arXiv subjects

Daniel Varjas

Publications and source records attributed to Daniel Varjas.

At least 19 recordsLinked to original sources

arXiv2026

Genus-protected higher-order topological phases

Higher-order topological phases (HOTPs) feature protected gapless modes on boundaries of higher codimension, such as the corners or hinges of a crystal. They are understood as being protected by lattice symmetries: If the latter are broken, it becomes possible to remove the boundary modes without closing the bulk gap. In this work, we present construction schemes for HOTPs protected solely by the bulk gap, by fundamental symmetries, and by the global topology of the system shape (its genus, or number of holes), independent of any crystalline symmetries. As long as the fundamental local symmetries are preserved, the resulting boundary states cannot be removed by any purely-surface perturbation.

cond-mat.mes-hall↗

arXiv2024

Computational quantum transport: a scattering approach perspective

This review is devoted to the different techniques that have been developed to compute the phase-coherent transport properties of quantum nanoelectronic systems connected to electrodes. Beside a review of the different algorithms proposed in the literature, we provide a comprehensive and pedagogical derivation of the two formalisms on which these techniques are based: the scattering approach and the (nonequilibrium) Green's function approach. We show that the scattering problem can be formulated as a system of linear equations and that different existing algorithms for solving this scattering problem amount to different sequences of Gaussian elimination. We explicitly prove the equivalence of the two formalisms. We discuss the stability and numerical complexity of the existing methods. The review ends with a selection of a few applications where numerical calculations were instrumental in shaping our understanding of the physics.

cond-mat.mes-hall↗

arXiv2024

Network model for magnetic higher-order topological phases

We propose a network-model realization of magnetic higher-order topological phases (HOTPs) in the presence of the combined space-time symmetry $C_4\mathcal{T}$ -- the product of a fourfold rotation and time-reversal symmetry. We show that the system possesses two types of HOTPs. The first type, analogous to Floquet topology, generates a total of $8$ corner modes at $0$ or $\pi$ eigenphase, while the second type, hidden behind a weak topological phase, yields a unique phase with $8$ corner modes at $\pm\pi/2$ eigenphase (after gapping out the counterpropagating edge states), arising from the product of particle-hole and phase rotation symmetry. By using a bulk $\mathbb{Z}_4$ topological index ($Q$), we found both HOTPs have $Q=2$, whereas $Q=0$ for the trivial and the conventional weak topological phase. Together with a $\mathbb{Z}_2$ topological index associated with the reflection matrix, we are able to fully distinguish all phases. Our work motivates further studies on magnetic topological phases and symmetry protected $2\pi/n$ boundary modes, as well as suggests that such phases may find their experimental realization in coupled-ring-resonator networks.

cond-mat.mes-hall↗

arXiv2024

Pymablock: an algorithm and a package for quasi-degenerate perturbation theory

A common technique in the study of complex quantum-mechanical systems is to reduce the number of degrees of freedom in the Hamiltonian by using quasi-degenerate perturbation theory. While the Schrieffer--Wolff transformation achieves this and constructs an effective Hamiltonian, its scaling is suboptimal, it is limited to two subspaces, and implementing it efficiently is both challenging and error-prone. We introduce an algorithm for constructing an equivalent effective Hamiltonian as well as a Python package, Pymablock, that implements it. Our algorithm combines an optimal asymptotic scaling and the ability to handle any number of subspaces with a range of other improvements. The package supports numerical and analytical calculations of any order and it is designed to be interoperable with any other packages for specifying the Hamiltonian. We demonstrate how the package handles constructing a k.p model, analyses a superconducting qubit, and computes the low-energy spectrum of a large tight-binding model. We also compare its performance with reference calculations and demonstrate its efficiency.

