investigated physics depends on the underlying structure of the FS, such as fermionic pairing and superfluidity.