arXiv subjects

David Vanderbilt

Publications and source records attributed to David Vanderbilt.

At least 19 recordsLinked to original sources

arXiv2026

Exact expression for the Berry connection in the projection gauge

The Berry connection encodes the momentum-space geometry of occupied Bloch states in gapped insulators and plays a central role in topological materials. While gauge-invariant quantities can be evaluated from overlap matrices between neighboring $k$ points, accessing the Berry connection itself as a smooth field requires specifying a continuous gauge over the Brillouin zone. Wannier-based workflows achieve this through projection onto localized orbitals, enabling stable evaluation of geometric quantities and response functions. In this setting, the Berry connection enters directly in Wannier-interpolated calculations of polarization, Berry curvature, and related response functions. In practical implementations, however, the projection-gauge Berry connection is typically constructed from finite-difference overlaps between neighboring $k$ points, discretizing momentum derivatives and introducing errors tied to $k$-mesh spacing and gauge alignment. These effects can become numerically delicate in systems with small band gaps or when evaluating higher-order responses such as the Chern-Simons axion angle. Here, we derive an exact expression for the non-Abelian Berry connection in the projection gauge that is local in crystal momentum. Starting from projected and orthonormalized Bloch-like states, we obtain a closed-form equation expressed entirely in terms of $k$-local quantities. We validate the formulation in one and three dimensions by computing the Berry phase and Chern-Simons axion angle in tight-binding models. The resulting framework provides a stable route to evaluating geometric properties within Wannier interpolation schemes and future first-principles implementations.

cond-mat.mes-hall↗

arXiv2025

Electrotoroidicity: New Paradigm for Transverse Electromagnetic Responses

The exploration of transverse electromagnetic responses in solids with broken spatial-inversion (I) and/or time-reversal (T) symmetries has unveiled numerous captivating phenomena, including the (anomalous) Hall effect, Faraday rotations, non-reciprocal directional dichroism, and off-diagonal linear magnetoelectricity, all within the framework of magnetotoroidicity. Here, we introduce a novel class of transverse electromagnetic responses originating from electrotoroidicity in ferro-rotational (FR) systems with preserved I and T symmetries, distinct from magnetotoroidicity. We discover a high-order off-diagonal magnetic susceptibility of FR domains and a reduced linear diagonal magnetic susceptibility at FR domain walls in doped ilmenite FeTiO3. The non-trivial "Hall-like" effect of the former corresponds to an anomalous transverse susceptibility in the presence of spontaneous electrotoroidal moments in FR materials. Our findings unveil an emergent type of transverse electromagnetic responses even in I and T symmetry-conserved conditions and illustrate new functionalities of abundant FR materials.

cond-mat.mtrl-sci↗

arXiv2025

Optical spatial dispersion via Wannier interpolation

We present a numerical implementation, based on Wannier interpolation, of a Kubo-Greenwood formalism for computing the spatially dispersive optical conductivity in crystals at first order in the wave vector of light. This approach is more efficient than direct $\textit{ab initio}$ methods because, with less computational cost, it allows for a much finer sampling of reciprocal space, resulting in better resolved spectra. Moreover, Wannier interpolation avoids errors arising from truncation of the sums over conduction bands when evaluating the spatially dispersive optical matrix elements. We validate our method by computing the optical activity spectrum of selected crystals, both polar (GaN) and chiral (trigonal Te, trigonal Se, and $\alpha$-quartz), and comparing with existing literature.

cond-mat.mtrl-sci↗

arXiv2025

Loop-current order through the kagome looking glass

In loop-current states, interacting electronic degrees of freedom collectively establish interatomic currents, in a rare example of magnetism in which spin degrees of freedom do not play the primary role. The main impact of such states on the electronic spectrum is not via the standard Zeeman term, but via the kinetic energy, in which hopping parameters develop non-trivial phases that break time-reversal symmetry. The recent proposal of loop-current states in kagome superconductors has stimulated renewed interest in this exotic type of magnetism. In this perspective, we use kagome materials as a scaffolding to frame the basic phenomenology of loop-current states. We provide an overview of the group-theoretical properties of loop currents, as well as of relevant microscopic models and ab initio methods. Particular emphasis is given to the comparison with spin-density waves in the presence of spin-orbit coupling, as well as to the anharmonic coupling with charge-density waves, which is present in systems with threefold rotational symmetry. We also provide a brief overview of the current status of loop-current order in kagome metals and discuss open challenges including their experimental detection and interplay with other orders.

