arXiv subjects

Ganpathy Murthy

Publications and source records attributed to Ganpathy Murthy.

At least 19 recordsLinked to original sources

arXiv2026

Skyrmion Excitations in the $\nu=-1$ Quantum Hall state in Monolayer Graphene

We investigate the skyrmion excited states atop the $SU(4)$ quantum Hall ferromagnetic ground state at filling factor $\nu=-1$ in monolayer graphene. The competition among short-range anisotropic interactions, the Zeeman coupling, and sublattice symmetry-breaking potential gives rise to four distinct spin-valley-ordered ground-state phases. Combining effective field theory with the Hartree--Fock approximation, we develop a variational framework that incorporates both the long-range Coulomb interaction and the symmetry-breaking terms on an equal footing. Variational minimization determines the optimal skyrmion texture, including both its spatial radial profile and internal $SU(4)$ spinor structure. We establish the phase diagram of skyrmion excitations, identify thirteen distinct skyrmion phases under different external-field conditions, and determine their spin-valley textures, energies, and characteristic sizes. The robustness of the results against different radial ans\"atze demonstrates the reliability of our variational approach. Our work provides a systematic framework for studying skyrmion excitations in multicomponent quantum Hall ferromagnets and can be naturally extended to more general $SU(4)$ quantum Hall systems.

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arXiv2025

Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States

We evaluate the transport gaps in the most prominent fractional quantum Hall states in the $\mathbf{n}{=}0$ and $\mathbf{n}{=}1$ Landau Levels of graphene, accounting for the Coulomb interaction, lattice-scale anisotropies, and one-body terms. We find that the fractional phases in the $\mathbf{n}{=}0$ Landau level are bond-ordered, while those in the $\mathbf{n}{=}1$ Landau level are spin-valley entangled. This resolves a long-standing experimental puzzle [Amet, $\textit{et al.}$, Nat. Comm. $\mathbf{6}$, 5838 (2015)] of the contrasting Zeeman dependence of the transport gaps in the two Landau levels. The spin-valley entangled phases host gapless Goldstone modes that can be probed via bulk thermal transport measurements. As a byproduct of our computations, we place strong constraints on the values of the microscopic anisotropic couplings such that these are consistent with all known experimental results.

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arXiv2024

Uniquely identifying quantum Hall phases in charge neutral graphene

Charge-neutral graphene in the quantum Hall regime is an example of a quantum Hall ferromagnet in a complex spin-valley space. This system exhibits a plethora of phases, with the particular spin-valley order parameters chosen by the system depending sensitively on the short-range anisotropic couplings, the Zeeman field, and the sublattice symmetry breaking field. A subset of order parameters related to lattice symmetry-breaking have been observed by scanning tunneling microscopy. However, other order parameters, particularly those which superpose spin and valley, are more elusive, making it difficult to pin down the nature of the phase. We propose a solution this problem by examining two types of experimentally measurable quantities; transport gaps and collective mode dispersions. We find that the variation of the transport gap with the Zeeman and sublattice symmetry breaking fields, in conjunction with the number of Larmor and gapless modes, provides a unique signature for each theoretically possible phase.

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arXiv2024

Fractional quantum Hall coexistence phases in higher Landau levels of graphene

Monolayer graphene under a strong magnetic field near charge neutrality manifests the integer and fractional quantum Hall effects. Since only some of the four spin/valley flavors available to the electrons in each Landau level manifold are filled, they also exhibit spontaneous symmetry breaking the in spin/valley sector, a phenomenon known as quantum Hall ferromagnetism. In this work, we study quantum Hall ferromagnets in the higher Landau level manifolds of monolayer graphene and show that there is an even richer set of symmetry-broken phases than in the lowest Landau level manifold. Specifically, both valley polarized and valley equatorial (where the occupied Landau levels are in an equal superposition of both valleys) ferromagnets, antiferromagnets, and canted antiferromagnets are found. Several types of spin valley entangled phases are found, all of which manifest the simultaneous spontaneous symmetry breaking of both magnetic and lattice symmetries.

