AM-Based Heterostructures

• AM-based heterostructures are engineered layered materials that interface altermagnets with superconductors or semiconductors to enable momentum-dependent spin transport without net magnetization.
• They employ spatially-resolved BdG Hamiltonians and scattering theory to quantify spin-resolved thermoelectric currents, achieving nearly 100% spin polarization under optimal conditions.
• Device configurations demonstrate nonreciprocal thermoelectric diode effects, offering tunable control for superconducting spintronics and quantum information processing.

AM-based heterostructures are a class of engineered layered or stacked materials in which an altermagnet (AM)—a magnetic system characterized by momentum-dependent spin splitting and zero net magnetization—is interfaced with other materials such as conventional superconductors, semiconductors, or other quantum materials. The unique electronic structure of altermagnets distinguishes them from traditional ferromagnets and antiferromagnets, leading to unconventional spin transport and emergent functionalities not achievable in conventional heterostructures. This distinction, rooted in symmetry-protected spin splitting without macroscopic magnetization, underpins novel strategies for controlling spin, heat, and charge in device platforms that exploit superconductivity, proximity effects, and thermoelectricity (Debnath et al., 15 Sep 2025).

1. Altermagnetic Symmetry and Electronic Structure

The defining attribute of an altermagnet is its non-relativistic, momentum-dependent spin splitting that does not arise from net magnetization. In minimal theoretical models, this is incorporated via a term in the Bloch Hamiltonian of the form $t_1 (k_y^2 - k_x^2)$, which results in the electronic bands for spin-up and spin-down quasiparticles splitting in distinct regions of momentum space. Importantly, the total macroscopic magnetization remains zero, precluding stray magnetic fields.

A secondary parameter, $t_2$, can be introduced to control the angular orientation of the altermagnetic spin-splitting lobes. The interplay between $t_1$ and $t_2$ provides tunability of the spin-splitting topology at interfaces, critical for tailoring the spin selectivity of the resulting heterostructure.

Such symmetry properties uniquely enable spin-polarized transport channels without the concomitant challenges of managing stray fields or strong spin-orbit coupling, which are typically required in ferromagnetic platforms.

2. Heterostructure Architectures

The canonical AM-based heterostructure, as considered in recent theoretical investigations, consists of a bilayer geometry with a $d$-wave altermagnet (AM) interfaced with a conventional $s$-wave superconductor (SC) (Debnath et al., 15 Sep 2025). The spatially-resolved Bogoliubov–de Gennes (BdG) Hamiltonian is written as:

• For $x < 0$ (AM region): includes the kinetic term, chemical potential, and the altermagnetic spin-splitting term $t_1(k_y^2 - k_x^2)$ (optionally $t_2 k_x k_y$).
• For $x > 0$ (SC region): features standard $s$-wave pairing potential $\Delta$.

Device configurations may be extended to AM-based Josephson junctions, where two $s$-wave superconductors are coupled via a central $d$-wave AM region, and a phase difference $\varphi$ is imposed between the superconductors.

A temperature bias $\delta T$ is applied across the junctions, introducing the possibility of thermoelectric effects mediated by spin-split quasiparticles. Additional symmetry breaking, such as Rashba spin–orbit interaction (RSOI), is implemented in the superconducting leads to further control transport directionality and nonreciprocity.

3. Spin-polarized Thermoelectric Transport

One of the hallmark predictions for AM-based superconductor heterostructures is the emergence of large thermoelectric spin-polarizations. When a thermal bias is applied across an AM/SC bilayer, the momentum-dependent spin splitting in the AM enables electron–hole asymmetry for each spin channel, breaking the conventional suppression of thermoelectricity in superconducting hybrids.

The spin-resolved thermoelectric quasiparticle current is given by: $$\mathcal{L}_\sigma = \frac{2e}{h T} \int_0^\infty (E - \mu) \left[1 - |r_N^\sigma|^2 + |r_A^\sigma|^2\right] \left(-\frac{\partial f}{\partial E}\right) dE$$ where $r_N^\sigma$ and $r_A^\sigma$ are the normal and Andreev reflection amplitudes for spin $\sigma$, $f(E,T)$ is the Fermi–Dirac distribution, $E$ is energy, and $\mu$ the chemical potential (Debnath et al., 15 Sep 2025).