cond-mat.str-el↗

arXiv2024

Reduced Wannier representation for topological bands

Bands with non-trivial topological indices have a topological obstruction preventing them from being represented by exponentially localized Wannier states. Here, we propose a procedure to construct exponentially localized Wannier functions that span a subspace of topologically obstructed bands through the use of the projection method. These Wannier functions form what we refer to as a "reduced Wannier representation," indicating that the Wannier functions necessarily do not span the full topological manifold. By constructing supercells, we obtain reduced Wannier functions that break the primitive translational symmetry while capturing a substantial portion of the topologically obstructed manifold. This approach effectively decomposes the topological manifold into two subspaces: an itinerant subspace inheriting the topology and a localized trivial subspace represented by reduced Wannier functions. We consider the Haldane and Kane-Mele tight-binding models as the platforms for our investigation.

cond-mat.mes-hall↗

arXiv2024

Inducing topological flat bands in bilayer graphene with electric and magnetic superlattices

It was recently argued that Bernal stacked bilayer graphene (BLG) exposed to a 2D superlattice (SL) potential exhibits a variety of intriguing behaviors [Ghorashi et al., Phys. Rev. Lett. 130, 196201 (2023)]. Chief among them is the appearance of flat Chern bands that are favorable to the appearance of fractional Chern insulator states. Here, we explore the application of spatially periodic out-of-plane orbital magnetic fields to the model of Ghorashi et al. to find additional means of inducing flat Chern bands. We focus on fields that vary on length scales much larger than the atomic spacing in BLG, generating what we refer to as magnetic SLs. The magnetic SLs we investigate either introduce no net magnetic flux to the SL unit cell, or a single quantum of flux. We find that magnetic SLs acting on their own can induce topological flat bands, but richer behavior, such as the appearance of flat and generic bands with high Chern numbers, can be observed when the magnetic SLs act in conjunction with commensurate electric SLs. Finally, we propose a method of generating unit-flux-quantum magnetic SLs along with concomitant electric SLs. The magnetic SL is generated by periodic arrays of flux vortices originating from type II superconductors, while the electric SL arises due to a magnetic SL-induced charge density on the surface of a magnetoelectric material. Tuning the vortex lattice and the magnetoelectric coupling permits control of both SLs, and we study their effects on the band structure of BLG.

cond-mat.mes-hall↗

arXiv2024

Magnetochiral Tunneling in Paramagnetic Co$_{1/3}$NbS$_2$

Electric currents have the intriguing ability to induce magnetization in nonmagnetic crystals with sufficiently low crystallographic symmetry. Some associated phenomena include the non-linear anomalous Hall effect in polar crystals and the nonreciprocal directional dichroism in chiral crystals when magnetic fields are applied. In this work, we demonstrate that the same underlying physics is also manifested in the electronic tunneling process between the surface of a nonmagnetic chiral material and a magnetized scanning probe. In the paramagnetic but chiral metallic compound Co$_{1/3}$NbS$_2$, the magnetization induced by the tunneling current is shown to become detectable by its coupling to the magnetization of the tip itself. This results in a contrast across different chiral domains, achieving atomic-scale spatial resolution of structural chirality. To support the proposed mechanism, we used first-principles theory to compute the chirality-dependent current-induced magnetization and Berry curvature in the bulk of the material. Our demonstration of this magnetochiral tunneling effect opens up a new avenue for investigating atomic-scale variations in the local crystallographic symmetry and electronic structure across the structural domain boundaries of low-symmetry nonmagnetic crystals.

cond-mat.mtrl-sci↗

arXiv2023

Vacancy-induced tunable Kondo effect in twisted bilayer graphene

In single sheets of graphene, vacancy-induced states have been shown to host an effective spin-1/2 hole that can be Kondo-screened at low temperatures. Here, we show how these vacancy-induced impurity states survive in twisted bilayer graphene (TBG), which thus provides a tunable system to probe the critical destruction of the Kondo effect in pseudogap hosts. Ab-initio calculations and atomic-scale modeling are used to determine the nature of the vacancy states in the vicinity of the magic angle in TBG, demonstrating that the vacancy can be treated as a quantum impurity. Utilizing this insight, we construct an Anderson impurity model with a TBG host that we solve using the numerical renormalization group combined with the kernel polynomial method. We determine the phase diagram of the model and show how there is a strict dichotomy between vacancies in the AA/BB versus AB/BA tunneling regions. In AB/BA vacancies, the Kondo temperature at the magic angle develops a broad distribution with a tail to vanishing temperatures due to multifractal wavefunctions at the magic angle. We argue that scanning tunneling microscopy in the vicinity of the vacancy can act as a probe of both the critical single-particle states and the underlying many-body ground state in magic-angle TBG.

