Gapless Fermionic Excitations Research Articles

Gapped quantum spin liquid in a triangular-lattice Ising-type antiferromagnet PrMgAl11O19

In the search of quantum spin liquid (QSL), spin-1/2 triangular-lattice Heisenberg antiferromagnets have always been viewed as fertile soils. Despite the true magnetically ordered ground state, anisotropy has been considered to play a significant role in stabilizing a QSL state. However, the nature and ground state of the most anisotropic case, the triangular-lattice Ising antiferromagnet (TLIAF), remain elusive and controversial. Here, we report specific-heat and thermal-conductivity measurements on a newly discovered Ising-type QSL candidate PrMgAl11O19. At zero field, the magnetic specific heat shows a quadratic temperature dependence. On the contrary, no direct positive magnetic contribution to thermal conductivity is detected, ruling out the presence of mobile gapless fermionic excitations. Further analysis of phonon thermal conductivity reveals that the phonons are strongly scattered by thermally activated magnetic excitations out of a gap, which exhibits a linear dependence with magnetic field. These results demonstrate that the spin-1/2 TLIAF PrMgAl11O19 has a gapped Z2 QSL ground state. Published by the American Physical Society 2024

Topological superconductivity from unconventional band degeneracy with conventional pairing

We present a new scheme for Majorana modes in systems with nonsymmorphic-symmetry-protected band degeneracy. We reveal that when the gapless fermionic excitations are encoded with conventional superconductivity and magnetism, which can be intrinsic or induced by proximity effect, topological superconductivity and Majorana modes can be obtained. We illustrate this outcome in a system which respects the space group P4/nmm and features a fourfold-degenerate fermionic mode at (π, π) in the Brillouin zone. We show that in the presence of conventional superconductivity, different types of topological superconductivity, i.e., first-order and second-order topological superconductivity, with coexisting fragile Wannier obstruction in the latter case, can be generated in accordance with the different types of magnetic orders; Majorana modes are shown to exist on the boundary, at the corner and in the vortices. To further demonstrate the effectiveness of our approach, another example related to the space group P4/ncc based on this scheme is also provided. Our study offers insights into constructing topological superconductors based on bulk energy bands and conventional superconductivity and helps to find new material candidates and design new platforms for realizing Majorana modes.

Heat transport of the kagome Heisenberg quantum spin liquid candidate YCu3(OH)6.5Br2.5 : Localized magnetic excitations and a putative spin gap

The spin-1/2 kagom\'{e} Heisenberg antiferromagnet is generally accepted as one of the most promising two-dimensional models to realize a quantum spin liquid state. Previous experimental efforts were almost exclusively on only one archetypal material, the herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$, which unfortunately suffers from the notorious orphan spins problem caused by magnetic disorders. Here we turn to YCu$_3$(OH)$_{6.5}$Br$_{2.5}$, recently recognized as another host of a globally undistorted kagom\'{e} Cu$^{2+}$ lattice free from the orphan spins, thus a more feasible system for studying the intrinsic kagom\'{e} quantum spin liquid physics. Our high-resolution low-temperature thermal conductivity measurements yield a vanishing small residual linear term of $\kappa/T$ ($T\rightarrow 0$), and thus clearly rule out itinerant gapless fermionic excitations. Unusual scattering of phonons grows exponentially with temperature, suggesting thermally activated phonon-spin scattering and hence a gapped magnetic excitation, consistent with a $\mathbb{Z}_2$ quantum spin liquid ground state. Additionally, the analysis of magnetic field impact on the thermal conductivity reveals a field closing of the spin gap, while the excitations remain localized.

Alternating twisted multilayer graphene: generic partition rules, double flat bands, and orbital magnetoelectric effect

Recently the alternating twisted trilayer graphene is discovered to exhibit unconventional superconductivity, which motivates us to study the electronic structures and possible correlation effects for this class of alternating twisted multilayer graphene (ATMG) systems. In this work we consider generic ATMG systems with M-L-N stacking configurations, in which the M (L) graphene layers and the L (N) layers are twisted by an angle θ (−θ). Based on analysis from a simplified k⋅p model approach, we derive generic partition rules for the low-energy electronic structures, which exhibit various band dispersions including two pairs of flat bands and flat bands co-existing with various gapless Fermionic excitations. For a mirror-symmetric ATMG system with doubled flat bands, we further find that Coulomb interactions may drive the system into a state with intertwined electric polarization and orbital magnetization orders, which can exhibit an interaction-driven orbital magnetoelectric effect.

