Particle-hole Symmetry Breaking Research Articles

Half-valley semimetal and largest inverse topological caloric effect at topological quantum criticality in the chiral-symmetric AIII class

Half-valley semimetal (HVSM) and single-valley states are the hallmark of valleytronics in two-dimensional honeycomb lattice materials, but their quasi-one-dimensional analog that takes advantage of quantum manipulation has not yet been realized. We propose a double-helical ladder model described by a coupled double Su–Schrieffer–Heeger chain, wherein the interchain coupling controlled by magnetic flux induces time-reversal and particle-hole symmetry breaking and preserves only the chiral symmetry, which is classified into the AIII symmetry class. It realizes valley polarization, single-valley topological insulator, and HVSM as the topological quantum criticality (TQC), signaling well valley filter or valve effects. Furthermore, the TQC produces the largest inverse topological caloric effect accompanied by a T-linear relation of isothermal entropy change at ultra-low temperatures. Our findings not only open alternative perspectives for multifunctional quantum devices in valleytronics but also shed light on the thermodynamic characterization of TQC and promote the rapid development of topological quantum refrigeration technology.

Ferromagnetic and metamagnetic transitions in itinerant electron systems: a microscopic study

We perform a microscopic study of itinerant ferromagnetic systems. We reveal a very rich phase diagram in the three-dimensional space spanned by the chemical potential, a magnetic field, and temperature beyond the Landau theory analyzed so far. Besides a generic wing structure near a tricritical point upon introducing the magnetic field, we find that an additional wing can be generated close to a quantum critical end point (QCEP) and also even from deeply inside the ferromagnetic phase. A tilting of the wing controls the entropy jump associated with the metamagnetic transition. Ferromagnetic and metamagnetic transitions are usually accompanied by a Lifshitz transition at low temperatures, i.e. a change of Fermi surface topology including the disappearance of the Fermi surface. In particular, the Fermi surface of either spin band vanishes at the QCEP. These rich phase diagrams are understood in terms of the density of states and the breaking of particle-hole symmetry in the presence of a next nearest-neighbor-hopping integral tʹ, which is expected in actual materials. The obtained phase diagrams are discussed in a possible connection to itinerant ferromagnetic systems such as UGe2, UCoAl, ZrZn2, and others including materials exhibiting the magnetocaloric effect.

Pseudomagnetic fields, particle-hole asymmetry, and microscopic effective continuum Hamiltonians of twisted bilayer graphene

Using the method developed in the companion paper, we construct the effective continuum theories for two different microscopic tight binding models of the twisted bilayer graphene at the twist angle of $1.05^\circ$, one Slater-Koster based and the other ab-initio Wannier based. The energy spectra obtained from the continuum theory -- either for rigid twist or including lattice relaxation -- are found to be in nearly perfect agreement with the spectra from the tight binding models when the gradient expansion is carried out to second order, demonstrating the validity of the method. We also analyze the properties of the Bloch states of the resulting narrow bands, finding non-negligible particle-hole symmetry breaking near the $\Gamma$ point in our continuum theory constructed for the ab-initio based microscopic model due to a term in the continuum theory that was previously overlooked. This reveals the difference with all existing continuum models where the particle-hole symmetry of the narrow band Hilbert space is nearly perfect.

Localization by particle–hole symmetry breaking: a loop expansion

Localization by a broken particle–hole (PH) symmetry in a random system of non-interacting quantum particles is studied on a d-dimensional lattice. Our approach is based on a chiral symmetry argument and the corresponding invariant measure, where the latter is described by a Grassmann functional integral. Within a loop expansion we find for small loops diffusion in the case of PH symmetry. Breaking the PH symmetry results in the creation of random dimers, which suppress diffusion and lead to localization on the scale , where D is the effective diffusion coefficient at PH symmetry and μ is the parameter related to PH symmetry breaking.

Bipolar thermoelectric Josephson engine.

Thermoelectric effects in metals are typically small due to the nearly perfect particle-hole symmetry around their Fermi surface. Furthermore, thermo-phase effects and linear thermoelectricity in superconducting systems have been identified only when particle-hole symmetry is explicitly broken, since thermoelectric effects were considered impossible in pristine superconductors. Here, we experimentally demonstrate that superconducting tunnel junctions develop a very large bipolar thermoelectricity in the presence of a sizable thermal gradient thanks to spontaneous particle-hole symmetry breaking. Our junctions show Seebeck coefficients of up to ±300 μV K-1, which is comparable with quantum dots and roughly 105 times larger than the value expected for normal metals at subkelvin temperatures. Moreover, by integrating our junctions into a Josephson interferometer, we realize a bipolar thermoelectric Josephson engine generating phase-tunable electric powers of up to ~140 nW mm-2. Notably, our device implements also the prototype for a persistent thermoelectric memory cell, written or erased by current injection. We expect that our findings will lead to applications in superconducting quantum technologies.