cond-mat.str-el↗

arXiv2023

Non-collinear 2k antiferromagnetism in the Zintl semiconductor Eu$_5$In$_2$Sb$_6$

Eu$_5$In$_2$Sb$_6$ is an orthorhombic non-symmorphic small band gap semiconductor with three distinct Eu$^{2+}$ sites and two low-temperature magnetic phase transitions. The material displays one of the greatest (negative) magnetoresistances of known stoichiometric antiferromagnets and belongs to a family of Zintl materials that may host an axion insulator. Using single crystal neutron diffraction, we show that the $T_{\mathrm{N1}}=14\mathrm{~K}$ second-order phase transition is associated with long-range antiferromagnetic order within the chemical unit cell $\left( k_1 = (000) \right)$. Upon cooling below $T_{\mathrm{N1}}$, the relative sublattice magnetizations of this structure vary until a second-order phase transition at $T_{\mathrm{N2}}=7\mathrm{~K}$ that doubles the unit cell along the $\hat{c}$ axis $\left( k_2 = \left(00\frac{1}{2}\right) \right)$. We show the anisotropic susceptibility and our magnetic neutron diffraction data are consistent with magnetic structures described by the $\Gamma_3$ irreducible representation with the staggered magnetization of the $k_1$ and $k_2$ components polarized along the $\hat{b}$ and $\hat{a}$ axis, respectively. As the $k_2$ component develops, the amplitude of the $k_1$ component is reduced, which indicates a 2k non-collinear magnetic structure. Density functional theory is used to calculate the energies of these magnetic structures and to show the $k_1$ phase is a metal so $T_{\mathrm{N1}}$ is a rare example of a unit-cell-preserving second-order phase transition from a paramagnetic semiconductor to an antiferromagnetic metal. DFT indicates the transition at $T_{\mathrm{N2}}$ to a doubled unit cell reduces the carrier density of the metal, which is consistent with resistivity data.

cond-mat.str-el↗

arXiv2023

Adiabatic dynamics of coupled spins and phonons in magnetic insulators

In conventional \textit{ab initio} methodologies, phonons are calculated by solving equations of motion involving static interatomic force constants and atomic masses. The Born-Oppenheimer approximation, where all electronic degrees of freedom are assumed to adiabatically follow the nuclear dynamics, is also adopted. This approach does not fully account for the effects of broken time-reversal symmetry in systems with magnetic order. Recent attempts to rectify this involve the inclusion of the velocity dependence of the interatomic forces in the equations of motion, which accounts for time-reversal symmetry breaking, and can result in chiral phonon modes with non-zero angular momentum even at the zone center. However, since the energy ranges of phonons and magnons typically overlap, the spins cannot be treated as adiabatically following the lattice degrees of freedom. Instead, phonon and spins must be treated on a similar footing. Focusing on zone-center modes, we propose a method involving Hessian matrices and Berry curvature tensors in terms of both phonon and spin degrees of freedom, and describe a first-principles methodology for calculating these. We then solve Lagrange's equations of motion to determine the energies and characters of the mixed excitations, allowing us to quantify, for example, the energy splittings between chiral pairs of phonons in some cases, and the degree of magnetically induced mixing between infrared and Raman modes in others. The approach is general, and can be applied to determine the adiabatic dynamics of any mixed set of slow variables.