Fermionic criticality of anisotropic nodal point semimetals away from the upper critical dimension: Exact exponents to leading order in 1Nf

We consider the fermionic quantum criticality of anisotropic nodal point semimetals in d=dL+dQ spatial dimensions that disperse linearly in dL dimensions, and quadratically in the remaining dQ dimensions. When subject to strong interactions, these systems are susceptible to semimetal-insulator transitions concurrent with spontaneous symmetry breaking. Such quantum critical points are described by effective field theories of anisotropic nodal fermions coupled to dynamical order parameter fields. We analyze the universal scaling in the physically relevant spatial dimensions, generalizing to a large number Nf of fermion flavors for analytic control. Landau damping by gapless fermionic excitations gives rise to nonanalytic self-energy corrections to the bosonic order-parameter propagator that dominate the long-wavelength behavior. We show that perturbative momentum shell RG leads to nonuniversal, cutof-dependent results, as it does not correctly account for this nonanalytic structure. In turn, using a completely general soft cutoff formulation, we demonstrate that the correct IR scaling of the dressed bosonic propagator can be deduced by enforcing that results are independent of the cutoff scheme. Using the soft cutoff RG with the dressed dynamical RPA boson propagator, we compute the exact critical exponents for anisotropic semi-Dirac fermions (dL=1, dQ=1) to leading order in 1/Nf and to all loop orders. Applying the same method to relativistic Dirac fermions, we reproduce the critical exponents obtained by other methods, such as conformal bootstrap. Unlike in the relativistic case, where the UV-IR connection is reestablished at the upper critical dimension, nonanalytic IR contributions persist near the upper critical line 2dL+dQ=4 of anisotropic nodal fermions. We present ε expansions in both the number of linear and quadratic dimensions. The corrections to critical exponents are nonanalytic in ε, with a functional form that depends on the starting point on the upper critical line.Received 3 August 2020Revised 22 September 2020Accepted 28 September 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.043265Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCritical phenomenaDirac fermionsFermionsQuantum phase transitionsTopological materialsCondensed Matter, Materials & Applied Physics

Unconventional thermal metallic state of charge-neutral fermions in an insulator

Quantum oscillations in transport and thermodynamic parameters at high magnetic fields are an unambiguous signature of the Fermi surface, the defining characteristic of a metal. Recent observations of quantum oscillations in insulating SmB6 and YbB12, therefore, have been a big surprise—despite the large charge gap inferred from the insulating behaviour of the resistivity, these compounds seemingly host a Fermi surface at high magnetic fields. However, the nature of the ground state in zero field has been little explored. Here, we report the use of low-temperature heat-transport measurements to discover gapless, itinerant, charge-neutral excitations in the ground state of YbB12. At zero field, sizeable linear temperature-dependent terms in the heat capacity and thermal conductivity are clearly resolved in the zero-temperature limit, indicating the presence of gapless fermionic excitations with an itinerant character. Remarkably, linear temperature-dependent thermal conductivity leads to a spectacular violation of the Wiedemann–Franz law: the Lorenz ratio is 104–105 times larger than that expected in conventional metals, indicating that YbB12 is a charge insulator and a thermal metal. Moreover, we find that these fermions couple to magnetic fields, despite their charge neutrality. Our findings expose novel quasiparticles in this unconventional quantum state. Despite being a charge insulator, YbB12 behaves like a thermal metal. Low-temperature heat-transport measurements of this compound showed its gapless, itinerant and charge-neutral excitations.