Distinct signatures of particle-hole symmetry breaking in transport coefficients for generic multi-Weyl semimetals

We propose and study generic multi-Weyl semimetal (mWSM) lattice Hamiltonians that break particle-hole symmetry. These models fall into two categories: model I (model II) where the gap and tilt terms are coupled (decoupled) can host type-I and type-II Weyl nodes simultaneously (separately) in a hybrid phase (type-I and type-II phases, respectively). We concentrate on the question of how anisotropy and non-linearity in the dispersions, gaps and tilt terms influence diffusive second order transport quantities namely, the circular photogalvanic effect (CPGE) and the Berry curvature dipole (BCD) as well as first order Magnus Hall effect (MHE) in the ballistic limit. The signatures of topological charges are clearly imprinted in the quantized CPGE response for the hybrid mWSM phase in model I. Such a quantization is also found in the type-I WSM phase for model II, however, the frequency profiles of the CPGE in these two cases is distinctively different owing to their different band dispersion irrespective of the identical topological properties. The contributions from the vicinity of Weyl nodes and away from the WNs are clearly manifested in the BCD response, respectively, for model I model II. The Fermi surface properties for the activated momentum lead to a few hallmark features on the MHE for both the models. Furthermore, we identify distinguishing signatures of the above responses for type-I, type-II and hybrid phases to provide an experimentally viable probe to differentiate these WSMs phases.

Majorana fermion arcs and the local density of states of UTe2

$\text{UTe}_2$ is a leading candidate for chiral p-wave superconductivity, and for hosting exotic Majorana fermion quasiparticles. Motivated by recent STM experiments in this system, we study particle-hole symmetry breaking in chiral p-wave superconductors. We compute the local density of states from Majorana fermion surface states in the presence of Rashba surface spin-orbit coupling, which is expected to be sizeable in heavy-fermion materials like UTe$_2$. We show that time-reversal and surface reflection symmetry breaking lead to a natural pairing tendency towards a triplet pair density wave state, which naturally can account for broken particle-hole symmetry.

Crystalline Weyl semimetal phase in Quantum Spin Hall systems under magnetic fields

We investigate an unconventional topological phase transition that occurs in quantum spin Hall (QSH) systems when applying an external in-plane magnetic field. We show that this transition between QSH and trivial insulator phases is separated by a stable topological gapless phase, which is protected by the combination of particle-hole and reflection symmetries, and thus, we dub it as crystalline Weyl semimetal. We explore the stability of this new phase when particle-hole symmetry breaking terms are present. Especially, we predict a robust unconventional topological phase transition to be visible for materials described by the Kane and Mele model even if particle-hole symmetry is significantly broken.

Interaction-induced particle-hole symmetry breaking and fractional exclusion statistics.

Quantum statistics plays a fundamental role in the laws of nature. Haldane fractional exclusion statistics (FES) generalizes the Pauli exclusion statistics, and can emerge in the properties of elementary particles and hole excitations of a quantum system consisting of conventional bosons or fermions. FES has a long history of intensive studies, but its simple realization in interacting physical systems is rare. Here we report a simple non-mutual FES that depicts the particle-hole symmetry breaking in interacting Bose gases at a quantum critical point. We show that the FES distribution directly comes from particle-hole symmetry breaking. Based on exact solutions, quantum Monte Carlo simulations and experiments, we find that, over a wide range of interaction strengths, the macroscopic physical properties of these gases are determined by non-interacting quasi-particles that obey non-mutual FES of the same form in one and two dimensions. Whereas strongly interacting Bose gases reach full fermionization in one dimension, they exhibit incomplete fermionization in two dimensions. Our results provide a generic connection between interaction-induced particle-hole symmetry breaking (depicted by FES) and macroscopic properties of many-body systems in arbitrary dimensions. Our work lays the groundwork for using FES to explore quantum criticality and other novel many-body phenomena in strongly correlated quantum systems.

Spontaneous symmetry breaking induced thermospin effect in superconducting tunnel junctions

We discuss the charge and the spin tunneling currents between two Bardeen-Cooper-Schrieffer (BCS) superconductors, where one density of states is spin-split. In the presence of a large temperature bias across the junction, we predict the generation of a spin-polarized thermoelectric current. This thermo-spin effect is the result of a spontaneous particle-hole symmetry breaking in the absence of a polarizing tunnel barrier. The two spin components, which move in opposite directions, generate a spin current larger than the purely polarized case when the thermo-active component dominates over the dissipative one.