cond-mat.mtrl-sci↗

arXiv2023

Cyclic Ferroelectric Switching and Quantized Charge Transport in CuInP$_2$S$_6$

The van der Waals layered ferroelectric CuInP$_2$S$_6$ has been found to exhibit a variety of intriguing properties arising from the fact that the Cu ions are unusually mobile in this system. While the polarization switching mechanism is usually understood to arise from Cu ion motion within the monolayers, a second switching path involving Cu motion across the van der Waals gaps has been suggested. In this work, we perform zero-temperature first-principles calculations on such switching paths, focusing on two types that preserve the periodicity of the primitive unit cell: ``cooperative" paths preserving the system's glide mirror symmetry, and ``sequential" paths in which the two Cu ions in the unit cell move independently of each other. We find that CuInP$_2$S$_6$ features a rich and varied energy landscape, and that sequential paths are clearly favored energetically both for cross-gap and through-layer paths. Importantly, these segments can be assembled to comprise a globally insulating cycle with the out-of-plane polarization evolving by a quantum as the Cu ions shift to neighboring layers. In this sense, we argue that CuInP$_2$S$_6$ embodies the physics of a quantized adiabatic charge pump.

cond-mat.mtrl-sci↗

arXiv2023

Bismuth antiphase domain wall: A three-dimensional manifestation of the Su-Schrieffer-Heeger model

The Su, Schrieffer and Heeger (SSH) model, describing the soliton excitations in polyacetylene due to the formation of antiphase domain walls (DW) from the alternating bond pattern, has served as a paradigmatic example of one-dimensional (1D) chiral topological insulators. While the SSH model has been realized in photonic and plasmonic systems, there have been limited analogues in three-dimensional (3D) electronic systems, especially regarding the formation of antiphase DWs. Here, we propose that pristine bulk Bi, in which the dimerization of $(111)$ atomic layers renders alternating covalent and van der Waals bonding within and between successive $(111)$ bilayers, respectively, serves as a 3D analogue of the SSH model. First, we confirm that the two dimerized Bi structures belong to different Zak phases of 0 and $\pi$ by considering the parity eigenvalues and Wannier charge centers, while the previously reported bulk topological phases of Bi remain invariant under the dimerization reversal. Next, we demonstrate the existence of topologically non-trivial $(111)$ and trivial $(11\bar{2})$ DWs in which the number of in-gap DW states (ignoring spin) is odd and even respectively, and show how this controls the interlinking of the Zak phases of the two adjacent domains. Finally, we derive general criteria specifying when a DW of arbitrary orientation exhibits a $\pi$ Zak phase based on the flip of parity eigenvalues. An experimental realization of dimerization in Bi and the formation of DWs may be achieved via intense femtosecond laser excitations that can alter the interatomic forces and bond lengths.

cond-mat.mes-hall↗

arXiv2022

Towards a theory of surface orbital magnetization

The theory of bulk orbital magnetization has been formulated both in reciprocal space based on Berry curvature and related quantities, and in real space in terms of the spatial average of a quantum mechanical local marker. Here we consider a three-dimensional antiferromagnetic material having a vanishing bulk but a nonzero surface orbital magnetization. We ask whether the surface-normal component of the surface magnetization is well defined, and if so, how to compute it. As the physical observable corresponding to this quantity, we identify the macroscopic current running along a hinge shared by two facets. However, the hinge current only constrains the difference of the surface magnetizations on the adjoined facets, leaving a potential ambiguity. By performing a symmetry analysis, we find that only crystals exhibiting a pseudoscalar symmetry admit well-defined magnetizations at their surfaces at the classical level. We then explore the possibility of computing surface magnetization via a coarse-graining procedure applied to a quantum local marker. We show that multiple expressions for the local marker exist, and apply constraints to filter out potentially meaningful candidates. Using several tight-binding models as our theoretical test bed and several potential markers, we compute surface magnetizations for slab geometries and compare their predictions with explicit calculations of the macroscopic hinge currents of rod geometries. We find that only a particular form of the marker consistently predicts the correct hinge currents.

cond-mat.mes-hall↗

arXiv2022

Magnetic phase crossover in strongly correlated EuMn2P2

Strong electron correlations underlie a plethora of electronic and magnetic components and devices and are often used to identify and probe novel ground states in quantum materials. Herein we report a magnetic phase crossover in EuMn2P2, an insulator which shows Eu antiferromagnetism at TN=17K, but no phase transition attributed to Mn magnetism. The absence of a Mn magnetic phase transition contrasts with the formation of long-range Mn order at T=130K in isoelectronic EuMn2Sb2 and EuMn2As2. Temperature-dependent specific heat and 31P NMR measurements provide evidence for the development of Mn magnetic correlations from T=250-100 K. Density functional theory calculations demonstrate an unusual sensitivity of the band structure to the details of the imposed Mn and Eu magnetic order, with antiferromagnetic Mn order required to recapitulate an insulating state. Our results imply a picture in which long range Mn magnetic order is suppressed by chemical pressure, but that magnetic correlations persist, narrowing bands and producing an insulating state.

