Two-dimensional Fermi System Research Articles

Time evolution of entanglement entropy after quenches in two-dimensional free fermion systems: A dimensional reduction treatment

Time evolution of entanglement entropy after quenches in two-dimensional free fermion systems: A dimensional reduction treatment

Majorana fermions in a two-band two-dimensional Fermi system

Majorana fermions represent potential candidates for realizing fault-tolerant topological quantum computation. We obtain the exact mapping between a two-band hybridized model and a model with a topological superconducting state supporting Majorana fermions. The antisymmetric hybridization employed resembles that of spin–orbit coupling. We consider the situation where the model Hamiltonian comprises only inter-band s-wave pairing, i.e. the one in which the superconducting pairing is formed by one fermion from one of the bands and another fermion of opposite spin and momentum from the other band. From this we obtain an effective Hamiltonian of the px+ipy superconductor and calculate the topological invariant that distinguishes the weak and strong pairing phases. We also obtain the gap parameter and chemical potential of the Fermi system under spin–orbit coupling beyond the mean-field approximation. We show that the spin–orbit coupling substantially enhances the density of states at the Fermi surface.

2D Fermionic SPT with CRT symmetry

An invariant of SPT-phases with on-site finite group G symmetry for two-dimensional Fermion systems is derived in the work of Ogata [Commun. Math. Phys. 395(1), 405–457 (2022)]. This invariant is doubled compared to the conjectured one from the invertible quantum field theory. We show that if we require CRT-symmetry (which holds automatically in quantum field theory) in addition, then our invariant reduces to the conjectured one.

Disorder effects on the quasiparticle and transport properties of two-dimensional Dirac fermionic systems

Disorder effects on the quasiparticle and transport properties of two-dimensional Dirac fermionic systems

Enforced symmetry breaking by invertible topological order

It is well known that two-dimensional fermionic systems with a nonzero Chern number must break the time-reversal symmetry, manifested by the appearance of chiral edge modes on an open boundary. Such an incompatibility between topology and symmetry can occur more generally. We will refer to this phenomenon as enforced symmetry breaking (ESB) by topological orders. In this work, we systematically study ESB of a finite symmetry group ${G}_{f}$ by fermionic invertible topological orders. Mathematically, the group ${G}_{f}$ is a central extension over a bosonic symmetry group $G$ by the fermion parity group ${\mathbb{Z}}_{2}^{f}$, characterized by a 2-cocycle $\ensuremath{\lambda}\ensuremath{\in}{\mathcal{H}}^{2}(G,{\mathbb{Z}}_{2})$. For given $G$ and $\ensuremath{\lambda}$, we are able to obtain a series of criteria on the existence or nonexistence of ESB by the corresponding fermionic invertible topological orders. For 2D systems, we define a set of physical quantities to describe symmetry-enriched invertible topological orders and derive obstruction functions using both fermionic and bosonic languages. The study in the bosonic language is performed after gauging the fermion parity, and we find that some obstruction functions are consequences of conditional anomalies of the bosonic symmetry-enriched topological states, with the conditions inherited from the original fermionic system. The obstruction functions are crucial components of the ESB criteria that we derive. With these criteria, we discover many new ESB examples, e.g., we find that the quaternion group ${Q}_{8}$ is incompatible with two copies of $p+ip$ superconductors. We also obtain explicit results on the ESB phenomena of the continuous group ${\mathrm{SU}}_{f}(N)$ by 2D invertible topological orders through a different argument.

Transport anisotropy and metal-insulator transition in striped Dirac fermion systems

Using the determinant quantum Monte Carlo method, we investigate the metal-insulator transitions induced by the stripe of charge density in an interacting two-dimensional Dirac fermion system. The stripe will introduce the transport anisotropy and insulating intermediate phase into the system, accompanied by the change of band structure and a peak of density of states around Fermi energy. In the case of strong correlation, stripe exhibits competition with Coulomb repulsion through closing the energy gap and disrupting the magnetic order and finally drives the system in the Mott insulating phase back to the metallic state. Our results may provide a feasible way to modify transport properties by setting charge stripes in experiments.