Edge magnetization and spin transport in an SU(2)-symmetric Kitaev spin liquid

We investigate the edge magnetism and the spin transport properties of an SU(2)-symmetric Kitaev spin liquid (KSL) model put forward by Yao and Lee [Phys. Rev. Lett. 107, 087205 (2011)] on the honeycomb lattice. In this model, the spin degrees of freedom fractionalize into a ${\mathbb{Z}}_{2}$ static gauge field and three species of either gapless (Dirac) or gapped (chiral) Majorana fermionic excitations. We find that, when a magnetic field is applied on a zigzag edge, the Dirac KSL exhibits a nonlocal magnetization associated with the existence of zero-energy edge modes. The application of a spin bias $V={\ensuremath{\mu}}_{\ensuremath{\uparrow}}\ensuremath{-}{\ensuremath{\mu}}_{\ensuremath{\downarrow}}$ at the interface of the spin system with a normal metal produces a spin current into the KSL, which depends as a power law on $V$, in the zero-temperature limit, for both Dirac and chiral KSLs, but with different exponents. Lastly, we study the longitudinal spin Seebeck effect, in which a spin current is driven by the combined action of a magnetic field perpendicular to the plane of the honeycomb lattice and a thermal gradient at the interface of the KSL with a metal. Our results suggest that edge magnetization and spin transport can be used to probe the existence of charge-neutral edge states in quantum spin liquids.

Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials.

Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the collisionless regime (ℏω≫k_{B}T) in the vicinity of a relativistic quantum critical point, separating two-dimensional (d=2) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such a critical point, gapless fermionic and bosonic excitations are strongly coupled, leading to a universal suppression of the interband OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in 1/N_{f}- and ε expansions, where N_{f} counts the fermion flavor number and ε=3-d. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from nonperturbative gauge-gravity duality, for example.

Mixed-valence insulators with neutral Fermi surfaces

Samarium hexaboride is a classic three-dimensional mixed valence system with a high-temperature metallic phase that evolves into a paramagnetic charge insulator below 40 K. A number of recent experiments have suggested the possibility that the low-temperature insulating bulk hosts electrically neutral gapless fermionic excitations. Here we show that a possible ground state of strongly correlated mixed valence insulators—a composite exciton Fermi liquid—hosts a three dimensional Fermi surface of a neutral fermion, that we name the “composite exciton.” We describe the mechanism responsible for the formation of such excitons, discuss the phenomenology of the composite exciton Fermi liquids and make comparison to experiments in SmB6.

Supersymmetry in closed chains of coupled Majorana modes

We consider a closed chain of even number of Majorana zero modes with nearest-neighbour couplings which are different site by site generically, thus no any crystal symmetry. Instead, we demonstrate the possibility of an emergent supersymmetry (SUSY), which is accompanied by gapless Fermionic excitations. In particular, the condition can be easily satisfied by tuning only one coupling, regardless of how many other couplings are there. Such a system can be realized by four Majorana modes on two parallel Majorana nanowires with their ends connected by Josephson junctions and bodies connected by an external superconducting ring. By tuning the Josephson couplings with a magnetic flux $\Phi$ through the ring, we get the gapless excitations at $\Phi_{SUSY}=\pm f\Phi_0$ with $\Phi_0= hc/2e$, which is signaled by a zero-bias conductance peak in tunneling conductance. We find this $f$ generally a fractional number and oscillating with increasing Zeeman fields that parallel to the nanowires, which provide a unique experimental signature for the existence of Majorana modes.

Coherent hole propagation in an exactly solvable gapless spin liquid

We examine the dynamics of a single hole in the gapless phase of the Kitaev honeycomb model, focusing on the slow-hole regime where the bare hopping amplitude $t$ is much less than the Kitaev exchange energy $J$. In this regime, the hole does not generate gapped flux excitations and is dressed only by the gapless fermion excitations. Investigating the single-hole spectral function, we find that the hole propagates coherently with a quasiparticle weight that is finite but approaches zero as $t/J \to 0$. This conclusion follows from two approximate treatments, which capture the same physics in complementary ways. Both treatments use the stationary limit as an exactly solvable starting point to study the spectral function approximately (i) by employing a variational approach in terms of a trial state that interpolates between the limits of a stationary hole and an infinitely fast hole and (ii) by considering a special point in the gapless phase that corresponds to a simplified one-dimensional problem.

