arxiv: 2605.10033 · v1 · submitted 2026-05-11 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

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Orbital and Spin Nernst Effects in Monolayers of Transition Metal Dichalcogenides

Arnab Bose, Saikat Saha, Sayantika Bhowal

Authors on Pith no claims yet

Pith reviewed 2026-05-12 02:23 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci

keywords orbital Nernst effectspin Nernst effecttransition metal dichalcogenidesBerry curvatureMoS2NbS2monolayersorbitronics

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The pith

Monolayers of transition metal dichalcogenides generate transverse orbital currents from temperature gradients without spin-orbit coupling.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes that monolayers of transition metal dichalcogenides serve as a platform for the orbital Nernst effect, in which a temperature gradient produces a transverse orbital current. The effect originates from the orbital Berry curvature and occurs even without spin-orbit coupling, as shown by both a low-energy valley model and full tight-binding calculations for MoS2 and NbS2. With spin-orbit coupling included, a spin Nernst effect appears that is proportional to the coupling strength and disappears without it. The results indicate that doping can tune the conductivities, with metallic NbS2 displaying the effects intrinsically while MoS2 requires carrier doping. Readers might care because this provides a way to thermally generate orbital and spin currents in atomically thin materials, potentially advancing orbitronics and spintronics applications.

Core claim

The central discovery is that the orbital Nernst effect in TMD monolayers arises from orbital Berry curvature and does not require spin-orbit coupling, while the spin Nernst effect does require it and scales with its magnitude; both can be calculated analytically in the valley approximation and numerically in the full Brillouin zone, with doping controlling the response in semiconducting cases.

What carries the argument

Orbital Berry curvature within the low-energy valley model and tight-binding band structure, which generates the Nernst conductivity for orbital angular momentum transport.

If this is right

The orbital Nernst conductivity is finite in doped MoS2 and intrinsic in NbS2.
The spin Nernst effect scales with spin-orbit coupling strength and vanishes without it.
Doping provides a route to tune both orbital and spin Nernst responses.
These effects can be detected in a setup with temperature gradient and transverse current measurement.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the orbital Nernst effect is confirmed, similar thermal orbital responses may exist in other valleytronic 2D systems.
Thermal generation of orbital currents could offer an energy-efficient alternative to electrical driving in orbitronic devices.
The separation of orbital and spin contributions allows independent study of each in materials with tunable SOC.

Load-bearing premise

The low-energy valley model and tight-binding calculations accurately represent the Berry curvatures responsible for the Nernst effects without major interference from disorder, scattering, or distant bands.

What would settle it

An experiment observing no transverse orbital current in a doped MoS2 monolayer under a temperature gradient, or a current that does not vanish when spin-orbit coupling is effectively absent, would contradict the claim.

Figures

Figures reproduced from arXiv: 2605.10033 by Arnab Bose, Saikat Saha, Sayantika Bhowal.

**Figure 2.** Figure 2: FIG. 2. Crystal structure of monolayer transition metal [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Orbital and spin Hall and Nernst conductivities in MoS [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Orbital and spin Hall and Nernst conductivities in NbS [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. The [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Variation of (a) SHC in units of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. The proposed device structure for the detection [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Momentum space distribution of the orbital Berry [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. Plot of orbital Berry curvature for NbS [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗

read the original abstract

In recent years, orbitronic effects have attracted growing attention as complementary counterparts to the well-established spintronic phenomena. In this work, we demonstrate that monolayers of transition metal dichalcogenides provide an excellent platform for the observation of the orbital Nernst effect, a relatively less explored phenomenon describing the generation of a transverse orbital current in response to an applied temperature gradient. We show that, similar to its electrical counterpart, viz., the orbital Hall effect, the orbital Nernst effect does not require the presence of spin-orbit coupling. Analytical results based on a low-energy valley model offer key insights into the underlying mechanisms, highlighting in particular the crucial role of electronic states at the Fermi energy for the emergence of this effect. The inclusion of spin-orbit coupling further gives rise to a spin Nernst effect, which scales with the strength of spin-orbit coupling and vanishes in its absence. We substantiate our analytical findings with full Brillouin-zone tight-binding results for two representative systems, monolayer 2H MoS$_2$ and 2H NbS$_2$. Our results show that while both orbital and spin Nernst conductivities in MoS$_2$ require electron or hole doping, both effects are intrinsically present in metallic NbS$_2$. Our work reveals the central role of orbital and spin Berry curvatures, identifies doping as an effective route for tuning orbital and spin Nernst responses, and proposes a possible experimental setup for detecting these effects in monolayer transition metal dichalcogenides.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

