We study the different phases in the Quantum Electrodynamics of 3D Dirac semimetals depending on the number $N$ of Dirac fermions, using renormalization group methods and the self-consistent resolution of the Schwinger-Dyson equation. We find that, for $N < 4$, a phase with dynamical generation of mass prevails at sufficiently strong coupling, sharing the same physics of the excitonic instability in 2D Dirac semimetals. For $N \geq 4$, we show that the phase diagram has instead a line of critical points characterized by the suppression of the quasiparticle weight at low energies, making the system to fall into the class of marginal Fermi liquids. Such a boundary marks the transition to a kind of strange metal which can be still defined in terms of electron quasiparticles, but with parameters that have large imaginary parts implying an increasing deviation from the conventional Fermi liquid picture.
We solve the two-band model for the transport across a junction between a semimetal and an excitonic insulator. We analyze the current in terms of two competing terms associated with neutral excitons and charged carriers, respectively. We find a high value for the interface resistance, extremely sensitive to the junction transparency. We explore favorable systems for experimental confirmation.
A sufficiently strong long-range Coulomb interaction can induce excitonic pairing in gapless Dirac semimetals, which generates a finite gap and drives semimetal-insulator quantum phase transition. This phenomenon is in close analogy to dynamical chiral symmetry breaking in high energy physics. In most realistic Dirac semimetals, including suspended graphene, Coulomb interaction is too weak to open an excitonic gap. The Coulomb interaction plays a more important role at low energies in a two-dimensional semi-Dirac semimetal, in which the fermion spectrum is linear in one component of momenta an…
From the solution of a two-band model, we predict that the thermal and electrical transport across the junction of a semimetal and an excitonic insulator will exhibit high resistance behavior and low entropy production at low temperatures, distinct from a junction of a semimetal and a normal semiconductor. This phenomenon, ascribed to the dissipationless exciton flow which dominates over the charge transport, is based on the much longer length scale of the change of the effective interface potential for electron scattering due to the coherence of the condensate than in the normal state.
The strong Coulomb interaction between massless Dirac fermions can drive a semimetal-insulator transition in single-layer graphene by dynamically generating an excitonic fermion gap. There is a critical interaction strength $λ_c$ that separates the semimetal phase from the insulator phase. We calculate the specific heat and susceptibility of the system and show that they exhibit distinct behaviors in the semimetal and insulator phases.
We investigate the interplay of Coulomb interactions and correlated disorder in pseudospin-3/2 semimetals, which exhibit birefringent spectra in the absence of interactions. Coulomb interactions drive the system to a marginal Fermi liquid, both for the two-dimensional (2d) and three-dimensional (3d) cases. Short-ranged correlated disorder in 2d, or a power-law correlated disorder 3d, has the same engineering dimension as the Coulomb term, in a renormalization group (RG) sense. In order to analyze the combined effects of these two kinds of interactions, we apply a dimensional regularization sch…
Tuning many-body electronic phases by an external handle is of both fundamental and practical importance in condensed matter science. The tunability mirrors the underlying interactions, and gigantic electric, optical and magnetic responses to minute external stimuli can be anticipated in the critical region of phase change. The excitonic insulator is one of the exotic phases of interacting electrons, produced by the Coulomb attraction between a small and equal number of electrons and holes, leading to the spontaneous formation of exciton pairs in narrow-gap semiconductors/semimetals. The layer…
There is a close connection between various new phenomena in Weyl semimetals and the existence of linear band crossings in the single particle description. We show, by a full self-consistent mean-field calculation, how this picture is modified in the presence of long-range Coulomb interactions. The chiral symmetry breaking occurs at strong enough interactions and the internode interband excitonic pairing channel is found to be significant, which determines the gap-opened band profile varying with interaction strength. Remarkably, in the resultant interacting phase, finite band Chern number jum…
Two-dimensional Dirac fermions are subjected to two types of interactions, namely the long-range Coulomb interaction and the short-range on-site interaction. The former induces excitonic pairing if its strength $α$ is larger than some critical value $α_c$, whereas the latter drives an antiferromagnetic Mott transition when its strength $U$ exceeds a threshold $U_c$. Here, we study the impacts of the interplay of these two interactions on excitonic pairing with the Dyson-Schwinger equation approach. We find that the critical value $α_c$ is increased by weak short-range interaction. As $U$ incre…
We compute the effects of electronic interactions on gapless spin-3/2 excitations that in a noninteracting system emerge at a bi-quadratic touching of Kramers degenerate valence and conduction bands, known as Luttinger semimetal. This model can describe the low-energy physics of HgTe, gray-Sn, 227 pyrochlore iridates and half-Heuslers. For the sake of concreteness we only consider the short-range components of the Coulomb interaction. By combining mean-field analysis with a renormalization group (RG) calculation, we construct multiple cuts of the global phase diagram of interacting spin-3/2 fe…
The assembly of suitably designed van der Waals (vdW) heterostructures represents a new approach to produce artificial systems with engineered electronic properties. Here, we apply this strategy to realize synthetic semimetals based on vdW interfaces formed by two different semiconductors. Guided by existing ab-initio calculations, we select WSe$_2$ and SnSe$_2$ mono and multilayers to assemble vdW interfaces, and demonstrate the occurrence of semimetallicity by means of different transport experiments. Semimetallicity manifests itself in a finite minimum conductance upon sweeping the gate ove…