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arXiv2024

Magnon transmission across $\nu=1|-1|1$ mono-layer graphene junction as a probe of electronic structure

We study magnon transmission across gate-controlled junctions in the $n=0$ manifold of Landau levels in monolayer graphene, in the presence of both spin and valley Zeeman fields. Specifically, we consider the $1|-1|1$ sandwich geometry. The nature of the interfaces between regions of different filling turns out to be crucial for magnon transmission. Using the Hartree-Fock approximation, we find that either the spin or the valley degrees of freedom of the occupied one-body states rotate across the interfaces. If the interfaces exhibit spin rotation, magnon transmission is suppressed at high energies, while if the interfaces have valley rotation, magnon transmission becomes perfect at high energies. The valley Zeeman coupling, which arises from partial alignment with the encapsulating Boron Nitride, is independent of perpendicular magnetic field $B$, while the spin Zeeman and other anisotropic couplings scale linearly with $B$. This allows the tuning of the relative strength of the valley Zeeman coupling in situ by varying $B$, which can drive phase transitions of the interfaces between spin-rotated and valley-rotated phases, leading to magnon transmission being either vanishing or perfect at high energies. Our analysis, along with the experimental measurements, can be used to determine the anisotropic couplings in the sample.

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arXiv2024

Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene

At and near charge neutrality, monolayer graphene in a perpendicular magnetic field is a quantum Hall ferromagnet. In addition to the highly symmetric Coulomb interaction, residual lattice-scale interactions, Zeeman, and sublattice couplings determine the fate of the ground state. Going beyond the simplest model with ultra-short-range residual couplings to more generic couplings, one finds integer phases that show the coexistence of magnetic and lattice order parameters. Here we show that fractional quantum Hall states in the vicinity of charge neutrality have even richer phase diagrams, with a plethora of phases with simultaneous magnetic and lattice symmetry breaking.

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arXiv2023

Topological nodal line semimetals with chiral symmetry

Topological semimetals in three dimensions display band-touchings at points (Weyl or Dirac semimetals) or nodal lines in the Brillouin zone. Weyl semimetals can occur with internal symmetries only (time-reversal ${\cal T}$, charge conjugation ${\cal C}$, and a product of the two, called chiral/sublattice symmetry ${\cal S}={\cal T}{\cal C}$). Nodal line semimetals possessing solely internal symmetries have only been classified abstractly, while those with SU(2) spin rotation or crystalline symmetries are known more explicitly. We show that chiral symmetry classes that are topologically nontrivial in three dimensions (namely class AIII, CII, CI, and DIII) always have a stable gapless phase, which is a topological nodal line semimetal. Our classification differs from previous approaches and has direct implications for gapless surface states.

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arXiv2023

Stable nodal line semimetals in the chiral classes in three dimensions

It has been realized over the past two decades that topological nontriviality can be present not only in insulators but also in gapless semimetals, the most prominent example being Weyl semimetals in three dimensions. Key to topological classification schemes are the three ``internal" symmetries, time reversal ${\cal T}$, charge conjugation ${\cal C}$, and their product, called chiral symmetry ${\cal S}={\cal T}{\cal C}$. In this work, we show that robust topological nodal line semimetal phases occur in $d=3$ in systems whose internal symmetries include ${\cal S}$, without invoking crystalline symmetries other than translations. Since the nodal loop semimetal naturally appears as an intermediate gapless phase between the topological and the trivial insulators, a sufficient condition for the nodal loop phase to exist is that the symmetry class must have a nontrivial topological insulator in $d=3$. Our classification uses the winding number on a loop that links the nodal line. A nonzero winding number on a nodal loop implies robust gapless drumhead states on the surface Brillouin zone. We demonstrate how our classification works in all the nontrivial chiral classes and how it differs from the previous understanding of topologically protected nodal line semimetals.

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arXiv2023

Phase diagram of the $\nu = 2$ quantum Hall state in bilayer graphene

Bilayer graphene exhibits a rich phase diagram in the quantum Hall regime, arising from a multitude of internal degrees of freedom, including spin, valley, and orbital indices. The variety of fractional quantum Hall states between filling factors $1 < \nu \leq 2$ suggests, among other things, a quantum phase transition between valley-unpolarized and polarized states at a perpendicular electric field $D^{*}$. We find the behavior of $D^{*}$ with $\nu$ changes markedly as $B$ is reduced. At $\nu = 2$, $D^{*}$ may even vanish when $B$ is sufficiently small. We present a theoretical model for lattice-scale interactions which explains these observations; surprisingly, both repulsive and attractive components in the interactions are required. Within this model we analyze the nature of the $\nu = 2$ state as a function of the magnetic and electric fields, and predict that valley-coherence may emerge for $D \sim D^{*}$ in the high $B$ regime. This suggests the system supports Kekule bond-ordering, which could in principle be verified via STM measurements.