Composite fermion mass enhancement and particle-hole symmetry of fractional quantum Hall states in the lowest Landau level under realistic conditions

Particle-hole symmetry breaking in the fractional quantum Hall effect has recently been studied both theoretically and experimentally with most works focusing on non-Abelian states in the second electronic Landau level. In this work, we theoretically investigate particle-hole symmetry breaking of incompressible fractional quantum Hall states in the lowest Landau level under the influence of the realistic effect of a finite magnetic field strength. A finite magnetic field induces Landau level and sub-band mixing which are known to break particle-hole symmetry at the level of the Hamiltonian. We analyze the Haldane pseudopotentials, energy spectra and energy gaps, and the wave functions themselves, under realistic conditions. We find that particle-hole symmetry is broken, as determined by energy gaps, between states related via particle-hole conjugation, however, we find that particle-hole symmetry is largely maintained as determined by the effective mass of composite fermions. Finally, we comment and make connection to recent experimental observations regarding particle-hole symmetry in the lowest Landau level fractional quantum Hall effect [Pan et al. Phys. Rev. Lett. 124, 156801 (2020)]

Identifying Majorana bound states by tunneling shot-noise tomography

Majorana fermions are promising building blocks of forthcoming technology in quantum computing. However, their non-ambiguous identification has remained a difficult issue because of the concomitant competition with other topologically trivial fermionic states, which poison their detection in most spectroscopic probes. By employing numerical and analytical methods, here we show that the Fano factor tomography is a key distinctive feature of a Majorana bound state, displaying a spatially constant Poissonian value equal to one. In contrast, the Fano factor of other trivial fermionic states, like the Yu-Shiba-Rusinov or Andreev ones, is strongly spatially dependent and exceeds one as a direct consequence of the local particle-hole symmetry breaking.

Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities

Building on previous work [N. Read, Phys. Rev. B 58, 16262 (1998); Z. Dong and T. Senthil, Phys. Rev. B 102, 205126 (2020)] on the system of bosons at filling factor $\ensuremath{\nu}=1$, we derive the Dirac composite fermion theory for a half-filled Landau level from first principles and apply the Hartree-Fock approach in a preferred representation. On the basis of the microscopic formulation, in the long-wavelength limit, we propose a noncommutative field-theoretical description, which in a commutative limit reproduces the Son's theory, with additional terms that may be expected on physical grounds. The microscopic representation of the problem is also used to discuss pairing instabilities of composite fermions. We find that a presence of a particle-hole symmetry breaking leads to a weak (BCS) coupling $p$-wave pairing in the lowest Landau level, and strong coupling $p$-wave pairing in the second Landau level that occurs in a band with nearly flat dispersion, a third power function of momentum.

Electron-boson-interaction induced particle-hole symmetry breaking of conductance into subgap states in superconductors

Particle-hole symmetry (PHS) of conductance into subgap states in superconductors is a fundamental consequence of a noninteracting mean-field theory of superconductivity. The breaking of this PHS has been attributed to a noninteracting mechanism, i.e., quasiparticle poisoning (QP), a process detrimental to the coherence of superconductor-based qubits.Here, we show that the ubiquitous electron-boson interactions in superconductors can also break the PHS of subgap conductances. We study the effect of such couplings on the PHS of subgap conductances in superconductors using both the rate equation and Keldysh formalism, which have different regimes of validity. In both regimes, we found that such couplings give rise to a particle-hole $asymmetry$ in subgap conductances which increases with increasing coupling strength, increasing subgap-state particle-hole content imbalance and decreasing temperature. Our proposed mechanism is general and applies even for experiments where the subgap-conductance PHS breaking cannot be attributed to QP.

Quantum thermal transport in the charged Sachdev-Ye-Kitaev model: Thermoelectric Coulomb blockade

We present a microscopic theory for quantum thermoelectric and heat transport in the Schwarzian regime of the Sachdev-Ye-Kitaev (SYK) model. As a charged fermion realization of the SYK model in nanostructures we assume a setup based on a quantum dot connected to the charge reservoirs through weak tunnel barriers. We analyze particle-hole symmetry breaking effects crucial for both Seebeck and Peltier coefficients. We show that the quantum charge and heat transport at low temperatures are defined by the interplay between elastic and inelastic processes such that the inelastic processes provide a leading contribution to the transport coefficients at the temperatures that are smaller compared to the charging energy. We demonstrate that both electric and thermal conductance obey a power law in temperature behavior, while thermoelectric, Seebeck, and Peltier coefficients are exponentially suppressed. This represents selective suppression of only nondiagonal transport coefficients. We discuss the validity of the Kelvin formula in the presence of a strong Coulomb blockade.