quant-ph↗

arXiv2023

Isotropic 3D topological phases with broken time reversal symmetry

Axial vectors, such as current or magnetization, are commonly used order parameters in time-reversal symmetry breaking systems. These vectors also break isotropy in three dimensional systems, lowering the spatial symmetry. We demonstrate that it is possible to construct a three-dimensional medium with average isotropy and inversion symmetry where time-reversal symmetry is systematically broken. We devise a model of an amorphous material with scalar time-reversal symmetry breaking, implemented by hopping through chiral magnetic clusters along the bonds. The presence of only average spatial symmetries -- continuous rotation and inversion -- is sufficient to protect a topological phase, yielding a statistical topological insulator. We demonstrate the topological nature of our model by constructing a bulk integer topological invariant for the effective continuum model, which guarantees gapless surface spectrum on any surface with an odd number of Dirac nodes, analogous to crystalline mirror Chern insulators. We also show the expected transport properties of a three-dimensional statistical topological insulator, which remains critical on the surface for odd values of the invariant.

cond-mat.mes-hall↗

arXiv2023

Establishing Coherent Momentum-Space Electronic States in Locally Ordered Materials

In our understanding of solids, the formation of highly spatially coherent electronic states, fundamental to command the quantum behavior of materials, relies on the existence of discrete translational symmetry of the crystalline lattice. In contrast, in the absence of long-range order, as in the case of non-crystalline materials, the electronic states are localized and electronic coherence does not develop. This brings forward the fundamental question whether long range order is necessary condition to establish coherence and structured momentum-dependent electronic state, and how to characterize it in the presence of short-range order. Here we study Bi$_2$Se$_3$, a material that exists in its crystalline form with long range order, in amorphous form, with short and medium range order, and in its nanocrystalline form, with reduced short range order. By using angle resolved photoemission spectroscopy to directly access the electronic states in a momentum resolved manner, we reveal that, even in the absence of long-range order, a well-defined real-space length scale is sufficient to produce dispersive band structures. Moreover, we observe for the first time a repeated Fermi surface structure of duplicated annuli, reminiscent of Brillouin zone-like repetitions. These results, together with our simulations using amorphous Hamiltonians, reveal that the typical momentum scale where coherence occurs is the inverse average nearest-neighbor distance, the direct fingerprint of the local order of the underlying atomic structure. These results, not only lead the way to a new understanding of electronic coherence in solids, but also open the way to the realization of novel momentum-dependent quantum phenomena such as momentum pairing and spin-orbit coupling, in a much broader class of materials than the currently studied ones, lacking long range crystalline translational symmetry.

cond-mat.mtrl-sci↗

arXiv2022

Generalizations of the Pfaffian to non-antisymmetric matrices

We study two generalizations of the Pfaffian to non-antisymmetric matrices and derive their properties and relation to each other. The first approach is based on the Wigner normal-form, applicable to conjugate-normal matrices, and retains most properties of the Pfaffian, including that it is the square-root of the determinant. The second approach is to take the Pfaffian of the antisymmetrized matrix, applicable to all matrices. We show that this formulation is equivalent to substituting a non-antisymmetric matrix into the polynomial definition of the Pfaffian. We find that the two definitions differ in a positive real factor, making the second definition violate the determinant identity.

math-ph↗

arXiv2022

Pfaffian invariant identifies magnetic obstructed atomic insulators

We derive a $\mathbb{Z}_4$ topological invariant that extends beyond symmetry eigenvalues and Wilson loops and classifies two-dimensional insulators with a $C_4 \mathcal{T}$ symmetry. To formulate this invariant, we consider an irreducible Brillouin zone and constrain the spectrum of the open Wilson lines that compose its boundary. We fix the gauge ambiguity of the Wilson lines by using the Pfaffian at high symmetry momenta. As a result, we distinguish the four $C_4 \mathcal{T}$-protected atomic insulators, each of which is adiabatically connected to a different atomic limit. We establish the correspondence between the invariant and the obstructed phases by constructing both the atomic limit Hamiltonians and a $C_4 \mathcal{T}$-symmetric model that interpolates between them. The phase diagram shows that $C_4 \mathcal{T}$ insulators allow $\pm 1$ and $2$ changes of the invariant, where the latter is overlooked by symmetry indicators.