Recently, magic-angle twisted bilayer graphene (MATBLG) has shown the emergence of various interaction-driven novel quantum phases at the commensurate fillings of the moir'e superlattice, while the charge neutrality point (CNP) remains mostly a vanilla insulator. Here, we show an emerging phase of nearly compensated semimetallicity at the CNP of twisted double bilayer graphene (TDBLG), a close cousin of MATBLG, with signatures of electronic correlation. Using electrical and thermal transport, we find almost two orders of magnitude enhancement of the thermopower in magnetic fields much smaller …
The topological nature of Weyl semimetals (WSMs) is corroborated by the presence of chiral surface states, which connect the projections of the bulk Weyl points by Fermi arcs (FAs). We study a bilayer structure realized by introducing a thin insulating spacer into a bulk WSM. Employing a self-consistent mean-field description of the interlayer Coulomb interaction, we propose that this system can develop an interlayer electron-hole pair condensate. The formation of this excitonic condensate leads to partial gapping of the FA dispersion. We obtain the dependence of the energy gap and the critica…
Recently it was suggested that transient excitonic instability can be realized in optically-pumped two-dimensional (2D) Dirac materials (DMs), such as graphene and topological insulator surface states. Here we discuss the possibility of achieving a transient excitonic condensate in optically-pumped three-dimensional (3D) DMs, such as Dirac and Weyl semimetals, described by non-equilibrium chemical potentials for photoexcited electrons and holes. Similar to the equilibrium case with long-range interactions, we find that for pumped 3D DMs with screened Coulomb potential two possible excitonic ph…
We report results of systematic measurements of charge transport properties of the 20.5nm wide HgTe-based quantum well in perpendicular magnetic field, performed under hydrostatic pressures up to 15.1 kbar. At ambient pressure transport is well described by the two-band semiclassical model.In contrast, at elevated pressure, we observed non-monotonic pressure dependence of resistivity at CNP. For pressures lower than $\approx9$ kbar, resistivity grows with pressure, in accord with expectations from the band structure calculations and the model incorporating effects of disorder on transport in 2…
We present a theoretical study of electronic transport in a hybrid junction consisting of an excitonic insulator sandwiched between a normal and a superconducting electrode. The normal region is described as a two-band semimetal and the superconducting lead as a two-band superconductor. In the excitonic insulator region, the coupling between carriers in the two bands leads to an excitonic condensate and a gap $Γ$ in the quasiparticle spectrum. We identify four different scattering processes at both interfaces. Two types of normal reflection, intra- and inter-band; and two different Andreev ref…
Recent pump-probe experiments demonstrate the possibility that Dirac materials may be driven into transient excited states describable by two chemical potentials, one for the electrons and one for the holes. Given the Dirac nature of the spectrum, such an inverted population allows the optical tunability of the density of states of the electrons and holes, effectively offering control of the strength of the Coulomb interaction. Here we discuss the feasibility of realizing transient excitonic instabilities in optically-pumped Dirac materials. We demonstrate, theoretically, the reduction of the …
Half a century ago, Mott noted that tuning the carrier density of a semimetal towards zero produces an insulating state in which electrons and holes form bound pairs. It was later argued that such pairing persists even if a semiconducting gap opens in the underlying band structure, giving rise to what has become known as the strong coupling limit of an `excitonic insulator.' While these `weak' and `strong' coupling extremes were subsequently proposed to be manifestations of the same excitonic state of electronic matter, the predicted continuity of such a phase across a band gap opening has not…
In the extreme quantum limit states under high magnetic fields, enhanced electronic correlation effects can stabilize anomalous quantum states. Using band-tuning with a magnetic field, we realized a spin-polarized quantum limit state in the field-induced semimetallic phase of a topological insulator Bi_{1-x}Sb_x. Further increase in the field injects more electrons and holes to this state and results in an unexpected reentrant insulator state in this topological semimetallic state. A single-particle picture cannot explain this reentrant insulator state, reminiscent of phase transitions due to …
Fermi liquid theory works very well in most normal metals, but is found violated in many strongly correlated electron systems, such as cuprate and heavy-fermion superconductors. A widely accepted criterion is that, the Fermi liquid theory is valid when the interaction-induced fermion damping rate approaches zero more rapidly than the energy. Otherwise, it is invalid. Here, we demonstrate that this criterion breaks down in topological double-and triple-Weyl semimetals. Renormalization group analysis reveals that, although the damping rate of double- and triple-Weyl fermions induced by the Coulo…
Anisotropic marginal Fermi liquid for Coulomb interacting generalized Weyl fermions
Rutgers University（罗格斯大学）；Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）；Lehigh University（利哈伊大学）；Indian Institute of Science（印度科学学院）；Universidad Técnica Federico Santa María（费德里科·圣塔·玛丽亚理工大学）
Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our focus is to investigate an unconventional class of the transitions between insulators and Dirac semimetals whose description is beyond conventional pseudo relativistic Dirac Hamiltonian. At the transition without the long-range Coulomb interaction, the electronic energy dispersion along one direction behaves like a relativistic particle, linear in momentum, but…