Chirality-protected Majorana zero modes at the gapless edge of Abelian quantum Hall states

We show that the $\nu=8$ integer quantum Hall state can support Majorana zero modes at domain walls between its two different stable chiral edge phases without superconductivity. This is due to the existence of an edge phase that does not support gapless fermionic excitations; all gapless excitations are bosonic in this edge phase. Majorana fermion zero modes occur at a domain wall between this edge phase and the more conventional one that does support gapless fermions. Remarkably, due to the chirality of the system, the topological degeneracy of these zero modes has exponential protection, as a function of the relevant length scales, in spite of the presence of gapless excitations, including gapless fermions. These results are compatible with charge conservation, but do not require it. We discuss generalizations to other integer and fractional quantum Hall states, and classify possible mechanisms for appearance of Majorana zero modes at domain walls.

Compressible Matter at a Holographic Interface

We study the interface between a fractional topological insulator and an ordinary insulator, both described using holography. By turning on a chemical potential we induce a finite density of matter localized at the interface. These are gapless surface excitations which are expected to have a fermionic character. We study the thermodynamics of the system, finding a symmetry preserving compressible state at low temperatures, whose excitations exhibit hyperscaling violation. These results are consistent with the expectation of gapless fermionic excitations forming a Fermi surface at finite density.

Spin Liquid Phases for Spin-1 Systems on the Triangular Lattice

Motivated by recent experiments on material Ba3NiSb2O9, we propose two novel spin liquid phases (A and B) for spin-1 systems on a triangular lattice. At the mean field level, both spin liquid phases have gapless fermionic spinon excitations with quadratic band touching; thus, in both phases the spin susceptibility and γ=C(v)/T saturate to a constant at zero temperature, which are consistent with the experimental results on Ba3NiSb2O9. On the lattice scale, these spin liquid phases have Sp(4)~SO(5) gauge fluctuation, while in the long wavelength limit this Sp(4) gauge symmetry is broken down to U(1)×Z(2) in the type A spin liquid phase, and broken down to Z(4) in the type B phase. We also demonstrate that the A phase is the parent state of the ferroquadrupole state, nematic state, and the noncollinear spin density wave state.

The nature of the low-energy excitations in the short-range-ordered region of Cs2CuCl4 as revealed by 133Cs nuclear magnetic resonance

We report nuclear magnetic resonance (NMR) measurements of the spin-1/2 anisotropic triangular lattice antiferromagnet Cs2CuCl4 as a function of temperature and applied magnetic field. The observed temperature and magnetic field dependence of the NMR relaxation rate suggests that low-energy excitations in the short-range-ordered region stabilized over a wide range of intermediate fields and temperatures of the phase diagram (sketched in figure 1(a)) are gapless or nearly gapless fermionic excitations. An upper bound on the size of the gap of 0.037 meV≈J/10 is established. The magnetization and NMR relaxation rate can be qualitatively described either by a quasi-1D picture of weakly coupled chains or by mean-field theories of specific 2D spin liquids; however, quantitative differences exist between data and theory in both cases. This comparison indicates that 2D interactions are quantitatively important in describing the low-energy physics.

Majorana fermions in strongly interacting helical liquids

Majorana fermions were proposed to occur at edges and interfaces of gapped one-dimensional systems where phases with different topological character meet due to an interplay of spin-orbit coupling, proximity-induced superconductivity and external magnetic fields. Here we investigate the effect of strong particle interactions, and show that the helical liquid offers a mechanism that protects the very existence of Majorana edge states: whereas moderate interactions close the proximity gap which supports the edge states, in helical liquids the gap re-opens due to two-particle processes. However, gapless fermionic excitations occur at spatial proximity to the Majorana states at interfaces and may jeopardize their long term Majorana coherence.