cond-mat.mes-hall↗

arXiv2022

Topological defects in a double-mirror quadrupole insulator displace diverging charge

We show that topological defects in quadrupole insulators do not host quantized fractional charges, contrary to what their Wannier representation indicates. In particular, we test the charge quantization hypothesis based on the Wannier representation of a parametric defect and a disclination. Against the expectations, we find that the local charge density decays as $\sim 1/r^2$ with distance, leading to a diverging defect charge. We identify sublattice symmetry and not higher order topology as the origin of the previously reported charge quantization.

cond-mat.mes-hall↗

arXiv2022

Exceptional dynamics of interacting spin liquids

We show that interactions in quantum spin liquids can result in non-Hermitian phenomenology that differs qualitatively from mean-field expectations. We demonstrate this in two prominent cases through the effects of phonons and disorder on a Kitaev honeycomb model. Using analytic and numerical calculations, we show the generic appearance of exceptional points and rings depending on the symmetry of the system. Their existence is reflected in dynamical observables including the dynamic structure function measured in neutron scattering. The results point to new phenomenological features in realizable spin liquids that must be incorporated into the analysis of experimental data and also indicate that spin liquids could be generically stable to wider classes of perturbations.

cond-mat.str-el↗

arXiv2022

Non-Hermitian topology in monitored quantum circuits

We demonstrate that genuinely non-Hermitian topological phases and corresponding topological phase transitions can be naturally realized in monitored quantum circuits, exemplified by the paradigmatic non-Hermitian Su-Schrieffer-Heeger model. We emulate this model by a 1D chain of spinless electrons evolving under unitary dynamics and subject to periodic measurements that are stochastically invoked. The non-Hermitian topology is visible in topological invariants adapted to the context of monitored circuits. For instance, the topological phase diagram of the monitored realization of the non-Hermitian Su-Schrieffer-Heeger model is obtained from the biorthogonal polarization computed from an effective Hamiltonian of the monitored system. Importantly, our monitored circuit realization allows direct access to steady state biorthogonal expectation values of generic observables, and hence, to measure physical properties of a genuine non-Hermitian model. We expect our results to be applicable more generally to a wide range of models that host non-Hermitian topological phases.

cond-mat.mes-hall↗

arXiv2021

Topological Lattice Models with Constant Berry Curvature

Band geometry plays a substantial role in topological lattice models. The Berry curvature, which resembles the effect of magnetic field in reciprocal space, usually fluctuates throughout the Brillouin zone. Motivated by the analogy with Landau levels, constant Berry curvature has been suggested as an ideal condition for realizing fractional Chern insulators. Here we show that while the Berry curvature cannot be made constant in a topological two-band model, lattice models with three or more degrees of freedom per unit cell can support exactly constant Berry curvature. However, contrary to the intuitive expectation, we find that making the Berry curvature constant does not always improve the properties of bosonic fractional Chern insulator states. In fact, we show that an "ideal flatband" cannot have constant Berry curvature, equivalently, we show that the density algebra of Landau levels cannot be realised in any tight-binding lattice system.

cond-mat.str-el↗

arXiv2020

Amorphous topological phases protected by continuous rotation symmetry

Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous topological materials, where the Hamiltonian is invariant on average under reflection over any axis due to continuous rotation symmetry. While the local disorder caused by the amorphous structure weakens the topological protection, we demonstrate that the edge remains protected from localization. In order to classify such phases we perform a systematic search over all the possible symmetry classes in two dimensions and construct the example models realizing each of the proposed topological phases. Finally, we compute the topological invariant of these phases as an integral along a meridian of the spherical Brillouin zone of an amorphous Hamiltonian.