TMD monolayers can host doping-tunable orbital Nernst effects without SOC, backed by valley analytics and full-zone TB, though the low-energy model’s accuracy at realistic fillings is not fully stress-tested.

read the letter

The main thing to know is that this paper shows orbital Nernst conductivity in TMD monolayers arises from Berry curvature at the Fermi level and does not need spin-orbit coupling, with clear differences between doped semiconducting MoS2 and metallic NbS2 where the effect is intrinsic. They also recover a spin Nernst term that tracks SOC strength. That combination of thermal transport, orbital focus, and material contrast is the concrete addition here. The low-energy valley model supplies the intuition that only states near the chemical potential matter, and the full Brillouin-zone tight-binding runs for both compounds serve as the numerical check. Those steps are standard but executed cleanly, and the separation of orbital versus spin channels is useful for orbitronics discussions. The doping dependence is mapped out explicitly, which gives a practical handle for experiments. The calculations rest on established Berry-phase methods and standard TB parameters, with no obvious circularity or invented quantities. One soft spot is the range of the analytic valley model. At the electron or hole dopings where the Nernst signals become appreciable, the chemical potential sits far enough from the K/K' edges that trigonal warping and remote bands can enter. The paper performs full-zone TB, yet it is not obvious from the abstract-level description whether they directly overlay the analytic orbital Nernst formula on the TB data at identical fillings to quantify the discrepancy. If that comparison is missing or only qualitative, the mechanistic claim that the effect is “intrinsically present” in NbS2 rests partly on an uncontrolled approximation. That is a fixable limitation rather than a fatal one. Readers working on thermal Hall or Nernst transport in 2D materials, or on orbital currents more generally, will get the most from the doping maps and the SOC-independence result. The work is clear enough and grounded enough to merit referee time; a specialized journal in mesoscopic physics or 2D materials should send it out rather than desk-reject.

Referee Report

2 major / 2 minor

Summary. The paper claims that monolayers of transition metal dichalcogenides (TMDs) such as MoS₂ and NbS₂ provide an excellent platform for the orbital Nernst effect, in which a temperature gradient generates a transverse orbital current. Analytical results from a low-energy valley model show that this effect arises from orbital Berry curvature at the Fermi energy and does not require spin-orbit coupling (SOC); inclusion of SOC additionally produces a spin Nernst effect that scales with SOC strength and vanishes without it. These analytic findings are substantiated by full Brillouin-zone tight-binding calculations, which indicate that both effects require doping in semiconducting MoS₂ but are intrinsic in metallic NbS₂. Doping is identified as a tuning parameter, and an experimental detection scheme is proposed.

Significance. If the central claims hold, the work establishes TMD monolayers as a tunable platform for orbitronic transport phenomena complementary to spintronics. The demonstration that the orbital Nernst effect is intrinsic (SOC-independent) and the explicit separation of orbital versus spin contributions via Berry curvature provide mechanistic clarity that could guide experiments. The contrast between doped MoS₂ and intrinsic NbS₂, together with the proposed measurement geometry, offers concrete predictions for thermoelectric and orbital-current devices.

major comments (2)

[low-energy valley model] The low-energy valley model (analytical section) assumes constant orbital moment and parabolic dispersion near K/K' valleys. At the doping levels where sizable Nernst signals appear (chemical potentials ~0.1–0.2 eV), trigonal warping and remote-band mixing become relevant; the manuscript provides no explicit range-of-validity estimate or error bound for the analytic orbital-Nernst formula once these terms are restored.
[tight-binding results for MoS₂ and NbS₂] Tight-binding results section: although full-BZ numerics are shown for MoS₂ and NbS₂, there is no direct quantitative comparison (e.g., overlay plot or table) of the valley-model orbital-Nernst conductivity versus the TB value evaluated at identical Fermi energies. Without this cross-check, the assertion that the low-energy model captures the essential physics—and therefore that the orbital Nernst effect is “intrinsically present” in NbS₂—remains unverified.