cond-mat.str-el↗

arXiv2022

Frequency splitting of chiral phonons from broken time reversal symmetry in CrI$_3$

Conventional approaches for lattice dynamics based on static interatomic forces do not fully account for the effects of time-reversal-symmetry breaking in magnetic systems. Recent approaches to rectify this involve incorporating the first-order change in forces with atomic velocities under the assumption of adiabatic separation of electronic and nuclear degrees of freedom. In this work, we develop a first-principles method to calculate this velocity-force coupling in extended solids, and show via the example of ferromagnetic CrI$_3$ that, due to the slow dynamics of the spins in the system, the assumption of adiabatic separation can result in large errors for splittings of zone-center chiral modes. We demonstrate that an accurate description of the lattice dynamics requires treating magnons and phonons on the same footing.

cond-mat.mtrl-sci↗

arXiv2022

Integer quantum Hall effect and enhanced g-factor in quantum confined Cd3As2 films

We investigate the integer quantum Hall effect in Cd3As2 thin films under conditions of strong to moderate quantum confinement (thicknesses of 10 nm, 12 nm, 15 nm). In all the films, we observe the integer quantum Hall effect in the spin-polarized lowest Landau level (filling factor {\nu} = 1) and at spin-degenerate higher index Landau levels with even filling factors ({\nu} = 2,4,6). With increasing quantum confinement, we also observe a lifting of the Landau level spin degeneracy at {\nu} = 3, manifest as the emergence of an anomaly in the longitudinal and Hall resistivity. Tight-binding calculations show that the enhanced g-factor likely arises from a combination of quantum confinement and corrections from nearby subbands. We also comment on the magnetic field induced transition from an insulator to a quantum Hall liquid when the chemical potential is near the charge neutrality point.

cond-mat.mes-hall↗

arXiv2022

Electronic structure of Humble defects in Ge and Ge$_{0.8}$Si$_{0.2}$

The group-IV diamond-structure elements are known to host a variety of planar defects, including {001} planar defects in C and {001}, {111} and {113} planar defects in Si and Ge. Among the {001} planar defects, the Humble defect, known for some time to occur in Ge, has recently also been observed in Si/Ge alloys, but the details of its electronic structure remain poorly understood. Here we perform first-principles density functional calculations to study Humble defects in both Ge and Ge$_{0.8}$Si$_{0.2}$. We also measure the Si L$_{2,3}$-edge electron energy loss spectra both at the defect and in a bulk-like region far from the defect, and compare with theoretical calculations on corresponding Si sites in our first-principles calculations. We find that inclusion of core-hole effects in the theory is essential for reproducing the observed L$_{2,3}$ edge spectra, and that once they are included, the results provide a set of fingerprints for different types of local atomic bonding environments in Ge$_{0.8}$Si$_{0.2}$. Our first-principles calculations reveal that the Humble defects have a tendency to enlarge the electronic band gap, which may have potential uses in band engineering. The use of hybrid functionals for an improved description of the band gap in these systems is also discussed.

cond-mat.mtrl-sci↗

arXiv2022

Direct visualization of surface spin-flip transition in MnBi4Te7

We report direct visualization of spin-flip transition of the surface layer in antiferromagnet MnBi4Te7, a natural superlattice of alternating MnBi2Te4 and Bi2Te3 layers, using cryogenic magnetic force microscopy (MFM). The observation of magnetic contrast across domain walls and step edges confirms that the antiferromagnetic order persists to the surface layers. The magnetic field dependence of the MFM images reveals that the surface magnetic layer undergoes a first-order spin-flip transition at a magnetic field that is lower than the bulk transition, in excellent agreement with a revised Mills' model. Our analysis indicates an enhancement of the order parameter in the surface magnetic layer, implying robust ferromagnetism in the single-layer limit. The direct visualization of surface spin-flip transition not only opens up exploration of surface metamagnetic transitions in layered antiferromagnets, but also provides experimental support for realizing quantized transport in ultra-thin films of MnBi4Te7 and other natural superlattice topological magnets.

cond-mat.mtrl-sci↗