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arXiv2022

Lattice Model For The Quantum Anomalous Hall Effect in Moir\'e Graphene

Inspired by experiments on magic angle twisted bilayer graphene, we present a lattice mean-field model for the quantum anomalous Hall effect in a moir\'e setting. Our hopping model thus provides a simple route to a moir\'e Chern insulator in commensurately twisted models. We present a study of our model in the ribbon geometry, in which we demonstrate the presence of thick chiral edge states that have a transverse localization that scales with the moir\'e lattice spacing. We also study the electronic structure of a domain wall between opposite Chern insulators. Our model and results are relevant to experiments that will image or manipulate the moir\'e quantum anomalous Hall edge states.

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arXiv2022

Global phase diagram of charge neutral graphene in the quantum Hall regime for generic interactions

Monolayer graphene at charge neutrality in a quantizing magnetic field is a quantum Hall ferromagnet. Due to the spin and valley (near) degeneracies, there is a plethora of possible ground states. Previous theoretical work, based on a stringent ultra short-range assumption on the symmetry-allowed interactions, predicts a phase diagram with distinct regions of spin-polarized, canted antiferromagnetic, inter-valley coherent, and charge density wave order. While early experiments suggested that the system was in the canted antiferromagnetic phase at a perpendicular field, recent scanning tunneling studies universally find Kekul\'e bond order, and sometimes also charge density wave order. Recently, it was found that if one relaxes the stringent assumption mentioned above, a phase with coexisting canted antiferromagnetic and Kekul\'e order exists in the region of the phase diagram believed to correspond to real samples. In this work, starting from the continuum limit appropriate for experiments, we present the complete phase diagram of $\nu=0$ graphene in the Hartree-Fock approximation, using generic symmetry-allowed interactions, assuming translation invariant ground states up to an intervalley coherence. Allowing for a sublattice potential (valley Zeeman coupling), we find numerous phases with different types of coexisting order. We conclude with a discussion of the physical signatures of the various states.

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arXiv2022

Absence of Edge States in The Valley Chern Insulator in Moir\'e Graphene

We study the edge spectrum of twisted sheets of single layer and bilayer graphene in cases where the continuum model predicts a valley Chern insulator -- an insulating state in which the occupied moir\'e mini-bands from each valley have a net Chern number, but both valleys together have no net Chern number, as required by time reversal symmetry. In a simple picture, such a state might be expected to have chiral valley polarized counter-propagating edge states. We present results from exact diagonalization of the tight-binding model of commensurate structures in the ribbon geometry. We find that for both the single-layer and bilayer moir\'e ribbons robust edge modes are generically absent. We attribute this lack of edge modes to the fact that the edge induces valley mixing. Further, even in the bulk, a sharp distinction between the valley Chern insulator and a trivial insulator requires an exact $C_3$ symmetry.

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arXiv2022

Electrically switchable tunneling across a graphene pn junction: evidence for canted antiferromagnetic phase in $\nu=0$ state

The ground state of a graphene sheet at charge neutrality in a perpendicular magnetic field remains enigmatic, with various experiments supporting canted antiferromagnetic, bond ordered, and even charge density wave phases. A promising avenue to elucidating the nature of this state is to sandwich it between regions of different filling factors, and study spin-dependent tunneling across the edge modes at the interfaces. Here we report on tunnel transport through a $\nu=0$ region in a graphite-gated, hexagonal boron nitride ($hBN$) encapsulated monolayer graphene device, with the $\nu=0$ strip sandwiched by spin-polarized $\nu=\pm1$ quantum Hall states. We observe finite tunneling ($t \sim 0.3-0.6$) between the $\nu=\pm1$ edges at not too small magnetic fields ($B>3T$) and low tunnel bias voltage ($<30-60\mu V$), which is surprising because electrons at the edge states nominally have opposite spins. Hartree-Fock calculations elucidate these phenomena as being driven by the formation of a CAF order parameter in the $\nu=0$ region at zero bias (for wide enough junctions) leading to non-orthogonal spins at the edges. Remarkably, this tunneling can be controllably switched off by increasing bias; bias voltage leads to a pileup of charge at the junction, leading to a collapse of the CAF order and a suppression of the tunneling.