cond-mat.mes-hall↗

arXiv2020

Minimal Zeeman field requirement for a topological transition in superconductors

Platforms for creating Majorana quasiparticles rely on superconductivity and breaking of time-reversal symmetry. By studying continuous deformations to known trivial states, we find that the relationship between superconducting pairing and time reversal breaking imposes rigorous bounds on the topology of the system. Applying these bounds to $s$-wave systems with a Zeeman field, we conclude that a topological phase transition requires that the Zeeman energy at least locally exceed the superconducting pairing by the energy gap of the full Hamiltonian. Our results are independent of the geometry and dimensionality of the system.

cond-mat.mes-hall↗

arXiv2020

Topological Weaire-Thorpe models of amorphous matter

Amorphous solids remain outside of the classification and systematic discovery of new topological materials, partially due to the lack of realistic models that are analytically tractable. Here we introduce the topological Weaire-Thorpe class of models, which are defined on amorphous lattices with fixed coordination number, a realistic feature of covalently bonded amorphous solids. Their short-range properties allow us to analytically predict spectral gaps. Their symmetry under permutation of orbitals allows us to analytically compute topological phase diagrams, which determine quantized observables like circular dichroism, by introducing symmetry indicators for the first time in amorphous systems. These models and our procedures to define invariants are generalizable to higher coordination number and dimensions, opening a route towards a complete classification of amorphous topological states in real space using quasilocal properties.

cond-mat.dis-nn↗

arXiv2019

Observation of spin-momentum locked surface states in amorphous Bi$_{2}$Se$_{3}$

Crystalline symmetries have played a central role in the identification of topological materials. The use of symmetry indicators and band representations have enabled a classification scheme for crystalline topological materials, leading to large scale topological materials discovery. In this work we address whether amorphous topological materials, which lie beyond this classification due to the lack of long-range structural order, exist in the solid state. We study amorphous Bi$_2$Se$_3$ thin films, which show a metallic behavior and an increased bulk resistance. The observed low field magnetoresistance due to weak antilocalization demonstrates a significant number of two dimensional surface conduction channels. Our angle-resolved photoemission spectroscopy data is consistent with a dispersive two-dimensional surface state that crosses the bulk gap. Spin resolved photoemission spectroscopy shows this state has an anti-symmetric spin texture resembling that of the surface state of crystalline Bi$_2$Se$_3$. These experimental results are consistent with theoretical photoemission spectra obtained with an amorphous tight-binding model that utilizes a realistic amorphous structure. This discovery of amorphous materials with topological properties uncovers an overlooked subset of topological matter outside the current classification scheme, enabling a new route to discover materials that can enhance the development of scalable topological devices.

cond-mat.mtrl-sci↗

arXiv2019

Hybrid kernel polynomial method

The kernel polynomial method allows to sample overall spectral properties of a quantum system, while sparse diagonalization provides accurate information about a few important states. We present a method combining these two approaches without loss of performance or accuracy. We apply this hybrid kernel polynomial method to improve the computation of thermodynamic quantities and the construction of perturbative effective models, in a regime where neither of the methods is sufficient on its own. To achieve this we develop a perturbative kernel polynomial method to compute arbitrary order series expansions of expectation values. We demonstrate the efficiency of our approach on three examples: the calculation of supercurrent and inductance in a Josephson junction, the interaction of spin qubits defined in a two dimensional electron gas, and the calculation of the effective band structure in a realistic model of a semiconductor nanowire.

cond-mat.mes-hall↗

arXiv2019

Computation of topological phase diagram of disordered Pb$_{1-x}$Sn$_{x}$Te using the kernel polynomial method

We present an algorithm to determine topological invariants of inhomogeneous systems, such as alloys, disordered crystals, or amorphous systems. Based on the kernel polynomial method, our algorithm allows us to study samples with more than $10^7$ degrees of freedom. Our method enables the study of large complex compounds, where disorder is inherent to the system. We use it to analyse Pb$_{1-x}$Sn$_{x}$Te and tighten the critical concentration for the phase transition.

cond-mat.mes-hall↗