Particle-Hole Symmetry Breaking in a Spin-Dimer System TlCuCl_{3} Observed at 100T.

The entire magnetization process of TlCuCl_{3} has been experimentally investigated up to 100T employing the single-turn technique. The upper critical field H_{c2} is observed to be 86.1T at 2K. A convex slope of the M-H curve between the lower and upper critical fields (H_{c1} and H_{c2}) is clearly observed, which indicates that a particle-hole symmetry is broken in TlCuCl_{3}. By quantum MonteCarlo simulation and the bond-operator theory method, we find that the particle-hole symmetry breaking results from strong interdimer interactions.

Collective modes and terahertz near-field response of superconductors

We theoretically study the low energy electromagnetic response of BCS type superconductors focusing on propagating collective modes that are observable with THz near field optics. The interesting frequency and momentum range is $\omega < 2\Delta$ and $q < 1/\xi$ where $\Delta$ is the gap and $\xi$ is the coherence length. We show that it is possible to observe the superfluid plasmons, amplitude (Higgs) modes, Bardasis-Schrieffer modes and Carlson-Goldman modes using THz near field technique, although none of these modes couple linearly to far field radiation. Coupling of THz near field radiation to the amplitude mode requires particle-hole symmetry breaking while coupling to the Bardasis-Schrieffer mode does not and is typically stronger. For parameters appropriate to layered superconductors of current interest, the Carlson-Goldman mode appears in the near field reflection coefficient as a weak feature in the sub-THz frequency range. In a system of two superconducting layers with nanometer scale separation, an acoustic phase mode appears as the antisymmetric density fluctuation mode of the system. This mode produces well defined resonance peaks in the near-field THz response and has strong anticrossings with the Bardasis-Schrieffer and amplitude modes, enhancing their response. In a slab consisting of many layers of quasi-two dimensional superconductors, realized for example in samples of high T$_c$ cuprate compounds, many branches of propagating Josephson plasmon modes are found to couple to the THz near field radiation.

Topological nature of step-edge states on the surface of the topological crystalline insulator Pb0.7Sn0.3Se

In addition to novel surface states, topological insulators can also exhibit robust gapless states at crystalline defects. Step edges constitute a class of common defects on the surface of crystals. In this work we establish the topological nature of one-dimensional (1D) bound states localized at step edges of the [001] surface of a topological crystalline insulator (TCI) Pb$_{0.7}$Sn$_{0.3}$Se, both theoretically and experimentally. We show that the topological stability of the step edge states arises from an emergent particle-hole symmetry of the surface low-energy physics, and demonstrate the experimental signatures of the particle-hole symmetry breaking. We also reveal the effects of an external magnetic field on the 1D bound states. Our work suggests the possibility of similar topological step edge modes in other topological materials with a rocks-salt structure.

Paired states at 5/2: Particle-hole Pfaffian and particle-hole symmetry breaking

We study Cooper pairing in the Dirac composite fermion (CF) system. The presence of the mass term in the Dirac CF description (which may simulate Landau level mixing) i.e. breaking of particle-hole (PH) symmetry in this system, is a necessary condition for the existence of a PH Pfaffian-like topological state. In the scope of RPA approximation and hydrodynamic approach, we find some signatures of pairing at finite frequencies. Motivated by this insight, we extend our analysis to the case of a different but still Dirac quasi-particle (CF) representation, appropriate in the presence of a mass term, and discuss the likelihood of PH Pfaffian pairing and Pfaffian pairing in general. On the basis of gauge field effects, we find for small Dirac mass anti-Pfaffian or Pfaffian instability depending on the sign of mass, while for large mass (Landau level mixing), irrespective of its sign, PH Pfaffian-like instability.

Magneto-optical conductivity of double Weyl semimetals

We investigate the magneto-optical response of double Weyl semimetals whose energy dispersion is intrinsically anisotropic. We find that in the presence of a magnetic field, the most salient feature of the optical conductivity is a series of resonant peaks with the corresponding frequencies scaling linearly with the strength of the magnetic field. In addition, the optical conductivity is found to be anisotropic, with two of the three longitudinal components residing at a linear background and the remaining one at a constant background. The effects of chemical potential, temperature, impurity scattering, and particle-hole symmetry breaking on the optical conductivity are also studied.