Thermodynamic and transport signatures of a fractionalized Fermi liquid

Several heavy-fermion metals display a quantum phase transition from an antiferromagnetic metal to a heavy Fermi liquid. In some materials, however, recent experiments seem to find that the heavy Fermi liquid phase can be directly tuned into a non-Fermi liquid phase without apparent magnetic order. We analyze a candidate state for this scenario where the local moment system forms a spin liquid with gapless fermionic excitations. We discuss the thermal conductivity and spin susceptibility of this fractionalized state both in two and, in particular, three spatial dimensions for different temperature regimes. We derive a variational functional for the thermal conductivity and solve it with a variational ansatz dictated by Keldysh formalism. In sufficiently clean samples and for an appropriate temperature window, we find that thermal transport is dominated by the spinon contribution which can be detected by a characteristic maximum in the Wiedemann-Franz ratio. For the spin susceptibility, the conduction electron Pauli paramagnetism is much smaller than the spinon contribution whose temperature dependence in three dimensions is logarithmically enhanced as compared to the Fermi liquid result.

Non-Fermi liquids from holography

We report on a potentially new class of non-Fermi liquids in (2+1)-dimensions. They are identified via the response functions of composite fermionic operators in a class of strongly interacting quantum field theories at finite density, computed using the AdS/CFT correspondence. We find strong evidence of Fermi surfaces: gapless fermionic excitations at discrete shells in momentum space. The spectral weight exhibits novel phenomena, including particle-hole asymmetry, discrete scale invariance, and scaling behavior consistent with that of a critical Fermi surface postulated by Senthil.

Effective field theory for quantum liquid in dwarf stars

An effective field theory approach is used to describe quantum matter at greater-than-atomic but less-than-nuclear densities which are encountered in white dwarf stars. We focus on the density and temperature regime for which charged spin-0 nuclei form an interacting charged Bose-Einstein condensate, while the neutralizing electrons form a degenerate fermi gas. After a brief introductory review, we summarize distinctive properties of the charged condensate, such as a mass gap in the bosonic sector as well as gapless fermionic excitations. Charged impurities placed in the condensate are screened with great efficiency, greater than in an equivalent uncondensed plasma. We discuss a generalization of the Friedel potential which takes into account bosonic collective excitations in addition to the fermionic excitations. We argue that the charged condensate could exist in helium-core white dwarf stars and discuss the evolution of these dwarfs. Condensation would lead to a significantly faster rate of cooling than that of carbon- or oxygen-core dwarfs with crystallized cores. This prediction can be tested observationally: signatures of charged condensation may have already been seen in the recently discovered sequence of helium-core dwarfs in the nearby globular cluster NGC 6397. Sufficiently strong magnetic fields can penetrate the condensate within Abrikosov-like vortices. We find approximate analytic vortex solutions and calculate the values of the lower and upper critical magnetic fields at which vortices are formed and destroyed respectively. The lower critical field is within the range of fields observed in white dwarfs, but tends toward the higher end of this interval. This suggests that for a significant fraction of helium-core dwarfs, magnetic fields are entirely expelled within the core.

Translation-symmetry-protected topological orders in quantum spin systems

In this paper we systematically study a simple class of translation-symmetry protected topological orders in quantum spin systems using slave-particle approach. The spin systems on square lattice are translation invariant, but may break any other symmetries. We consider topologically ordered ground states that do not spontaneously break any symmetry. Those states can be described by Z2A or Z2B projective symmetry group. We find that the Z2A translation symmetric topological orders can still be divided into 16 sub-classes corresponding to 16 new translation-symmetry protected topological orders. We introduced four $Z_2$ topological indices $\zeta_{\v{k}}=0,1$ at $\v {k}=(0,0)$, $(0,\pi)$, $(\pi, 0)$, $(\pi ,\pi)$ to characterize those 16 new topological orders. We calculated the topological degeneracies and crystal momenta for those 16 topological phases on even-by-even, even-by-odd, odd-by-even, and odd-by-odd lattices, which allows us to physically measure such topological orders. We predict the appearance of gapless fermionic excitations at the quantum phase transitions between those symmetry protected topological orders. Our result can be generalized to any dimensions. We find 256 translation-symmetry protected Z2A topological orders for a system on 3D lattice.