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arXiv2021

Coexistence of Canted Antiferromagnetism and Bond-order in $\nu=0$ Graphene

Motivated by experimental studies of graphene in the quantum Hall regime, we revisit the phase diagram of a single sheet of graphene at charge neutrality. Because of spin and valley degeneracies, interactions play a crucial role in determining the nature of ground state. We show that, generically, in the regime of interest there is a region of coexistence between magnetic and bond orders in the phase diagram. We demonstrate this result both in continuum and lattice models, and argue that the coexistence phase naturally provides an explanation for unreconciled experimental observations on the quantum Hall effect in graphene.

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arXiv2021

Time-reversal-broken Weyl semimetal in the Hofstadter regime

We study the phase diagram for a lattice model of a time-reversal-broken three-dimensional Weyl semimetal (WSM) in an orbital magnetic field $B$ with a flux of $p/q$ per unit cell ($0\le p \le q-1$), with minimal crystalline symmetry. We find several interesting phases: (i) WSM phases with $2q$, $4q$, $6q$, and $8q$ Weyl nodes and corresponding surface Fermi arcs, (ii) a layered Chern insulating (LCI) phase, gapped in the bulk, but with gapless surface states, (iii) a phase in which some bulk bands are gapless with Weyl nodes, coexisting with others that are gapped but topologically nontrivial, adiabatically connected to an LCI phase, (iv) a new gapped trivially insulating phase (I$'$) with (non-topological) counter-propagating surface states, which could be gapped out in the absence of crystal symmetries. Importantly, we are able to obtain the phase boundaries analytically for all $p,q$. Analyzing the gaps for $p=1$ and very large $q$ enables us to smoothly take the zero-field limit, even though the phase diagrams look ostensibly very different for $q=1, B=0$, and $q\to\infty, B\to 0$.

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arXiv2021

Dc Electrical Current Generated by Upstream Neutral Modes

Quantum Hall phases are gapped in the bulk but support chiral edge modes, both charged and neutral. Here we consider a circuit where the path from the source of electric current to the drain necessarily passes through a segment consisting solely of neutral modes. We find that upon biasing the source, a dc electric current is detected at the drain, provided there is backscattering between counter-propagating modes under the contacts placed in certain locations. Thus, neutral modes carry information that can be used to nonlocally reconstruct a dc charge current. Our protocol can be used to detect any neutral mode that counterpropagates with respect to all charge modes. Our protocol applies not only to the edge modes of a quantum Hall system, but also to systems that have neutral modes of non-quantum Hall origin. We conclude with a possible experimental realization of this phenomenon.

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arXiv2021

Weyl Semimetal Path to Valley Filtering in Graphene

We propose a device in which a sheet of graphene is coupled to a Weyl semimetal, allowing for the physical access to the study of tunneling from two-dimensional to three dimensional massless Dirac fermions. Due to the reconstructed band structure, we find that this device acts as a robust valley filter for electrons in the graphene sheet. We show that, by appropriate alignment, the Weyl semimetal draws away current in one of the two graphene valleys while allowing current in the other to pass unimpeded. In contrast to other proposed valley filters, the mechanism of our proposed device occurs in the bulk of the graphene sheet, obviating the need for carefully shaped edges or dimensions.

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arXiv2021

Fermi arc reconstruction at the interface of twisted Weyl semimetals

Three-dimensional Weyl semimetals have pairs of topologically protected Weyl nodes, whose projections onto the surface Brillouin zone are the end points of zero energy surface states called Fermi arcs. At the endpoints of the Fermi arcs, surface states extend into and are hybridized with the bulk. Here, we consider a two-dimensional junction of two identical Weyl semimetals whose surfaces are twisted with respect to each other and tunnel-coupled. Confining ourselves to commensurate angles (such that a larger unit cell preserves a reduced translation symmetry at the interface) enables us to analyze arbitrary strengths of the tunnel-coupling. We study the evolution of the Fermi arcs at the interface, in detail, as a function of the twisting angle and the strength of the tunnel-coupling. We show unambiguously that in certain parameter regimes, all surface states decay exponentially into the bulk, and the Fermi arcs become Fermi loops without endpoints. We study the evolution of the `Fermi surfaces' of these surface states as the tunnel-coupling strengths vary. We show that changes in the connectivity of the Fermi arcs/loops have interesting signatures in the optical conductivity in the presence of a magnetic field perpendicular to the surface.

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