Towards a complete classification of nonchiral topological phases in two-dimensional fermion systems

In recent years, fermionic topological phases of quantum matter has attracted a lot of attention. In a pioneer work by Gu, Wang, and Wen, the concept of equivalence classes of fermionic local unitary (FLU) transformations was proposed to systematically understand nonchiral topological phases in 2D fermion systems and an incomplete classification was obtained. On the other hand, the physical picture of fermion condensation and its corresponding super pivotal categories give rise to a generic mathematical framework to describe fermionic topological phases of quantum matter. In particular, it has been pointed out that in certain fermionic topological phases, there exists the so-called q-type anyon excitations, which have no analogues in bosonic theories. In this paper, we generalize the Gu, Wang, and Wen construction to include those fermionic topological phases with q-type anyon excitations. We argue that all nonchiral fermionic topological phases in $2+1\mathrm{D}$ are characterized by a set of tensors $({N}_{k}^{ij},{F}_{k}^{ij},{F}_{kln,\ensuremath{\chi}\ensuremath{\delta}}^{ijm,\ensuremath{\alpha}\ensuremath{\beta}},{n}_{i},{d}_{i})$, which satisfy a set of nonlinear algebraic equations parameterized by phase factors ${\mathrm{\ensuremath{\Xi}}}_{kl}^{ijm,\ensuremath{\alpha}\ensuremath{\beta}}$ and ${\mathrm{\ensuremath{\Xi}}}_{kln,\ensuremath{\chi}\ensuremath{\delta}}^{ij}$. Moreover, consistency conditions among algebraic equations give rise to additional constraints on these phase factors, which allow us to construct a topological invariant partition for an arbitrary triangulation of 3D spin manifold. Finally, several examples with q-type anyon excitations are discussed, including the fermionic topological phase from Tambara-Yamagami category for ${\mathbb{Z}}_{2N}$, which can be regarded as the ${\mathbb{Z}}_{2N}$ parafermion generalization of Ising fermionic topological phase.

Unremovable linked nodal structures protected by crystalline symmetries in stacked bilayer graphene with Kekulé texture

Linking structure is a new concept characterizing topological semimetals, which indicates the interweaving of gap-closing nodes at the Fermi energy ($E_F$) with other nodes below $E_F$. As the number of linked nodes can be changed only via pair-creation or pair-annihilation, a linked node is more stable and robust than ordinary nodes without linking. Here we propose a new type of a linked nodal structure between a nodal line (nodal surface) at $E_F$ with another nodal line (nodal surface) below $E_F$ in two-dimensional (three-dimensional) spinless fermion systems with $\mathcal{IT}$ symmetry where $\mathcal{I}$ and $\mathcal{T}$ indicate inversion and time-reversal symmetries, respectively. Because of additional chiral and rotational symmetries, in our system, a double band inversion creates a pair of linked nodes carrying the same topological charges, thus the pair are unremovable via a Lifshiftz transition, which is clearly distinct from the cases of the linked nodes reported previously. A realistic tight binding model and effective theory are developed for such a linking structure. Also, using density functional theory calculations, we propose a class of materials, composed of stacked bilayer graphene with Kekul\'{e} texture, as a candidate system hosting the new type of the linked nodal structure.

An Invariant of Symmetry Protected Topological Phases with On-Site Finite Group Symmetry for Two-Dimensional Fermion Systems

We consider SPT-phases with on-site finite group G symmetry for two-dimensional Fermion systems. We derive an invariant of the classification.

Magnetic phase transition in disordered interacting Dirac fermion systems via the Zeeman field

Using the determinant quantum Monte Carlo method, we investigate the antiferromagnetic phase transition that is induced by the Zeeman field in a disordered interacting two-dimensional Dirac fermion system. At a fixed interaction strength $U$, the antiferromagnetic correlation is enhanced as the magnetic field increases and, when the magnetic field is larger than a ${B}_{c}(U)$, the antiferromagnetic correlation shall be suppressed by the increased magnetic field. The impact of Zeeman field $B$, Coulomb repulsion $U$, and disorder $\mathrm{\ensuremath{\Delta}}$ is not isolated. The intensity of magnetic field effect on the antiferromagnetic correlation shall be strongly suppressed by disorder. Differently, it will be promoted by weak interaction, but, when $U$ becomes larger than ${U}_{c}=4.5$, the increased interaction will suppress the intensity of this effect and here ${U}_{c}=4.5$ coincides with the critical strength inducing the metal-Mott insulator transition in a clean system. Moreover, at a fixed magnetic field $B$, strong interaction shall suppress the antiferromagnetic phase rather than promote it.

Robust Nonequilibrium Edge Currents with and without Band Topology.