As the altermagnetic parameter $t_1$ increases, a regime is reached in which the thermoelectric current for one spin species is strongly suppressed while the other dominates, resulting in a spin polarization

$$\mathcal{P} = \frac{\mathcal{L}_{\uparrow} - \mathcal{L}_{\downarrow}}{\mathcal{L}_{\uparrow} + \mathcal{L}_{\downarrow}}$$

that approaches $\pm100\%$ in the strong altermagnetic limit.

The sign and amplitude of spin polarization can be further modulated by varying the chemical potential, $t_2$, or the orientation of the AM interface, offering gate-tunable and geometry-sensitive control of spin–caloritronic effects.

4. Diode Effect and Nonreciprocal Thermoelectricity

Extending the analysis to Josephson junctions with a central AM region, the interaction of the altermagnetic spin-splitting and externally imposed symmetry-breaking (e.g., RSOI) yields pronounced nonreciprocal thermoelectric transport. Specifically, the forward and backward thermoelectric currents under applied phase bias and thermal gradients are inequivalent, forming the basis of a thermoelectric diode.

The diode efficiency is quantified as: $$\eta = \frac{(\mathcal{L}^f - \mathcal{L}^b)}{(\mathcal{L}^f + \mathcal{L}^b)}\times 100\%$$ where $\mathcal{L}^f$ and $\mathcal{L}^b$ are the forward and reverse thermoelectric current, respectively. In AM-based JJs, the efficiency can reach up to $\sim 80\%$ and, uniquely, can change sign upon tuning the altermagnet parameters or device geometry.

This nonreciprocal diode effect is fundamentally tied to the combined breaking of time-reversal and inversion symmetry, as realized by the synergy of altermagnetic splitting and RSOI in the appropriate device context.

5. Methodological Framework

All analyses of AM-based heterostructures leverage spatially-resolved Bogoliubov–de Gennes Hamiltonians, with stepwise spatial profiles for kinetic, pairing, and exchange terms. Spin-resolved scattering coefficients are computed at the AM/SC interfaces, and transport is calculated in the linear response regime using a Landauer–Büttiker approach.

The inclusion of $d$-wave ($t_1$) and mixed-symmetry ($t_2$) spin-splitting modifies both the density of states and interfacial transmission probabilities, directly impacting the magnitude and polarization of the resultant thermoelectric currents.

For the Josephson diode phenomena, the transport calculations are extended to include superconducting phase differences and RSOI-induced inversion symmetry breaking. Even and odd components of current with respect to superconducting phase are extracted to distinguish between dissipative (thermoelectric) and non-dissipative (Josephson) contributions.

6. Applications and Implications

AM-based heterostructures introduce a new paradigm in spin-caloritronics by enabling spin-polarized thermoelectric current generation without net magnetization or external magnetic fields. The realization of nearly 100% spin-polarization is a key advantage for spintronic energy harvesting, spin logic, and quantum sensors.

The pronounced diode effect in Josephson geometries supports nonreciprocal heat and charge management in superconducting circuits, offering applications in superconducting rectifiers and thermal management.

Programmable diode efficiency—controllable via chemical potential, geometry, and Rashba interaction—suggests potential for dynamically reconfigurable devices, serving as functional building blocks for unconventional quantum information processing and hybrid superconducting–spintronic circuits.

7. Outlook

The theoretical framework developed for AM-based heterostructures (Debnath et al., 15 Sep 2025) establishes their fundamental role as enabling platforms for the next generation of superconducting spintronics. Unique capabilities—such as gate-and geometry-tunable spin-caloritronic response, zero-stray-field spin polarization, and nonreciprocal Josephson transport—offer pathways toward devices that integrate information, spin, and heat flows without conventional magnetic constraints. Ongoing advances in material synthesis, interface engineering, and the detection of momentum-dependent spin textures are likely to further unlock the application space of AM-based heterostructures for both basic research and emergent quantum technologies.