minor comments (2)

[abstract and results] The abstract states that both effects “require electron or hole doping” in MoS₂; the main text should explicitly quote the doping window (in eV or carrier density) over which the TB conductivities are appreciable.
[methods] Notation for the Nernst conductivity tensor (orbital versus spin components) could be introduced once in the methods and used consistently in all figures and equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and constructive feedback on our manuscript. We agree that clarifying the validity range of the low-energy model and providing a direct quantitative comparison with the tight-binding results will strengthen the presentation. Below we address each major comment and commit to revisions that incorporate these points.

read point-by-point responses

Referee: [low-energy valley model] The low-energy valley model (analytical section) assumes constant orbital moment and parabolic dispersion near K/K' valleys. At the doping levels where sizable Nernst signals appear (chemical potentials ~0.1–0.2 eV), trigonal warping and remote-band mixing become relevant; the manuscript provides no explicit range-of-validity estimate or error bound for the analytic orbital-Nernst formula once these terms are restored.

Authors: We acknowledge that the low-energy valley model is an effective approximation whose accuracy decreases at higher doping where trigonal warping and remote-band effects become non-negligible. Our full Brillouin-zone tight-binding calculations already incorporate these higher-order terms and show that the orbital Nernst conductivity remains sizable and qualitatively consistent with the analytic prediction even at chemical potentials of 0.1–0.2 eV. To make this explicit, we will add a dedicated paragraph in the revised manuscript that estimates the doping range of validity by comparing the analytic formula against the tight-binding results and notes the doping level at which deviations exceed 20%. revision: yes
Referee: [tight-binding results for MoS₂ and NbS₂] Tight-binding results section: although full-BZ numerics are shown for MoS₂ and NbS₂, there is no direct quantitative comparison (e.g., overlay plot or table) of the valley-model orbital-Nernst conductivity versus the TB value evaluated at identical Fermi energies. Without this cross-check, the assertion that the low-energy model captures the essential physics—and therefore that the orbital Nernst effect is “intrinsically present” in NbS₂—remains unverified.

Authors: We agree that an explicit side-by-side comparison is needed to quantify how well the valley model reproduces the full-band results. In the revised manuscript we will add a new figure (or panel) that overlays the orbital Nernst conductivity obtained from the analytic valley model against the tight-binding value evaluated at the same Fermi energies for both MoS₂ (doped) and NbS₂ (intrinsic). A supplementary table will also list the relative deviation at representative doping levels. This cross-check will directly support our claim that the low-energy model captures the essential physics and that the orbital Nernst effect is intrinsic in metallic NbS₂. revision: yes

Circularity Check

0 steps flagged

No circularity: derivations use independent standard models

full rationale

The paper computes orbital and spin Nernst conductivities from Berry curvatures obtained via a standard low-energy valley model (parabolic/linear dispersion near K/K' points) and full Brillouin-zone tight-binding Hamiltonians for MoS2 and NbS2. These band structures and the Nernst formulas are not defined in terms of each other; the models pre-exist the target observables and are not fitted to Nernst data. No self-citations, uniqueness theorems, or ansatzes from the authors' prior work are invoked as load-bearing steps. The chain is therefore self-contained and externally verifiable against known TMD band structures.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard condensed-matter assumptions for TMD band structures; the abstract introduces no new free parameters, invented entities, or ad-hoc axioms beyond the low-energy valley approximation and tight-binding framework.

axioms (2)

domain assumption Low-energy valley model approximates the band structure near K and K' points sufficiently for Nernst conductivity calculations
Invoked for analytical results on orbital and spin Nernst effects
domain assumption Tight-binding model for 2H-MoS2 and 2H-NbS2 captures the essential orbital and spin Berry curvatures across the full Brillouin zone
Used to substantiate analytical findings numerically

pith-pipeline@v0.9.0 · 5585 in / 1523 out tokens · 62093 ms · 2026-05-12T02:23:59.992161+00:00 · methodology

discussion (0)

Reference graph

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