We study two-dimensional bosonic and fermionic lattice systems under nonequilibrium conditions corresponding to a sharp gradient of temperature imposed by two thermal baths. In particular, we consider a lattice model with broken time-reversal symmetry that exhibits both topologically trivial and nontrivial phases. Using a nonperturbative Green function approach, we characterize the nonequilibrium current distribution in different parameter regimes. For both bosonic and fermionic systems, we find chiral edge currents that are robust against coupling to reservoirs and to the presence of defects on the boundary or in the bulk. This robustness not only originates from topological effects at zero temperature but, remarkably, also persists as a result of dissipative symmetries in regimes where band topology plays no role. Chirality of the edge currents implies that energy locally flows against the temperature gradient without any external work input. In the fermionic case, there is also a regime with topologically protected boundary currents, which nonetheless do not circulate around all system edges.

Observation of possible nonlinear anomalous Hall effect in organic two-dimensional Dirac fermion system

We report the observation of nonlinear anomalous Hall effect (NLAHE) in the multilayered organic conductor α-(BEDT-TTF)2I3 in the charge order (CO) insulating phase just under the critical pressure for transition into two-dimensional (2D) massless Dirac fermion (DF) phase. We successfully extracted the finite nonlinear Hall voltage proportional to square current at zero magnetic field. The observed NLAHE features, current direction dependence and correlation with CO, are consistent with the previous estimation assuming 2D massive DF with a pair of tilted Dirac cones. This is the first observation of topological transport in organic conductors, and also the first example of NLAHE in the electronic phase with spontaneous symmetry breaking.

Thermoelectric Effect at Quantum Limit in Two-Dimensional Organic Dirac Fermion System with Zeeman Splitting

The thermoelectric effect in a two-dimensional (2D) massless Dirac fermion (DF) system at the quantum limit is discussed to verify the prediction of high-performance thermopower in an organic conductor \alpha-(BEDT-TTF)2I3. Because of relatively large Zeeman splitting in \alpha-(BEDT-TTF)2I3, the boundless increase of thermopower at high magnetic fields, predicted without the Zeeman effect, is hardly expected, whereas there appears to be a broad local maximum. This is characteristic of 2D DF systems with Zeeman splitting and is recognized in the previous experiment. In contrast to 3D Dirac/Weyl semimetals with robust gapless features, it might be difficult to realize high-performance thermopower in real 2D DF systems under high magnetic fields.

Graphene\u2019s non-equilibrium fermions reveal Doppler-shifted magnetophonon resonances accompanied by Mach supersonic and Landau velocity effects

Oscillatory magnetoresistance measurements on graphene have revealed a wealth of novel physics. These phenomena are typically studied at low currents. At high currents, electrons are driven far from equilibrium with the atomic lattice vibrations so that their kinetic energy can exceed the thermal energy of the phonons. Here, we report three non-equilibrium phenomena in monolayer graphene at high currents: (i) a “Doppler-like” shift and splitting of the frequencies of the transverse acoustic (TA) phonons emitted when the electrons undergo inter-Landau level (LL) transitions; (ii) an intra-LL Mach effect with the emission of TA phonons when the electrons approach supersonic speed, and (iii) the onset of elastic inter-LL transitions at a critical carrier drift velocity, analogous to the superfluid Landau velocity. All three quantum phenomena can be unified in a single resonance equation. They offer avenues for research on out-of-equilibrium phenomena in other two-dimensional fermion systems.

De Haas–van Alphen oscillations near the Lifshitz transition from two electron pockets to one in the two-dimensional Dirac fermion systems

We theoretically study the de Haas-van Alphen (dHvA) oscillations in the system with changing the topology of the Fermi surface (the Lifshitz transition) by electron dopings. We employ the two-dimensional tight binding model for $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure which has two Dirac points in the first Brillouin zone. When this system is slightly doped, there exists two closed Fermi surfaces with the same area and the dHvA oscillations become saw-tooth pattern or inversed saw-tooth pattern for both cases of fixed electron filling ($\nu$) or fixed chemical potential ($\mu$) with respect to the magnetic field, respectively. By increasing dopings, the system approaches the Lifshitz transition, where two closed Fermi surfaces are close each other. Then, we find that the pattern of the dHvA oscillations changes. A jump of the magnetization appears at the center of the fundamental period and its magnitude increases in the case of the fixed electron filling, while a jump is separated into a pair of jumps and its separation becomes large in the case of the fixed chemical potential. This is due to the lifting of double degeneracy in the Landau levels. Since this lifting is seen in the two-dimensional Dirac fermion system with two Dirac points, the obtained results in this study can be applied to not only $\alpha$-(BEDT-TTF)$_2$I$_3$ but also other materials with closely located Dirac points such as graphene under the uniaxial strain, in black phosphorus, twisted bilayer graphene, and so on.

Inducing a metal-insulator transition in disordered interacting Dirac fermion systems via an external magnetic field

We investigate metal-insulator transitions on an interacting two-dimensional Dirac fermion system using the determinant quantum Monte Carlo method. The interplay between Coulomb repulsion, disorder and magnetic fields, drives the otherwise semi-metallic regime to insulating phases exhibiting different characters. In particular, with the focus on the transport mechanisms, we uncover that their combination exhibits dichotomic effects. On the one hand, the critical Zeeman field $B_c$, responsible for triggering the band-insulating phase due to spin-polarization on the carriers, is largely reduced by the presence of the electronic interaction and quenched disorder. On the other hand, the insertion of a magnetic field induces a more effective localization of the fermions, facilitating the onset of Mott or Anderson insulating phases. Yet these occur at moderate values of $B$, and cannot be explained by the full spin-polarization of the electrons.

Possible Nonlinear Anomalous Thermoelectric Effect in Organic Massive Dirac Fermion System

We propose a novel current-induced thermoelectric phenomenon, the nonlinear anomalous Ettingshausen effect (AEE), at zero magnetic field in inversion-asymmetric conductors. As an example, we discuss the weak charge ordering state in a layered organic conductor alpha-(BEDT-TTF)2I3, which is a two-dimensional massive Dirac fermion system with a pair of tilted Dirac cones. The nonlinear AEE is a thermoelectric analogue of the nonlinear anomalous Hall effect, which is recently observed in alpha-(BEDT-TTF)2I3, and these two effects generally appear simultaneously. The nonlinear AEE generates a transverse heat current, which exhibits rectifying characteristics, namely unidirectionality even under an AC current.

Know the enemy: 2D Fermi liquids

We describe an analytical theory investigating the regime of validity of the Fermi liquid theory in interacting, via the long-range Coulomb coupling, two-dimensional Fermi systems comparing it with the corresponding 3D systems. We find that the 2D Fermi liquid theory and 2D quasiparticles are robust up to high energies and temperatures of the order of Fermi energy above the Fermi surface, very similar to the corresponding three-dimensional situation. We calculate the phase diagram in the frequency–temperature space separating the collisionless ballistic regime and the collision-dominated hydrodynamic regime for 2D and 3D interacting electron systems. We also provide the temperature corrections up to third order for the renormalized effective mass, and comment on the validity of 2D Wiedemann–Franz law and 2D Kadawoki–Woods relation.

Possible Current-Induced Phenomena and Domain Control in an Organic Dirac Fermion System with Weak Charge Ordering

We show that when the electron and hole densities are unbalanced, observable nonlinear anomalous Hall effect and current-induced orbital magnetization appear at zero magnetic field in the weak charge ordering (CO) state of an organic two-dimensional Dirac fermion system, α-(BEDT-TTF)2I3. These current-induced phenomena are caused by a finite Berry curvature dipole resulting from inversion symmetry breaking and Dirac cone tilting. In the actual system, however, these effects are canceled out between different types of inversion asymmetric CO domains. To avoid the cancellation, we propose a new experimental method to realize the selective formation of a single type of domain using the current-induced magnetization.

Entanglement production and convergence properties of the variational quantum eigensolver

We perform a systematic investigation of variational forms (wave function Ans\"atze), to determine the ground state energies and properties of two-dimensional model fermionic systems on triangular lattices (with and without periodic boundary conditions), using the Variational Quantum Eigensolver (VQE) algorithm. In particular, we focus on the nature of the entangler blocks which provide the most efficient convergence to the system ground state inasmuch as they use the minimal number of gate operations, which is key for the implementation of this algorithm in NISQ computers. Using the concurrence measure, the amount of entanglement of the register qubits is monitored during the entire optimization process, illuminating its role in determining the efficiency of the convergence. Finally, we investigate the scaling of the VQE circuit depth as a function of the desired energy accuracy. We show that the number of gates required to reach a solution within an error $\varepsilon$ follows the Solovay-Kitaev scaling, $\mathcal{O}(\log^c(1/\varepsilon))$, with an exponent $c = 1.31 {\rm{\pm}}0.13$.